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1. Shard Calculation

Query:

Response:

Calculated Shard: 135 (from laksa078)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa135.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://testbook.com/physics-formulas/hookes-law-formula\')), getAhrefsUnparsedNoserviceFromURL(\'https://testbook.com/physics-formulas/hookes-law-formula\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/testbook.com\/physics-formulas\/hookes-law-formula","crawl_time":1775157379,"first_indexed_time":1677593447,"http_code":200,"src_unparsed":"com,testbook!\/physics-formulas\/hookes-law-formula s443","src_root_hash":"12665880941046989535","history_drop_reason":null,"meta_title":"Hookes Law Formula: Learn Definition, Formula, Numerical, FAQ's","meta_descriptions":["Hooke's Law observation was proposed by Robert Hooke and is given as F = – K x. Learn more about Hooke's Law Formula, with numerical, explanation and FAQ's"],"attrs_boilerpipe_text":"A spring is a common object which almost everybody of us has seen. We know that when we stretch a spring we have to exert\nenergy\nand when we release the stretched spring it coils back up again. Since we exert energy when stretching a spring, then that energy should go there. And since on releasing the stretched spring it coils back again without any additional force required, the general conclusion should be that the spring stores the energy exerted by us into itself, which it then uses to go back to its coiled position. This observation was quantified by Robert Hooke who gave\nHooke's Law\n. This\nPhysics\narticle will explain Hooke's Law Formula along with some solved examples. \nHooke’s Law\nThe Hooke’s law states that within the elastic limit, the stress applied on a body is directly proportional to the strain produced. This mean that the\nforce\nrequired to stretch or compress a spring over a certain distance is directly proportional to the distance through which the spring is stretched or compressed. The force is equal to the product of the spring constant and the distance over which the spring is stretched or compressed. Hooke’s law essentially defines elastic limit. In the stress-strain curve, Hooke’s law holds good up to the limit of proportionality. In simple words, it is applicable within the limit of proportionality.\nHooke's Law Formula \nThe formula for Hooke’s Law is mathematically defined as \n\\(F = -kx\\) \nThe minus sign in the equation indicates that the force exerted by the spring is in the opposite direction to the displacement. In other words, if you stretch a spring, it will exert a force that tries to return it to its equilibrium position, and if you compress a spring, it will exert a force that tries to expand back to its equilibrium position.\nWhere, \nF = Force required to change the linear dimension of the spring \nk = Spring Constant, in the units of N\/m. \nx = Distance over which the spring is stretched or compressed. It is positive in sign when the\nSpring is stretched and negative when it is compressed. \nLimitations of Hooke’s Law\nHooke’s law has some limitations that must be taken into consideration. \nHooke's Law is only valid up to a certain point, known as the\nelastic limit\n. Beyond this limit, the material will start to deform permanently and the relationship between force and displacement will no longer be linear. \nSome materials do not follow a linear relationship between force and displacement, and their behaviour cannot be accurately described by Hooke's Law.\nHooke's Law assumes that materials are isotropic. Therefore, anisotropic materials do not follow Hooke’s law. \nWhen a material is subjected to a force beyond its elastic limit, it undergoes plastic deformation and does not return to its original shape. Hooke's Law does not apply in this case.\nTemperature can affect the stiffness of a material and alter its behaviour, making it deviate from Hooke's Law.\nApplication of Hooke’s Law\nSome common applications of Hooke’s law are as follows:\nHooke's Law is commonly used to design and analyze springs.\nIt helps in understanding the behaviour of pendulums, springs, etc. \nIt is used to study the elasticity and stiffness of a material. \nIt is also used to test the mechanical properties of a material such as tensile strength, modulus of elasticity, and compressive strength.\nHooke's Law Formula Solved Examples \nExample 1.\nA spring with a spring constant of 2 N\/m is stretched to a distance of 2 m. Calculate the force required. \nSolution 1: Since, k = 2 N\/m \nx = 2 m \nSince, \\(F = -kx\\) \nThus, \\(F = -2 \\times 2\\) \n\\(F = -4 N\\) \nExample 2.\nA spring with a spring constant of 2 N\/m is stretched to a distance of 0.2 m. Calculate the force required. \nSolution 2: Since, k = 2 N\/m \nx = 0.2 m \nSince, \\(F = -kx\\) \nThus, \\(F = -2 \\times 0.2\\) \n\\(F = -0.4 N\\) \nExample 3.\nA spring with a spring constant of 4 N\/m is stretched to a distance of 0.95 m. Calculate the force required. \nSolution 3: Since, k = 4 N\/m \nx = 0.95 m \nSince, \\(F = -kx\\) \nThus, \\(F = -4 \\times 0.95\\) \n\\(F = -3.8 N\\) \nExample 4\n. A spring with a spring constant of 4 N\/m is stretched to a distance of 0.55 m. Calculate the force required. \nSolution 4: Since, k = 4 N\/m \nx = 0.55 m \nSince, \\(F = -kx\\) \nThus, \\(F = -4 \\times 0.55\\) \n\\(F = -2.2 N\\) \nHope this article about the Hooke’s Law formula was able to get the concept of this topic in motion. There are many such interesting topics and their real-life applications to learn about, just download the\nTestbook app\nand start browsing to get insights on them which can clear all your concepts regarding them.","attrs_markdown":"- [English](https:\/\/testbook.com\/physics-formulas\/hookes-law-formula)\n- [Get Started](https:\/\/testbook.com\/login?tile=signup \"Sign Up\")\n\n- [Exams](https:\/\/testbook.com\/exams)\n- [SuperCoaching](https:\/\/testbook.com\/super-coaching)\n- [Live Classes FREE](https:\/\/testbook.com\/free-live-classes)\n- [Test Series](https:\/\/testbook.com\/online-test-series)\n- [Previous Year Papers](https:\/\/testbook.com\/previous-year-papers)\n- [Books](https:\/\/link.testbook.com\/e\/books)\n- [Pass]()\n  [Pass](https:\/\/testbook.com\/pass)\n  \n  [Pass Pro](https:\/\/testbook.com\/pass-pro)\n  \n  [Pass Elite](https:\/\/testbook.com\/pass-elite)\n- [Pass](https:\/\/testbook.com\/pass)\n- [Pass Pro](https:\/\/testbook.com\/pass-pro)\n- [Pass Elite](https:\/\/testbook.com\/pass-elite)\n- [Rank Predictor](https:\/\/testbook.com\/rank-predictor)\n- [IAS Preparation](https:\/\/testbook.com\/ias-preparation)\n- [More]()\n  [Free Live Classes](https:\/\/testbook.com\/free-live-classes)  [Free Live Tests & Quizzes](https:\/\/testbook.com\/free-live-tests-and-quizzes)  [Free Quizzes](https:\/\/testbook.com\/free-online-quizzes)  [Previous Year Papers](https:\/\/testbook.com\/previous-year-papers)  [Doubts](https:\/\/testbook.com\/doubts)  [Practice](https:\/\/testbook.com\/practice-questions)  [Refer and Earn](https:\/\/testbook.com\/referrals)  [All Exams](https:\/\/testbook.com\/exams)  [Our Selections](https:\/\/testbook.com\/success-stories)  [Careers](https:\/\/testbook.com\/careers)  [IAS Preparation](https:\/\/testbook.com\/ias-preparation)  [Current Affairs](https:\/\/testbook.com\/current-affairs)  [Global Careers](https:\/\/globalcareers.testbook.com\/)\n- [Practice](https:\/\/testbook.com\/practice-questions)\n- [GK & Current Affairs](https:\/\/testbook.com\/current-affairs\/current-affairs-quiz)\n- [Blog](https:\/\/testbook.com\/blog\/)\n- [Refer & Earn](https:\/\/testbook.com\/referrals)\n  [Our Selections](https:\/\/testbook.com\/success-stories)\n  [Global Careers](https:\/\/globalcareers.testbook.com\/)\n\n[Home](https:\/\/testbook.com\/physics-formulas\/hookes-law-formula)  [Physics Formulas](https:\/\/testbook.com\/physics-formulas\/physics-formulas)\n\nHookes Law Formula\n\n![Hooke's Law Formula: Explained With Solved Examples](https:\/\/cdn.testbook.com\/resources\/productionimages\/Physics%20Formula%20Logo_All_1670493719.png)\n\n# Hooke's Law Formula: Explained With Solved Examples\n[Download as PDF](https:\/\/testbook.com\/login?redirect_url=https%3A%2F%2Ftestbook.com%2Fphysics-formulas%2Fhookes-law-formula&referrer=customChildPage-hookes-law-formula&referrerType=CustomChildPage&referrerPagePath=undefined)\n\n![Hooke's Law Formula: Explained With Solved Examples Exam Preparation](https:\/\/testbook.com\/physics-formulas\/assets\/img\/banner-bg\/bottom-banner-preparation.svg)\n\nA spring is a common object which almost everybody of us has seen. We know that when we stretch a spring we have to exert [energy](https:\/\/testbook.com\/physics\/energy) and when we release the stretched spring it coils back up again. Since we exert energy when stretching a spring, then that energy should go there. And since on releasing the stretched spring it coils back again without any additional force required, the general conclusion should be that the spring stores the energy exerted by us into itself, which it then uses to go back to its coiled position. This observation was quantified by Robert Hooke who gave [Hooke's Law](https:\/\/testbook.com\/physics\/hookes-law). This [Physics](https:\/\/testbook.com\/physics) article will explain Hooke's Law Formula along with some solved examples.\n\n## Hooke’s Law\nThe Hooke’s law states that within the elastic limit, the stress applied on a body is directly proportional to the strain produced. This mean that the [force](https:\/\/testbook.com\/physics\/force) required to stretch or compress a spring over a certain distance is directly proportional to the distance through which the spring is stretched or compressed. The force is equal to the product of the spring constant and the distance over which the spring is stretched or compressed. Hooke’s law essentially defines elastic limit. In the stress-strain curve, Hooke’s law holds good up to the limit of proportionality. In simple words, it is applicable within the limit of proportionality.\n\n## Hooke's Law Formula\nThe formula for Hooke’s Law is mathematically defined as\n\n\\\\(F = -kx\\\\)\n\nThe minus sign in the equation indicates that the force exerted by the spring is in the opposite direction to the displacement. In other words, if you stretch a spring, it will exert a force that tries to return it to its equilibrium position, and if you compress a spring, it will exert a force that tries to expand back to its equilibrium position.\n\nWhere,\n\nF = Force required to change the linear dimension of the spring\n\nk = Spring Constant, in the units of N\/m.\n\nx = Distance over which the spring is stretched or compressed. It is positive in sign when the\n\nSpring is stretched and negative when it is compressed.\n\n[![](https:\/\/cdn.testbook.com\/static\/assets\/assets\/img\/media\/signup_desktop.webp)](https:\/\/testbk.co\/1fgwm)\n\n[![Pass pro banner mobile](https:\/\/cdn.testbook.com\/static\/assets\/assets\/img\/media\/result_blocker_3x.webp)](https:\/\/testbk.co\/1g48a)\n\n## Limitations of Hooke’s Law\nHooke’s law has some limitations that must be taken into consideration.\n\n- Hooke's Law is only valid up to a certain point, known as the [elastic limit](https:\/\/testbook.com\/physics\/elastic-limit). Beyond this limit, the material will start to deform permanently and the relationship between force and displacement will no longer be linear.\n- Some materials do not follow a linear relationship between force and displacement, and their behaviour cannot be accurately described by Hooke's Law.\n- Hooke's Law assumes that materials are isotropic. Therefore, anisotropic materials do not follow Hooke’s law.\n- When a material is subjected to a force beyond its elastic limit, it undergoes plastic deformation and does not return to its original shape. Hooke's Law does not apply in this case.\n- Temperature can affect the stiffness of a material and alter its behaviour, making it deviate from Hooke's Law.\n\n## Application of Hooke’s Law\nSome common applications of Hooke’s law are as follows:\n\n- Hooke's Law is commonly used to design and analyze springs.\n- It helps in understanding the behaviour of pendulums, springs, etc.\n- It is used to study the elasticity and stiffness of a material.\n- It is also used to test the mechanical properties of a material such as tensile strength, modulus of elasticity, and compressive strength.\n\n## Hooke's Law Formula Solved Examples\n**Example 1.** A spring with a spring constant of 2 N\/m is stretched to a distance of 2 m. Calculate the force required.\n\nSolution 1: Since, k = 2 N\/m\n\nx = 2 m\n\nSince, \\\\(F = -kx\\\\)\n\nThus, \\\\(F = -2 \\\\times 2\\\\)\n\n\\\\(F = -4 N\\\\)\n\n**Example 2.** A spring with a spring constant of 2 N\/m is stretched to a distance of 0.2 m. Calculate the force required.\n\nSolution 2: Since, k = 2 N\/m\n\nx = 0.2 m\n\nSince, \\\\(F = -kx\\\\)\n\nThus, \\\\(F = -2 \\\\times 0.2\\\\)\n\n\\\\(F = -0.4 N\\\\)\n\n**Example 3.** A spring with a spring constant of 4 N\/m is stretched to a distance of 0.95 m. Calculate the force required.\n\nSolution 3: Since, k = 4 N\/m\n\nx = 0.95 m\n\nSince, \\\\(F = -kx\\\\)\n\nThus, \\\\(F = -4 \\\\times 0.95\\\\)\n\n\\\\(F = -3.8 N\\\\)\n\n**Example 4**. A spring with a spring constant of 4 N\/m is stretched to a distance of 0.55 m. Calculate the force required.\n\nSolution 4: Since, k = 4 N\/m\n\nx = 0.55 m\n\nSince, \\\\(F = -kx\\\\)\n\nThus, \\\\(F = -4 \\\\times 0.55\\\\)\n\n\\\\(F = -2.2 N\\\\)\n\nHope this article about the Hooke’s Law formula was able to get the concept of this topic in motion. There are many such interesting topics and their real-life applications to learn about, just download the [Testbook app](https:\/\/link.testbook.com\/0DRQgVCiWyb) and start browsing to get insights on them which can clear all your concepts regarding them.\n\nMore Articles for Physics Formulas\n\n- [Surface Tension Formula](https:\/\/testbook.com\/physics-formulas\/surface-tension-formula)\n- [Tangential Velocity Formula](https:\/\/testbook.com\/physics-formulas\/tangential-velocity-formula)\n- [Voltage Divider Formula](https:\/\/testbook.com\/physics-formulas\/voltage-divider-formula)\n- [Absolute pressure formula](https:\/\/testbook.com\/physics-formulas\/absolute-pressure-formula)\n- [Intensity Formula](https:\/\/testbook.com\/physics-formulas\/intensity-formula)\n- [Heat Rate Formula](https:\/\/testbook.com\/physics-formulas\/heat-rate-formula)\n- [Specific Heat Formula](https:\/\/testbook.com\/physics-formulas\/specific-heat-formula)\n- [Heat Of Vaporization Formula](https:\/\/testbook.com\/physics-formulas\/heat-of-vaporization-formula)\n- [Initial velocity formula](https:\/\/testbook.com\/physics-formulas\/initial-velocity-formula)\n- [Kinetic Energy Formula](https:\/\/testbook.com\/physics-formulas\/kinetic-energy-formula)\n\n## Hooke's Law Formula FAQs\n### How do I calculate Hooke's law?\nHooke’s Law is calculated by using the formula \\[latex\\]F = -kx\\[\/latex\\]\n\n### What is K in Hooke's law formula?\n‘k’ in Hooke’s law is the spring constant.\n\n### Why is there a negative in F =- kx?\nA negative sign is added in Hooke’s Law to signify the restoring force being exerted by the spring.\n\n### State Hooke's law\nHooke’s law states that the strain of the spring is proportional to the stress applied to it within its elastic limit.\n\n### What is the unit of the spring constant?\nThe unit of the spring constant is N\/m.\n\n[Report An Error](https:\/\/docs.google.com\/forms\/d\/e\/1FAIpQLScQq-lUmFGqdXTyJ0EhM-cgQd6SiMauQoS9UMGWUdDKX0lJqQ\/viewform?usp=pp_url&entry.1289850337=https:\/\/testbook.com\/physics-formulas\/hookes-law-formula)\n\n[![promotional banner](https:\/\/cdn.testbook.com\/1774895879928-960X1200%20%2827%29.jpg\/1774895881.jpeg)](https:\/\/link.testbook.com\/giw3rN1dYZb)\n\nImportant Links\n\n[Overview](https:\/\/testbook.com\/physics-formulas)\n\n[Capacitive Reactance Formula](https:\/\/testbook.com\/physics-formulas\/capacitive-reactance-formula)[Binding Energy Formula](https:\/\/testbook.com\/physics-formulas\/binding-energy-formula)[Charge Density Formula](https:\/\/testbook.com\/physics-formulas\/charge-density-formula)[Magnetic Field Strength Formula](https:\/\/testbook.com\/physics-formulas\/magnetic-field-strength-formula)[Work Formula](https:\/\/testbook.com\/physics-formulas\/work-formula)[Reynolds Number Formula](https:\/\/testbook.com\/physics-formulas\/reynolds-number-formula)[Free Fall 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Previous Year Papers](https:\/\/testbook.com\/ssc-selection-post\/previous-year-papers)[SSC GD Constable Previous Year Papers](https:\/\/testbook.com\/ssc-gd-constable\/previous-year-papers)[RRB Group D Previous Year Papers](https:\/\/testbook.com\/rrb-group-d\/previous-year-papers)[RPF Constable Previous Year Papers](https:\/\/testbook.com\/rpf-constable\/previous-year-papers)[SSC JE Previous Year Papers](https:\/\/testbook.com\/ssc-je\/previous-year-papers)[CGPSC Previous Year Papers](https:\/\/testbook.com\/cgpsc\/previous-year-papers)[AIIMS CRE Previous Year Papers](https:\/\/testbook.com\/aiims-cre\/previous-year-papers)[EPFO Personal Assistant Previous Year Papers](https:\/\/testbook.com\/epfo-personal-assistant\/previous-year-papers)[FCI Manager Previous Year Papers](https:\/\/testbook.com\/fci-manager\/previous-year-papers)[JKPSC KAS Previous Year Papers](https:\/\/testbook.com\/jkpsc-kas\/previous-year-papers)[OPSC OAS Previous Year Papers](https:\/\/testbook.com\/opsc-oas\/previous-year-papers)[UPPCS Previous Year Papers](https:\/\/testbook.com\/uppcs\/previous-year-papers)[NEET Previous Year Papers](https:\/\/testbook.com\/neet\/previous-year-papers)[MHT CET Previous Year Papers](https:\/\/testbook.com\/mah-cet-mba\/previous-year-papers)[TANCET Previous Year Papers](https:\/\/testbook.com\/tancet\/previous-year-papers)[AAI ATC Previous Year Papers](https:\/\/testbook.com\/aai-je-atc\/previous-year-papers)[MP Vyapam Sub Engineer Previous Year Papers](https:\/\/testbook.com\/mp-vyapam-sub-engineer\/previous-year-papers)[RSMSSB Junior Engineer Previous Year Papers](https:\/\/testbook.com\/rsmssb-junior-engineer\/previous-year-papers)\n\n[SSC CGL Previous Year Papers](https:\/\/testbook.com\/ssc-cgl-exam\/previous-year-papers)[SSC MTS Previous Year Papers](https:\/\/testbook.com\/ssc-mts\/previous-year-papers)[RRB ALP Previous Year Papers](https:\/\/testbook.com\/rrb-alp\/previous-year-papers)[RPF SI Previous Year Papers](https:\/\/testbook.com\/rpf-si\/previous-year-papers)[APPSC Group 1 Previous Year Papers](https:\/\/testbook.com\/appsc-group-1\/previous-year-papers)[GPSC Class 1 2 Previous Year Papers](https:\/\/testbook.com\/gpsc-class-1-2\/previous-year-papers)[CBSE Assistant Secretary Previous Year Papers](https:\/\/testbook.com\/cbse-assistant-secretary\/previous-year-papers)[FCI Previous Year Papers](https:\/\/testbook.com\/fci\/previous-year-papers)[FCI Watchman Previous Year Papers](https:\/\/testbook.com\/fci-watchman\/previous-year-papers)[Kerala PSC KAS Previous Year Papers](https:\/\/testbook.com\/kerala-psc-kas\/previous-year-papers)[RPSC RAS Previous Year Papers](https:\/\/testbook.com\/rpsc-ras\/previous-year-papers)[WBCS Previous Year Papers](https:\/\/testbook.com\/wbcs\/previous-year-papers)[JEE Main Previous Year Papers](https:\/\/testbook.com\/jee-main\/previous-year-papers)[CAT Previous Year Papers](https:\/\/testbook.com\/cat-exam\/previous-year-papers)[CTET Previous Year Papers](https:\/\/testbook.com\/ctet\/previous-year-papers)[BPSC AE Previous Year Papers](https:\/\/testbook.com\/bpsc-ae\/previous-year-papers)[MPPSC AE Previous Year Papers](https:\/\/testbook.com\/mppsc-ae\/previous-year-papers)[UPPSC AE Previous Year Papers](https:\/\/testbook.com\/uppsc-ae\/previous-year-papers)\n\n[SSC CHSL Previous Year Papers](https:\/\/testbook.com\/ssc-chsl\/previous-year-papers)[SSC CPO Previous Year Papers](https:\/\/testbook.com\/ssc-cpo\/previous-year-papers)[RRB NTPC Previous Year Papers](https:\/\/testbook.com\/rrb-ntpc\/previous-year-papers)[RRB Technician Grade-1 Previous Year Papers](https:\/\/testbook.com\/rrb-technician-grade-1\/previous-year-papers)[BPSC Previous Year Papers](https:\/\/testbook.com\/bpsc-exam\/previous-year-papers)[HPSC HCS Previous Year Papers](https:\/\/testbook.com\/haryana-civil-services\/previous-year-papers)[CBSE Junior Assistant Previous Year Papers](https:\/\/testbook.com\/cbse-junior-assistant\/previous-year-papers)[FCI Grade 3 Previous Year Papers](https:\/\/testbook.com\/fci-grade-3\/previous-year-papers)[FSSAI Personal Assistant Previous Year Papers](https:\/\/testbook.com\/fssai-personal-assistant\/previous-year-papers)[KPSC KAS Previous Year Papers](https:\/\/testbook.com\/kpsc-kas\/previous-year-papers)[TNPSC Group 1 Previous Year Papers](https:\/\/testbook.com\/tnpsc-group-1\/previous-year-papers)[CUET Previous Year Papers](https:\/\/testbook.com\/cuet\/previous-year-papers)[JEE Advance Previous Year Papers](https:\/\/testbook.com\/jee-advanced\/previous-year-papers)[CMAT Previous Year Papers](https:\/\/testbook.com\/cmat-exam\/previous-year-papers)[REET Previous Year Papers](https:\/\/testbook.com\/reet\/previous-year-papers)[ISRO Scientist Previous Year Papers](https:\/\/testbook.com\/isro-scientist\/previous-year-papers)[PGCIL Diploma Trainee Previous Year Papers](https:\/\/testbook.com\/pgcil-diploma-trainee\/previous-year-papers)[UPSC IES Previous Year Papers](https:\/\/testbook.com\/upsc-ies\/previous-year-papers)\n\n[SSC CPO Previous Year Papers](https:\/\/testbook.com\/ssc-cpo\/previous-year-papers)[SSC Stenographer Previous Year Papers](https:\/\/testbook.com\/ssc-stenographer\/previous-year-papers)[RRB Technician Previous Year Papers](https:\/\/testbook.com\/rrb-technician\/previous-year-papers)[RRB JE Previous Year Papers](https:\/\/testbook.com\/rrb-je\/previous-year-papers)[MPSC Prevoius Year Papers](https:\/\/testbook.com\/mpsc-state-service\/previous-year-papers)[AAI Junior Assistant Previous Year Papers](https:\/\/testbook.com\/aai-junior-assistant\/previous-year-papers)[CSIR Junior Secretariat Assistant Previous Year Papers](https:\/\/testbook.com\/csir-junior-secretariat-assistant\/previous-year-papers)[FCI Je Previous Year Papers](https:\/\/testbook.com\/fci-je\/previous-year-papers)[NIELIT Scientist B Previous Year Papers](https:\/\/testbook.com\/nielit-scientist-b\/previous-year-papers)[MPPSC Exam Previous Year Papers](https:\/\/testbook.com\/mppsc-state-service\/previous-year-papers)[TSPSC Group 1 Previous Year Papers](https:\/\/testbook.com\/tspsc-group-1\/previous-year-papers)[CUET PG Previous Year Papers](https:\/\/testbook.com\/cuet-pg\/previous-year-papers)[JEECUP Previous Year Papers](https:\/\/testbook.com\/up-polytechnic-jeecup\/previous-year-papers)[MAH MBA CET Previous Year Papers](https:\/\/testbook.com\/mah-cet-mba\/previous-year-papers)[BHEL Engineer Trainee Previous Year Papers](https:\/\/testbook.com\/bhel-engineer-trainee\/previous-year-papers)[Mahatransco AE Previous Year Papers](https:\/\/testbook.com\/mahatransco-ae\/previous-year-papers)[TSGENCO AE Previous Year Papers](https:\/\/testbook.com\/tsgenco-ae\/previous-year-papers)\n\nSyllabus\n\n[SSC CGL Syllabus](https:\/\/testbook.com\/ssc-cgl-exam\/syllabus)[SSC MTS Syllabus](https:\/\/testbook.com\/ssc-mts\/syllabus-exam-pattern)[RRB NTPC Syllabus](https:\/\/testbook.com\/rrb-ntpc\/syllabus)[SSC JE Syllabus](https:\/\/testbook.com\/ssc-je\/syllabus)[JEE Main Syllabus](https:\/\/testbook.com\/jee-main\/syllabus)[NIFT Syllabus](https:\/\/testbook.com\/nift-exam\/syllabus)[AAI Junior Assistant Syllabus](https:\/\/testbook.com\/aai-junior-assistant\/syllabus-exam-pattern)[CSIR Junior Secretariat Assistant Syllabus](https:\/\/testbook.com\/csir-junior-secretariat-assistant\/syllabus-exam-pattern)[FCI Syllabus](https:\/\/testbook.com\/fci\/syllabus)[FCI Stenographer Syllabus](https:\/\/testbook.com\/fci-stenographer\/syllabus-exam-pattern)[NIELIT Scientist B Syllabus](https:\/\/testbook.com\/nielit-scientist-b\/syllabus-exam-pattern)[AAI ATC Syllabus](https:\/\/testbook.com\/aai-je-atc\/syllabus-exam-pattern)[BPSC AE Syllabus](https:\/\/testbook.com\/bpsc-ae\/syllabus-exam-pattern)[RSMSSB Junior Engineer Syllabus](https:\/\/testbook.com\/rsmssb-junior-engineer\/syllabus-exam-pattern)[CUET Accountancy Book Keeping Syllabus](https:\/\/testbook.com\/cuet\/accountancy-book-keeping-syllabus)[CUET Ba Syllabus](https:\/\/testbook.com\/cuet\/ba-syllabus-exam-pattern)[CUET Business Economics Syllabus](https:\/\/testbook.com\/cuet\/business-economics-syllabus)[CUET Computer Science Syllabus](https:\/\/testbook.com\/cuet\/computer-science-syllabus)[CUET Environmental Studies Syllabus](https:\/\/testbook.com\/cuet\/environmental-studies-syllabus)[CUET Commerce Syllabus](https:\/\/testbook.com\/cuet\/commerce-syllabus)[CUET Hindi Syllabus](https:\/\/testbook.com\/cuet\/hindi-syllabus-exam-pattern)[CUET Malayalam Syllabus](https:\/\/testbook.com\/cuet\/malayalam-syllabus-exam-pattern)[CUET Physical Education Syllabus](https:\/\/testbook.com\/cuet\/physical-education-syllabus)[CUET Sanskrit Syllabus](https:\/\/testbook.com\/cuet\/sanskrit-syllabus)[BPSC Exam Syllabus](https:\/\/testbook.com\/bpsc-exam\/syllabus-exam-pattern)[JKPSC KAS Syllabus](https:\/\/testbook.com\/jkpsc-kas\/syllabus-exam-pattern)[OPSC OAS Syllabus](https:\/\/testbook.com\/opsc-oas\/syllabus-exam-pattern)[WBCS Exam Syllabus](https:\/\/testbook.com\/wbcs\/syllabus-exam-pattern)[TSPSC Group 1 Syllabus](https:\/\/testbook.com\/tspsc-group-1\/syllabus-exam-pattern)[BPSC Exam Syllabus](https:\/\/testbook.com\/bpsc-exam\/syllabus-exam-pattern)\n\n[SSC CHSL Syllabus](https:\/\/testbook.com\/ssc-chsl\/syllabus)[SSC Stenographer Syllabus](https:\/\/testbook.com\/ssc-stenographer\/syllabus-exam-pattern)[RRB Technician Syllabus](https:\/\/testbook.com\/rrb-technician\/syllabus-exam-pattern)[RRB JE Syllabus](https:\/\/testbook.com\/rrb-je\/syllabus)[JEE Advanced Syllabus](https:\/\/testbook.com\/jee-advanced\/syllabus)[WB JEE Syllabus](https:\/\/testbook.com\/wb-jee\/syllabus-exam-pattern)[AIIMS CRE Syllabus](https:\/\/testbook.com\/aiims-cre\/syllabus-exam-pattern)[CSIR Npl Technician Syllabus](https:\/\/testbook.com\/csir-npl-technician\/syllabus-exam-pattern)[FCI Grade 3 Syllabus](https:\/\/testbook.com\/fci-grade-3\/syllabus-exam-pattern)[FCI Typist Syllabus](https:\/\/testbook.com\/fci-typist\/syllabus-exam-pattern)[CUET Maths Syllabus](https:\/\/testbook.com\/cuet\/mathematics-syllabus)[BHEL Engineer Trainee Syllabus](https:\/\/testbook.com\/bhel-engineer-trainee\/salary-job-profile)[MP Vyapam Sub Engineer Syllabus](https:\/\/testbook.com\/mp-vyapam-sub-engineer\/syllabus-exam-pattern)[TSGENCO AE Syllabus](https:\/\/testbook.com\/tsgenco-ae\/syllabus-exam-pattern)[CUET Agriculture Syllabus](https:\/\/testbook.com\/cuet\/agriculture-syllabus)[CUET BCA Syllabus](https:\/\/testbook.com\/cuet\/bca-syllabus-exam-pattern)[CUET Business Studies Syllabus](https:\/\/testbook.com\/cuet\/business-studies-syllabus)[CUET Engineering Graphics Syllabus](https:\/\/testbook.com\/cuet\/engineering-graphics-syllabus)[CUET Fine Arts Syllabus](https:\/\/testbook.com\/cuet\/fine-arts-syllabus)[CUET Geography Syllabus](https:\/\/testbook.com\/cuet\/geography-syllabus)[CUET History Syllabus](https:\/\/testbook.com\/cuet\/history-syllabus)[CUET Marathi Syllabus](https:\/\/testbook.com\/cuet\/marathi-syllabus-exam-pattern)[CUET Political Science Syllabus](https:\/\/testbook.com\/cuet\/political-science-syllabus)[CUET Sociology Syllabus](https:\/\/testbook.com\/cuet\/sociology-syllabus)[CGPSC Syllabus](https:\/\/testbook.com\/cgpsc\/syllabus)[Kerala PSC KAS Syllabus](https:\/\/testbook.com\/kerala-psc-kas\/syllabus-exam-pattern)[RPSC RAS Syllabus](https:\/\/testbook.com\/rpsc-ras\/syllabus)[HPPSC HPAS Syllabus](https:\/\/testbook.com\/hppsc-hpas\/syllabus-exam-pattern)[UKPSC Upper PCS Syllabus](https:\/\/testbook.com\/ukpsc-combined-upper-subordinate-service\/syllabus-exam-pattern)[CGPSC Syllabus](https:\/\/testbook.com\/cgpsc\/syllabus)\n\n[SSC CPO Syllabus](https:\/\/testbook.com\/ssc-cpo\/syllabus)[RRB Group D Syllabus](https:\/\/testbook.com\/rrb-group-d\/syllabus)[RPF Constable Syllabus](https:\/\/testbook.com\/rpf-constable\/syllabus-exam-pattern)[CUET Syllabus](https:\/\/testbook.com\/cuet\/exam-syllabus)[JEECUP Syllabus](https:\/\/testbook.com\/up-polytechnic-jeecup\/syllabus-exam-pattern)[GUJCET Syllabus](https:\/\/testbook.com\/gujcet\/syllabus)[CBSE Assistant Secretary Syllabus](https:\/\/testbook.com\/cbse-assistant-secretary\/syllabus-exam-pattern)[CWC Junior Superintendent Syllabus](https:\/\/testbook.com\/cwc-junior-superintendent\/syllabus-exam-pattern)[FCI Je Syllabus](https:\/\/testbook.com\/fci-je\/syllabus-exam-pattern)[FCI Watchman Syllabus](https:\/\/testbook.com\/fci-watchman\/syllabus-exam-pattern)[CUET Physics Syllabus](https:\/\/testbook.com\/cuet\/physics-syllabus)[Mahagenco Technician Syllabus](https:\/\/testbook.com\/mahagenco-technician\/syllabus-exam-pattern)[MPPSC AE Syllabus](https:\/\/testbook.com\/mppsc-ae\/syllabus-exam-pattern)[UPPSC AE Syllabus](https:\/\/testbook.com\/uppsc-ae\/syllabus)[CUET Anthropology Syllabus](https:\/\/testbook.com\/cuet\/anthropology-syllabus)[CUET Bengali Syllabus](https:\/\/testbook.com\/cuet\/bengali-syllabus-exam-pattern)[CUET Chemistry Syllabus](https:\/\/testbook.com\/cuet\/chemistry-syllabus)[CUET English Syllabus](https:\/\/testbook.com\/cuet\/english-syllabus-exam-pattern)[CUET French Syllabus](https:\/\/testbook.com\/cuet\/french-syllabus-exam-pattern)[CUET German Syllabus](https:\/\/testbook.com\/cuet\/german-syllabus-exam-pattern)[CUET Home Science Syllabus](https:\/\/testbook.com\/cuet\/home-science-syllabus)[CUET Mass Media Syllabus](https:\/\/testbook.com\/cuet\/mass-media-syllabus)[CUET Psychology Syllabus](https:\/\/testbook.com\/cuet\/psychology-syllabus)[CUET Teaching Aptitude Syllabus](https:\/\/testbook.com\/cuet\/teaching-aptitude-syllabus)[GPSC Class 1 2 Syllabus](https:\/\/testbook.com\/gpsc-class-1-2\/syllabus-exam-pattern)[KPSC KAS Syllabus](https:\/\/testbook.com\/kpsc-kas\/syllabus-exam-pattern)[TNPSC Group 1 Syllabus](https:\/\/testbook.com\/tnpsc-group-1\/syllabus-exam-pattern)[MPPSC Forest Services Syllabus](https:\/\/testbook.com\/mppsc-forest-service\/syllabus-exam-pattern)[UKPSC Lower PCS Syllabus](https:\/\/testbook.com\/ukpsc-lower-pcs\/syllabus-exam-pattern)\n\n[SSC GD Constable Syllabus](https:\/\/testbook.com\/ssc-gd-constable\/syllabus-exam-pattern)[RRB ALP Syllabus](https:\/\/testbook.com\/rrb-alp\/syllabus-exam-pattern)[RPF SI Syllabus](https:\/\/testbook.com\/rpf-si\/syllabus-exam-pattern)[NEET Syllabus](https:\/\/testbook.com\/neet\/syllabus)[MHT CET Syllabus](https:\/\/testbook.com\/mht-cet\/syllabus)[CUET Commerce Syllabus](https:\/\/testbook.com\/cuet\/commerce-syllabus)[CBSE Junior Assistant Syllabus](https:\/\/testbook.com\/cbse-junior-assistant\/syllabus-exam-pattern)[EPFO Personal Assistant Syllabus](https:\/\/testbook.com\/epfo-personal-assistant\/syllabus-exam-pattern)[FCI Manager Syllabus](https:\/\/testbook.com\/fci-manager\/syllabus-exam-pattern)[FSSAI Personal Assistant Syllabus](https:\/\/testbook.com\/fssai-personal-assistant\/syllabus-exam-pattern)[CUET Biology Syllabus](https:\/\/testbook.com\/cuet\/biology-syllabus)[BMC JE Syllabus](https:\/\/testbook.com\/bmc-je\/syllabus-exam-pattern)[PGCIL Diploma Trainee Syllabus](https:\/\/testbook.com\/pgcil-diploma-trainee\/syllabus-exam-pattern)[UPSC IES Syllabus](https:\/\/testbook.com\/upsc-ies\/syllabus)[CUET Assamese Syllabus](https:\/\/testbook.com\/cuet\/assamese-syllabus-exam-pattern)[CUET Bsc Syllabus](https:\/\/testbook.com\/cuet\/bsc-syllabus-exam-pattern)[CUET Commerce Syllabus](https:\/\/testbook.com\/cuet\/commerce-syllabus)[CUET Entrepreneurship Syllabus](https:\/\/testbook.com\/cuet\/entrepreneurship-syllabus)[CUET General Test Syllabus](https:\/\/testbook.com\/cuet\/general-test-syllabus)[CUET Gujarati Syllabus](https:\/\/testbook.com\/cuet\/gujarati-syllabus-exam-pattern)[CUET Legal Studies Syllabus](https:\/\/testbook.com\/cuet\/legal-studies-syllabus)[CUET Odia Syllabus](https:\/\/testbook.com\/cuet\/odia-syllabus-exam-pattern)[CUET Punjabi Syllabus](https:\/\/testbook.com\/cuet\/punjabi-syllabus-exam-pattern)[APPSC Group 1 Syllabus](https:\/\/testbook.com\/appsc-group-1\/syllabus-exam-pattern)[HPSC HCS Syllabus](https:\/\/testbook.com\/haryana-civil-services\/syllabus-exam-pattern)[MPPSC Exam Syllabus](https:\/\/testbook.com\/mppsc-state-service\/syllabus-exam-pattern)[UPPCS Exam Syllabus](https:\/\/testbook.com\/uppcs\/syllabus-exam-pattern)[MPSC Rajyaseva Syllabus](https:\/\/testbook.com\/mpsc-state-service\/syllabus-exam-pattern)[APPSC Group 1 Syllabus](https:\/\/testbook.com\/appsc-group-1\/syllabus-exam-pattern)\n\nBoard Exams\n\n[Haryana Board](https:\/\/testbook.com\/hbse-class-12th)[Gujarat Board](https:\/\/testbook.com\/gseb-class-12)[Maharashtra Board](https:\/\/testbook.com\/maharashtra-hsc-exam)[Telangana Board](https:\/\/testbook.com\/ts-intermediate)\n\n[AP Board](https:\/\/testbook.com\/ap-inter-2nd-year)[ICSE](https:\/\/testbook.com\/isc-class-12)[Madhya Pradesh Board](https:\/\/testbook.com\/mp-board-12th)[Uttar Pradesh Board](https:\/\/testbook.com\/up-board-class-12)\n\n[Bihar Board](https:\/\/testbook.com\/bihar-board-12th)[Jharkhand Board](https:\/\/testbook.com\/jac-class-12)[Punjab Board](https:\/\/testbook.com\/pseb-class-12)[West Bengal Board](https:\/\/testbook.com\/wbchse-class-12)\n\n[CBSE](https:\/\/testbook.com\/cbse-class-12)[Karnataka Board](https:\/\/testbook.com\/karnataka-2nd-puc)[Rajasthan Board](https:\/\/testbook.com\/rbse-class-12)\n\nCoaching\n\n[SSC CGL Coaching](https:\/\/testbook.com\/ssc-cgl-coaching)[SSC GD Constable Coaching](https:\/\/testbook.com\/ssc-gd-coaching)[RRB ALP Coaching](https:\/\/testbook.com\/rrb-alp-coaching)[RPF SI Coaching](https:\/\/testbook.com\/rpf-constable-and-si-coaching)\n\n[SSC CHSL 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Ltd.: All rights reserved\n\n[User Policy](https:\/\/testbook.com\/acceptable-use-policy)[Terms](https:\/\/testbook.com\/terms-of-service)[Privacy](https:\/\/testbook.com\/privacy-policy)","attrs_readable_markdown":"A spring is a common object which almost everybody of us has seen. We know that when we stretch a spring we have to exert [energy](https:\/\/testbook.com\/physics\/energy) and when we release the stretched spring it coils back up again. Since we exert energy when stretching a spring, then that energy should go there. And since on releasing the stretched spring it coils back again without any additional force required, the general conclusion should be that the spring stores the energy exerted by us into itself, which it then uses to go back to its coiled position. This observation was quantified by Robert Hooke who gave [Hooke's Law](https:\/\/testbook.com\/physics\/hookes-law). This [Physics](https:\/\/testbook.com\/physics) article will explain Hooke's Law Formula along with some solved examples.\n\n## Hooke’s Law\nThe Hooke’s law states that within the elastic limit, the stress applied on a body is directly proportional to the strain produced. This mean that the [force](https:\/\/testbook.com\/physics\/force) required to stretch or compress a spring over a certain distance is directly proportional to the distance through which the spring is stretched or compressed. The force is equal to the product of the spring constant and the distance over which the spring is stretched or compressed. Hooke’s law essentially defines elastic limit. In the stress-strain curve, Hooke’s law holds good up to the limit of proportionality. In simple words, it is applicable within the limit of proportionality.\n\n## Hooke's Law Formula\nThe formula for Hooke’s Law is mathematically defined as\n\n\\\\(F = -kx\\\\)\n\nThe minus sign in the equation indicates that the force exerted by the spring is in the opposite direction to the displacement. In other words, if you stretch a spring, it will exert a force that tries to return it to its equilibrium position, and if you compress a spring, it will exert a force that tries to expand back to its equilibrium position.\n\nWhere,\n\nF = Force required to change the linear dimension of the spring\n\nk = Spring Constant, in the units of N\/m.\n\nx = Distance over which the spring is stretched or compressed. It is positive in sign when the\n\nSpring is stretched and negative when it is compressed.\n\n## Limitations of Hooke’s Law\nHooke’s law has some limitations that must be taken into consideration.\n\n- Hooke's Law is only valid up to a certain point, known as the [elastic limit](https:\/\/testbook.com\/physics\/elastic-limit). Beyond this limit, the material will start to deform permanently and the relationship between force and displacement will no longer be linear.\n- Some materials do not follow a linear relationship between force and displacement, and their behaviour cannot be accurately described by Hooke's Law.\n- Hooke's Law assumes that materials are isotropic. Therefore, anisotropic materials do not follow Hooke’s law.\n- When a material is subjected to a force beyond its elastic limit, it undergoes plastic deformation and does not return to its original shape. Hooke's Law does not apply in this case.\n- Temperature can affect the stiffness of a material and alter its behaviour, making it deviate from Hooke's Law.\n\n## Application of Hooke’s Law\nSome common applications of Hooke’s law are as follows:\n\n- Hooke's Law is commonly used to design and analyze springs.\n- It helps in understanding the behaviour of pendulums, springs, etc.\n- It is used to study the elasticity and stiffness of a material.\n- It is also used to test the mechanical properties of a material such as tensile strength, modulus of elasticity, and compressive strength.\n\n## Hooke's Law Formula Solved Examples\n**Example 1.** A spring with a spring constant of 2 N\/m is stretched to a distance of 2 m. Calculate the force required.\n\nSolution 1: Since, k = 2 N\/m\n\nx = 2 m\n\nSince, \\\\(F = -kx\\\\)\n\nThus, \\\\(F = -2 \\\\times 2\\\\)\n\n\\\\(F = -4 N\\\\)\n\n**Example 2.** A spring with a spring constant of 2 N\/m is stretched to a distance of 0.2 m. Calculate the force required.\n\nSolution 2: Since, k = 2 N\/m\n\nx = 0.2 m\n\nSince, \\\\(F = -kx\\\\)\n\nThus, \\\\(F = -2 \\\\times 0.2\\\\)\n\n\\\\(F = -0.4 N\\\\)\n\n**Example 3.** A spring with a spring constant of 4 N\/m is stretched to a distance of 0.95 m. Calculate the force required.\n\nSolution 3: Since, k = 4 N\/m\n\nx = 0.95 m\n\nSince, \\\\(F = -kx\\\\)\n\nThus, \\\\(F = -4 \\\\times 0.95\\\\)\n\n\\\\(F = -3.8 N\\\\)\n\n**Example 4**. A spring with a spring constant of 4 N\/m is stretched to a distance of 0.55 m. Calculate the force required.\n\nSolution 4: Since, k = 4 N\/m\n\nx = 0.55 m\n\nSince, \\\\(F = -kx\\\\)\n\nThus, \\\\(F = -4 \\\\times 0.55\\\\)\n\n\\\\(F = -2.2 N\\\\)\n\nHope this article about the Hooke’s Law formula was able to get the concept of this topic in motion. There are many such interesting topics and their real-life applications to learn about, just download the [Testbook app](https:\/\/link.testbook.com\/0DRQgVCiWyb) and start browsing to get insights on them which can clear all your concepts regarding them.","meta_canonical":null}

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Boilerpipe Text	A spring is a common object which almost everybody of us has seen. We know that when we stretch a spring we have to exert energy and when we release the stretched spring it coils back up again. Since we exert energy when stretching a spring, then that energy should go there. And since on releasing the stretched spring it coils back again without any additional force required, the general conclusion should be that the spring stores the energy exerted by us into itself, which it then uses to go back to its coiled position. This observation was quantified by Robert Hooke who gave Hooke's Law . This Physics article will explain Hooke's Law Formula along with some solved examples. Hooke’s Law The Hooke’s law states that within the elastic limit, the stress applied on a body is directly proportional to the strain produced. This mean that the force required to stretch or compress a spring over a certain distance is directly proportional to the distance through which the spring is stretched or compressed. The force is equal to the product of the spring constant and the distance over which the spring is stretched or compressed. Hooke’s law essentially defines elastic limit. In the stress-strain curve, Hooke’s law holds good up to the limit of proportionality. In simple words, it is applicable within the limit of proportionality. Hooke's Law Formula The formula for Hooke’s Law is mathematically defined as \(F = -kx\) The minus sign in the equation indicates that the force exerted by the spring is in the opposite direction to the displacement. In other words, if you stretch a spring, it will exert a force that tries to return it to its equilibrium position, and if you compress a spring, it will exert a force that tries to expand back to its equilibrium position. Where, F = Force required to change the linear dimension of the spring k = Spring Constant, in the units of N/m. x = Distance over which the spring is stretched or compressed. It is positive in sign when the Spring is stretched and negative when it is compressed. Limitations of Hooke’s Law Hooke’s law has some limitations that must be taken into consideration. Hooke's Law is only valid up to a certain point, known as the elastic limit . Beyond this limit, the material will start to deform permanently and the relationship between force and displacement will no longer be linear. Some materials do not follow a linear relationship between force and displacement, and their behaviour cannot be accurately described by Hooke's Law. Hooke's Law assumes that materials are isotropic. Therefore, anisotropic materials do not follow Hooke’s law. When a material is subjected to a force beyond its elastic limit, it undergoes plastic deformation and does not return to its original shape. Hooke's Law does not apply in this case. Temperature can affect the stiffness of a material and alter its behaviour, making it deviate from Hooke's Law. Application of Hooke’s Law Some common applications of Hooke’s law are as follows: Hooke's Law is commonly used to design and analyze springs. It helps in understanding the behaviour of pendulums, springs, etc. It is used to study the elasticity and stiffness of a material. It is also used to test the mechanical properties of a material such as tensile strength, modulus of elasticity, and compressive strength. Hooke's Law Formula Solved Examples Example 1. A spring with a spring constant of 2 N/m is stretched to a distance of 2 m. Calculate the force required. Solution 1: Since, k = 2 N/m x = 2 m Since, \(F = -kx\) Thus, \(F = -2 \times 2\) \(F = -4 N\) Example 2. A spring with a spring constant of 2 N/m is stretched to a distance of 0.2 m. Calculate the force required. Solution 2: Since, k = 2 N/m x = 0.2 m Since, \(F = -kx\) Thus, \(F = -2 \times 0.2\) \(F = -0.4 N\) Example 3. A spring with a spring constant of 4 N/m is stretched to a distance of 0.95 m. Calculate the force required. Solution 3: Since, k = 4 N/m x = 0.95 m Since, \(F = -kx\) Thus, \(F = -4 \times 0.95\) \(F = -3.8 N\) Example 4 . A spring with a spring constant of 4 N/m is stretched to a distance of 0.55 m. Calculate the force required. Solution 4: Since, k = 4 N/m x = 0.55 m Since, \(F = -kx\) Thus, \(F = -4 \times 0.55\) \(F = -2.2 N\) Hope this article about the Hooke’s Law formula was able to get the concept of this topic in motion. There are many such interesting topics and their real-life applications to learn about, just download the Testbook app and start browsing to get insights on them which can clear all your concepts regarding them.
Markdown	- [English](https://testbook.com/physics-formulas/hookes-law-formula) - [Get Started](https://testbook.com/login?tile=signup "Sign Up") - [Exams](https://testbook.com/exams) - [SuperCoaching](https://testbook.com/super-coaching) - [Live Classes FREE](https://testbook.com/free-live-classes) - [Test Series](https://testbook.com/online-test-series) - [Previous Year Papers](https://testbook.com/previous-year-papers) - [Books](https://link.testbook.com/e/books) - [Pass]() [Pass](https://testbook.com/pass) [Pass Pro](https://testbook.com/pass-pro) [Pass Elite](https://testbook.com/pass-elite) - [Pass](https://testbook.com/pass) - [Pass Pro](https://testbook.com/pass-pro) - [Pass Elite](https://testbook.com/pass-elite) - [Rank Predictor](https://testbook.com/rank-predictor) - [IAS Preparation](https://testbook.com/ias-preparation) - [More]() [Free Live Classes](https://testbook.com/free-live-classes) [Free Live Tests & Quizzes](https://testbook.com/free-live-tests-and-quizzes) [Free Quizzes](https://testbook.com/free-online-quizzes) [Previous Year Papers](https://testbook.com/previous-year-papers) [Doubts](https://testbook.com/doubts) [Practice](https://testbook.com/practice-questions) [Refer and Earn](https://testbook.com/referrals) [All Exams](https://testbook.com/exams) [Our Selections](https://testbook.com/success-stories) [Careers](https://testbook.com/careers) [IAS Preparation](https://testbook.com/ias-preparation) [Current Affairs](https://testbook.com/current-affairs) [Global Careers](https://globalcareers.testbook.com/) - [Practice](https://testbook.com/practice-questions) - [GK & Current Affairs](https://testbook.com/current-affairs/current-affairs-quiz) - [Blog](https://testbook.com/blog/) - [Refer & Earn](https://testbook.com/referrals) [Our Selections](https://testbook.com/success-stories) [Global Careers](https://globalcareers.testbook.com/) [Home](https://testbook.com/physics-formulas/hookes-law-formula) [Physics Formulas](https://testbook.com/physics-formulas/physics-formulas) Hookes Law Formula ![Hooke's Law Formula: Explained With Solved Examples](https://cdn.testbook.com/resources/productionimages/Physics%20Formula%20Logo_All_1670493719.png) # Hooke's Law Formula: Explained With Solved Examples [Download as PDF](https://testbook.com/login?redirect_url=https%3A%2F%2Ftestbook.com%2Fphysics-formulas%2Fhookes-law-formula&referrer=customChildPage-hookes-law-formula&referrerType=CustomChildPage&referrerPagePath=undefined) ![Hooke's Law Formula: Explained With Solved Examples Exam Preparation](https://testbook.com/physics-formulas/assets/img/banner-bg/bottom-banner-preparation.svg) A spring is a common object which almost everybody of us has seen. We know that when we stretch a spring we have to exert [energy](https://testbook.com/physics/energy) and when we release the stretched spring it coils back up again. Since we exert energy when stretching a spring, then that energy should go there. And since on releasing the stretched spring it coils back again without any additional force required, the general conclusion should be that the spring stores the energy exerted by us into itself, which it then uses to go back to its coiled position. This observation was quantified by Robert Hooke who gave [Hooke's Law](https://testbook.com/physics/hookes-law). This [Physics](https://testbook.com/physics) article will explain Hooke's Law Formula along with some solved examples. ## Hooke’s Law The Hooke’s law states that within the elastic limit, the stress applied on a body is directly proportional to the strain produced. This mean that the [force](https://testbook.com/physics/force) required to stretch or compress a spring over a certain distance is directly proportional to the distance through which the spring is stretched or compressed. The force is equal to the product of the spring constant and the distance over which the spring is stretched or compressed. Hooke’s law essentially defines elastic limit. In the stress-strain curve, Hooke’s law holds good up to the limit of proportionality. In simple words, it is applicable within the limit of proportionality. ## Hooke's Law Formula The formula for Hooke’s Law is mathematically defined as \\(F = -kx\\) The minus sign in the equation indicates that the force exerted by the spring is in the opposite direction to the displacement. In other words, if you stretch a spring, it will exert a force that tries to return it to its equilibrium position, and if you compress a spring, it will exert a force that tries to expand back to its equilibrium position. Where, F = Force required to change the linear dimension of the spring k = Spring Constant, in the units of N/m. x = Distance over which the spring is stretched or compressed. It is positive in sign when the Spring is stretched and negative when it is compressed. [![](https://cdn.testbook.com/static/assets/assets/img/media/signup_desktop.webp)](https://testbk.co/1fgwm) [![Pass pro banner mobile](https://cdn.testbook.com/static/assets/assets/img/media/result_blocker_3x.webp)](https://testbk.co/1g48a) ## Limitations of Hooke’s Law Hooke’s law has some limitations that must be taken into consideration. - Hooke's Law is only valid up to a certain point, known as the [elastic limit](https://testbook.com/physics/elastic-limit). Beyond this limit, the material will start to deform permanently and the relationship between force and displacement will no longer be linear. - Some materials do not follow a linear relationship between force and displacement, and their behaviour cannot be accurately described by Hooke's Law. - Hooke's Law assumes that materials are isotropic. Therefore, anisotropic materials do not follow Hooke’s law. - When a material is subjected to a force beyond its elastic limit, it undergoes plastic deformation and does not return to its original shape. Hooke's Law does not apply in this case. - Temperature can affect the stiffness of a material and alter its behaviour, making it deviate from Hooke's Law. ## Application of Hooke’s Law Some common applications of Hooke’s law are as follows: - Hooke's Law is commonly used to design and analyze springs. - It helps in understanding the behaviour of pendulums, springs, etc. - It is used to study the elasticity and stiffness of a material. - It is also used to test the mechanical properties of a material such as tensile strength, modulus of elasticity, and compressive strength. ## Hooke's Law Formula Solved Examples Example 1. A spring with a spring constant of 2 N/m is stretched to a distance of 2 m. Calculate the force required. Solution 1: Since, k = 2 N/m x = 2 m Since, \\(F = -kx\\) Thus, \\(F = -2 \\times 2\\) \\(F = -4 N\\) Example 2. A spring with a spring constant of 2 N/m is stretched to a distance of 0.2 m. Calculate the force required. Solution 2: Since, k = 2 N/m x = 0.2 m Since, \\(F = -kx\\) Thus, \\(F = -2 \\times 0.2\\) \\(F = -0.4 N\\) Example 3. A spring with a spring constant of 4 N/m is stretched to a distance of 0.95 m. Calculate the force required. Solution 3: Since, k = 4 N/m x = 0.95 m Since, \\(F = -kx\\) Thus, \\(F = -4 \\times 0.95\\) \\(F = -3.8 N\\) Example 4. A spring with a spring constant of 4 N/m is stretched to a distance of 0.55 m. Calculate the force required. Solution 4: Since, k = 4 N/m x = 0.55 m Since, \\(F = -kx\\) Thus, \\(F = -4 \\times 0.55\\) \\(F = -2.2 N\\) Hope this article about the Hooke’s Law formula was able to get the concept of this topic in motion. There are many such interesting topics and their real-life applications to learn about, just download the [Testbook app](https://link.testbook.com/0DRQgVCiWyb) and start browsing to get insights on them which can clear all your concepts regarding them. More Articles for Physics Formulas - [Surface Tension Formula](https://testbook.com/physics-formulas/surface-tension-formula) - [Tangential Velocity Formula](https://testbook.com/physics-formulas/tangential-velocity-formula) - [Voltage Divider Formula](https://testbook.com/physics-formulas/voltage-divider-formula) - [Absolute pressure formula](https://testbook.com/physics-formulas/absolute-pressure-formula) - [Intensity Formula](https://testbook.com/physics-formulas/intensity-formula) - [Heat Rate Formula](https://testbook.com/physics-formulas/heat-rate-formula) - [Specific Heat Formula](https://testbook.com/physics-formulas/specific-heat-formula) - [Heat Of Vaporization Formula](https://testbook.com/physics-formulas/heat-of-vaporization-formula) - [Initial velocity formula](https://testbook.com/physics-formulas/initial-velocity-formula) - [Kinetic Energy Formula](https://testbook.com/physics-formulas/kinetic-energy-formula) ## Hooke's Law Formula FAQs ### How do I calculate Hooke's law? Hooke’s Law is calculated by using the formula \[latex\]F = -kx\[/latex\] ### What is K in Hooke's law formula? ‘k’ in Hooke’s law is the spring constant. ### Why is there a negative in F =- kx? A negative sign is added in Hooke’s Law to signify the restoring force being exerted by the spring. ### State Hooke's law Hooke’s law states that the strain of the spring is proportional to the stress applied to it within its elastic limit. ### What is the unit of the spring constant? The unit of the spring constant is N/m. 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Papers](https://testbook.com/ssc-je/previous-year-papers)[CGPSC Previous Year Papers](https://testbook.com/cgpsc/previous-year-papers)[AIIMS CRE Previous Year Papers](https://testbook.com/aiims-cre/previous-year-papers)[EPFO Personal Assistant Previous Year Papers](https://testbook.com/epfo-personal-assistant/previous-year-papers)[FCI Manager Previous Year Papers](https://testbook.com/fci-manager/previous-year-papers)[JKPSC KAS Previous Year Papers](https://testbook.com/jkpsc-kas/previous-year-papers)[OPSC OAS Previous Year Papers](https://testbook.com/opsc-oas/previous-year-papers)[UPPCS Previous Year Papers](https://testbook.com/uppcs/previous-year-papers)[NEET Previous Year Papers](https://testbook.com/neet/previous-year-papers)[MHT CET Previous Year Papers](https://testbook.com/mah-cet-mba/previous-year-papers)[TANCET Previous Year Papers](https://testbook.com/tancet/previous-year-papers)[AAI ATC Previous Year Papers](https://testbook.com/aai-je-atc/previous-year-papers)[MP Vyapam 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Papers](https://testbook.com/fci-watchman/previous-year-papers)[Kerala PSC KAS Previous Year Papers](https://testbook.com/kerala-psc-kas/previous-year-papers)[RPSC RAS Previous Year Papers](https://testbook.com/rpsc-ras/previous-year-papers)[WBCS Previous Year Papers](https://testbook.com/wbcs/previous-year-papers)[JEE Main Previous Year Papers](https://testbook.com/jee-main/previous-year-papers)[CAT Previous Year Papers](https://testbook.com/cat-exam/previous-year-papers)[CTET Previous Year Papers](https://testbook.com/ctet/previous-year-papers)[BPSC AE Previous Year Papers](https://testbook.com/bpsc-ae/previous-year-papers)[MPPSC AE Previous Year Papers](https://testbook.com/mppsc-ae/previous-year-papers)[UPPSC AE Previous Year Papers](https://testbook.com/uppsc-ae/previous-year-papers) [SSC CHSL Previous Year Papers](https://testbook.com/ssc-chsl/previous-year-papers)[SSC CPO Previous Year Papers](https://testbook.com/ssc-cpo/previous-year-papers)[RRB NTPC Previous Year Papers](https://testbook.com/rrb-ntpc/previous-year-papers)[RRB Technician Grade-1 Previous Year Papers](https://testbook.com/rrb-technician-grade-1/previous-year-papers)[BPSC Previous Year Papers](https://testbook.com/bpsc-exam/previous-year-papers)[HPSC HCS Previous Year Papers](https://testbook.com/haryana-civil-services/previous-year-papers)[CBSE Junior Assistant Previous Year Papers](https://testbook.com/cbse-junior-assistant/previous-year-papers)[FCI Grade 3 Previous Year Papers](https://testbook.com/fci-grade-3/previous-year-papers)[FSSAI Personal Assistant Previous Year Papers](https://testbook.com/fssai-personal-assistant/previous-year-papers)[KPSC KAS Previous Year Papers](https://testbook.com/kpsc-kas/previous-year-papers)[TNPSC Group 1 Previous Year Papers](https://testbook.com/tnpsc-group-1/previous-year-papers)[CUET Previous Year Papers](https://testbook.com/cuet/previous-year-papers)[JEE Advance Previous Year 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Papers](https://testbook.com/aai-junior-assistant/previous-year-papers)[CSIR Junior Secretariat Assistant Previous Year Papers](https://testbook.com/csir-junior-secretariat-assistant/previous-year-papers)[FCI Je Previous Year Papers](https://testbook.com/fci-je/previous-year-papers)[NIELIT Scientist B Previous Year Papers](https://testbook.com/nielit-scientist-b/previous-year-papers)[MPPSC Exam Previous Year Papers](https://testbook.com/mppsc-state-service/previous-year-papers)[TSPSC Group 1 Previous Year Papers](https://testbook.com/tspsc-group-1/previous-year-papers)[CUET PG Previous Year Papers](https://testbook.com/cuet-pg/previous-year-papers)[JEECUP Previous Year Papers](https://testbook.com/up-polytechnic-jeecup/previous-year-papers)[MAH MBA CET Previous Year Papers](https://testbook.com/mah-cet-mba/previous-year-papers)[BHEL Engineer Trainee Previous Year Papers](https://testbook.com/bhel-engineer-trainee/previous-year-papers)[Mahatransco AE Previous Year Papers](https://testbook.com/mahatransco-ae/previous-year-papers)[TSGENCO AE Previous Year Papers](https://testbook.com/tsgenco-ae/previous-year-papers) Syllabus [SSC CGL Syllabus](https://testbook.com/ssc-cgl-exam/syllabus)[SSC MTS Syllabus](https://testbook.com/ssc-mts/syllabus-exam-pattern)[RRB NTPC Syllabus](https://testbook.com/rrb-ntpc/syllabus)[SSC JE Syllabus](https://testbook.com/ssc-je/syllabus)[JEE Main Syllabus](https://testbook.com/jee-main/syllabus)[NIFT Syllabus](https://testbook.com/nift-exam/syllabus)[AAI Junior Assistant Syllabus](https://testbook.com/aai-junior-assistant/syllabus-exam-pattern)[CSIR Junior Secretariat Assistant Syllabus](https://testbook.com/csir-junior-secretariat-assistant/syllabus-exam-pattern)[FCI Syllabus](https://testbook.com/fci/syllabus)[FCI Stenographer Syllabus](https://testbook.com/fci-stenographer/syllabus-exam-pattern)[NIELIT Scientist B Syllabus](https://testbook.com/nielit-scientist-b/syllabus-exam-pattern)[AAI ATC Syllabus](https://testbook.com/aai-je-atc/syllabus-exam-pattern)[BPSC AE Syllabus](https://testbook.com/bpsc-ae/syllabus-exam-pattern)[RSMSSB Junior Engineer Syllabus](https://testbook.com/rsmssb-junior-engineer/syllabus-exam-pattern)[CUET Accountancy Book Keeping Syllabus](https://testbook.com/cuet/accountancy-book-keeping-syllabus)[CUET Ba Syllabus](https://testbook.com/cuet/ba-syllabus-exam-pattern)[CUET Business Economics Syllabus](https://testbook.com/cuet/business-economics-syllabus)[CUET Computer Science Syllabus](https://testbook.com/cuet/computer-science-syllabus)[CUET Environmental Studies Syllabus](https://testbook.com/cuet/environmental-studies-syllabus)[CUET Commerce Syllabus](https://testbook.com/cuet/commerce-syllabus)[CUET Hindi Syllabus](https://testbook.com/cuet/hindi-syllabus-exam-pattern)[CUET Malayalam Syllabus](https://testbook.com/cuet/malayalam-syllabus-exam-pattern)[CUET Physical Education Syllabus](https://testbook.com/cuet/physical-education-syllabus)[CUET Sanskrit Syllabus](https://testbook.com/cuet/sanskrit-syllabus)[BPSC Exam Syllabus](https://testbook.com/bpsc-exam/syllabus-exam-pattern)[JKPSC KAS Syllabus](https://testbook.com/jkpsc-kas/syllabus-exam-pattern)[OPSC OAS Syllabus](https://testbook.com/opsc-oas/syllabus-exam-pattern)[WBCS Exam Syllabus](https://testbook.com/wbcs/syllabus-exam-pattern)[TSPSC Group 1 Syllabus](https://testbook.com/tspsc-group-1/syllabus-exam-pattern)[BPSC Exam Syllabus](https://testbook.com/bpsc-exam/syllabus-exam-pattern) [SSC CHSL Syllabus](https://testbook.com/ssc-chsl/syllabus)[SSC Stenographer Syllabus](https://testbook.com/ssc-stenographer/syllabus-exam-pattern)[RRB Technician Syllabus](https://testbook.com/rrb-technician/syllabus-exam-pattern)[RRB JE Syllabus](https://testbook.com/rrb-je/syllabus)[JEE Advanced Syllabus](https://testbook.com/jee-advanced/syllabus)[WB JEE Syllabus](https://testbook.com/wb-jee/syllabus-exam-pattern)[AIIMS CRE Syllabus](https://testbook.com/aiims-cre/syllabus-exam-pattern)[CSIR Npl Technician Syllabus](https://testbook.com/csir-npl-technician/syllabus-exam-pattern)[FCI Grade 3 Syllabus](https://testbook.com/fci-grade-3/syllabus-exam-pattern)[FCI Typist Syllabus](https://testbook.com/fci-typist/syllabus-exam-pattern)[CUET Maths Syllabus](https://testbook.com/cuet/mathematics-syllabus)[BHEL Engineer Trainee Syllabus](https://testbook.com/bhel-engineer-trainee/salary-job-profile)[MP Vyapam Sub Engineer Syllabus](https://testbook.com/mp-vyapam-sub-engineer/syllabus-exam-pattern)[TSGENCO AE Syllabus](https://testbook.com/tsgenco-ae/syllabus-exam-pattern)[CUET Agriculture Syllabus](https://testbook.com/cuet/agriculture-syllabus)[CUET BCA Syllabus](https://testbook.com/cuet/bca-syllabus-exam-pattern)[CUET Business Studies Syllabus](https://testbook.com/cuet/business-studies-syllabus)[CUET Engineering Graphics Syllabus](https://testbook.com/cuet/engineering-graphics-syllabus)[CUET Fine Arts Syllabus](https://testbook.com/cuet/fine-arts-syllabus)[CUET Geography Syllabus](https://testbook.com/cuet/geography-syllabus)[CUET History Syllabus](https://testbook.com/cuet/history-syllabus)[CUET Marathi Syllabus](https://testbook.com/cuet/marathi-syllabus-exam-pattern)[CUET Political Science Syllabus](https://testbook.com/cuet/political-science-syllabus)[CUET Sociology Syllabus](https://testbook.com/cuet/sociology-syllabus)[CGPSC Syllabus](https://testbook.com/cgpsc/syllabus)[Kerala PSC KAS Syllabus](https://testbook.com/kerala-psc-kas/syllabus-exam-pattern)[RPSC RAS Syllabus](https://testbook.com/rpsc-ras/syllabus)[HPPSC HPAS Syllabus](https://testbook.com/hppsc-hpas/syllabus-exam-pattern)[UKPSC Upper PCS Syllabus](https://testbook.com/ukpsc-combined-upper-subordinate-service/syllabus-exam-pattern)[CGPSC Syllabus](https://testbook.com/cgpsc/syllabus) [SSC CPO Syllabus](https://testbook.com/ssc-cpo/syllabus)[RRB Group D Syllabus](https://testbook.com/rrb-group-d/syllabus)[RPF Constable Syllabus](https://testbook.com/rpf-constable/syllabus-exam-pattern)[CUET Syllabus](https://testbook.com/cuet/exam-syllabus)[JEECUP Syllabus](https://testbook.com/up-polytechnic-jeecup/syllabus-exam-pattern)[GUJCET Syllabus](https://testbook.com/gujcet/syllabus)[CBSE Assistant Secretary Syllabus](https://testbook.com/cbse-assistant-secretary/syllabus-exam-pattern)[CWC Junior Superintendent Syllabus](https://testbook.com/cwc-junior-superintendent/syllabus-exam-pattern)[FCI Je Syllabus](https://testbook.com/fci-je/syllabus-exam-pattern)[FCI Watchman Syllabus](https://testbook.com/fci-watchman/syllabus-exam-pattern)[CUET Physics Syllabus](https://testbook.com/cuet/physics-syllabus)[Mahagenco Technician Syllabus](https://testbook.com/mahagenco-technician/syllabus-exam-pattern)[MPPSC AE Syllabus](https://testbook.com/mppsc-ae/syllabus-exam-pattern)[UPPSC AE Syllabus](https://testbook.com/uppsc-ae/syllabus)[CUET Anthropology Syllabus](https://testbook.com/cuet/anthropology-syllabus)[CUET Bengali Syllabus](https://testbook.com/cuet/bengali-syllabus-exam-pattern)[CUET Chemistry Syllabus](https://testbook.com/cuet/chemistry-syllabus)[CUET English Syllabus](https://testbook.com/cuet/english-syllabus-exam-pattern)[CUET French Syllabus](https://testbook.com/cuet/french-syllabus-exam-pattern)[CUET German Syllabus](https://testbook.com/cuet/german-syllabus-exam-pattern)[CUET Home Science Syllabus](https://testbook.com/cuet/home-science-syllabus)[CUET Mass Media Syllabus](https://testbook.com/cuet/mass-media-syllabus)[CUET Psychology Syllabus](https://testbook.com/cuet/psychology-syllabus)[CUET Teaching Aptitude Syllabus](https://testbook.com/cuet/teaching-aptitude-syllabus)[GPSC Class 1 2 Syllabus](https://testbook.com/gpsc-class-1-2/syllabus-exam-pattern)[KPSC KAS Syllabus](https://testbook.com/kpsc-kas/syllabus-exam-pattern)[TNPSC Group 1 Syllabus](https://testbook.com/tnpsc-group-1/syllabus-exam-pattern)[MPPSC Forest Services Syllabus](https://testbook.com/mppsc-forest-service/syllabus-exam-pattern)[UKPSC Lower PCS Syllabus](https://testbook.com/ukpsc-lower-pcs/syllabus-exam-pattern) [SSC GD Constable Syllabus](https://testbook.com/ssc-gd-constable/syllabus-exam-pattern)[RRB ALP Syllabus](https://testbook.com/rrb-alp/syllabus-exam-pattern)[RPF SI Syllabus](https://testbook.com/rpf-si/syllabus-exam-pattern)[NEET Syllabus](https://testbook.com/neet/syllabus)[MHT CET Syllabus](https://testbook.com/mht-cet/syllabus)[CUET Commerce Syllabus](https://testbook.com/cuet/commerce-syllabus)[CBSE Junior Assistant Syllabus](https://testbook.com/cbse-junior-assistant/syllabus-exam-pattern)[EPFO Personal Assistant Syllabus](https://testbook.com/epfo-personal-assistant/syllabus-exam-pattern)[FCI Manager Syllabus](https://testbook.com/fci-manager/syllabus-exam-pattern)[FSSAI Personal Assistant Syllabus](https://testbook.com/fssai-personal-assistant/syllabus-exam-pattern)[CUET Biology Syllabus](https://testbook.com/cuet/biology-syllabus)[BMC JE Syllabus](https://testbook.com/bmc-je/syllabus-exam-pattern)[PGCIL Diploma Trainee Syllabus](https://testbook.com/pgcil-diploma-trainee/syllabus-exam-pattern)[UPSC IES Syllabus](https://testbook.com/upsc-ies/syllabus)[CUET Assamese Syllabus](https://testbook.com/cuet/assamese-syllabus-exam-pattern)[CUET Bsc Syllabus](https://testbook.com/cuet/bsc-syllabus-exam-pattern)[CUET Commerce Syllabus](https://testbook.com/cuet/commerce-syllabus)[CUET Entrepreneurship Syllabus](https://testbook.com/cuet/entrepreneurship-syllabus)[CUET General Test Syllabus](https://testbook.com/cuet/general-test-syllabus)[CUET Gujarati Syllabus](https://testbook.com/cuet/gujarati-syllabus-exam-pattern)[CUET Legal Studies Syllabus](https://testbook.com/cuet/legal-studies-syllabus)[CUET Odia Syllabus](https://testbook.com/cuet/odia-syllabus-exam-pattern)[CUET Punjabi Syllabus](https://testbook.com/cuet/punjabi-syllabus-exam-pattern)[APPSC Group 1 Syllabus](https://testbook.com/appsc-group-1/syllabus-exam-pattern)[HPSC HCS Syllabus](https://testbook.com/haryana-civil-services/syllabus-exam-pattern)[MPPSC Exam Syllabus](https://testbook.com/mppsc-state-service/syllabus-exam-pattern)[UPPCS Exam Syllabus](https://testbook.com/uppcs/syllabus-exam-pattern)[MPSC Rajyaseva Syllabus](https://testbook.com/mpsc-state-service/syllabus-exam-pattern)[APPSC Group 1 Syllabus](https://testbook.com/appsc-group-1/syllabus-exam-pattern) Board Exams [Haryana Board](https://testbook.com/hbse-class-12th)[Gujarat Board](https://testbook.com/gseb-class-12)[Maharashtra Board](https://testbook.com/maharashtra-hsc-exam)[Telangana Board](https://testbook.com/ts-intermediate) [AP Board](https://testbook.com/ap-inter-2nd-year)[ICSE](https://testbook.com/isc-class-12)[Madhya Pradesh Board](https://testbook.com/mp-board-12th)[Uttar Pradesh Board](https://testbook.com/up-board-class-12) [Bihar Board](https://testbook.com/bihar-board-12th)[Jharkhand Board](https://testbook.com/jac-class-12)[Punjab Board](https://testbook.com/pseb-class-12)[West Bengal Board](https://testbook.com/wbchse-class-12) [CBSE](https://testbook.com/cbse-class-12)[Karnataka Board](https://testbook.com/karnataka-2nd-puc)[Rajasthan Board](https://testbook.com/rbse-class-12) Coaching [SSC CGL Coaching](https://testbook.com/ssc-cgl-coaching)[SSC GD Constable Coaching](https://testbook.com/ssc-gd-coaching)[RRB ALP Coaching](https://testbook.com/rrb-alp-coaching)[RPF SI Coaching](https://testbook.com/rpf-constable-and-si-coaching) [SSC CHSL Coaching](https://testbook.com/ssc-chsl-coaching)[SSC CPO Coaching](https://testbook.com/ssc-cpo-coaching)[RRB NTPC Coaching](https://testbook.com/rrb-ntpc1-coaching)[SSC JE Coaching](https://testbook.com/ssc-je-civil-2025-coaching) [SSC CPO Coaching](https://testbook.com/ssc-cpo-coaching)[SSC Stenographer Coaching](https://testbook.com/ssc-stenographer-coaching)[RRB Technician Grade 1 Coaching](https://testbook.com/rrb-technician-grade-1-signal-coaching)[RRB JE Coaching](https://testbook.com/rrb-je-civil-engineering-coaching) [SSC MTS Coaching](https://testbook.com/ssc-mts-coaching)[RRB Group D Coaching](https://testbook.com/rrb-groupd-coaching)[RPF Constable Coaching](https://testbook.com/rpf-constable-and-si-coaching) Eligibility [SSC CGL Eligibility](https://testbook.com/ssc-cgl-exam/eligibility-criteria)[SSC GD Constable Eligibility](https://testbook.com/ssc-gd-constable/eligibility-criteria)[RRB ALP Eligibility](https://testbook.com/rrb-alp/eligibility-criteria)[RPF SI Eligibility](https://testbook.com/rpf-si/eligibility-criteria)[BPSC Exam Eligibility](https://testbook.com/bpsc-exam/eligibility-criteria)[JKPSC KAS Eligibility](https://testbook.com/jkpsc-kas/eligibility-criteria)[OPSC OAS Eligibility](https://testbook.com/opsc-oas/eligibility-criteria)[WBCS Exam Eligibility](https://testbook.com/wbcs/eligibility-criteria)[TSPSC Group 1 Eligibility](https://testbook.com/tspsc-group-1/eligibility-criteria)[AIIMS CRE Eligibility](https://testbook.com/aiims-cre/eligibility-criteria)[CBSE Junior Assistant Eligibility](https://testbook.com/cbse-junior-assistant/eligibility-criteria)[FCI Assistant Grade 3 Eligibility](https://testbook.com/fci-grade-3/eligibility-criteria)[EPFO Personal Assistant Eligibility](https://testbook.com/epfo-personal-assistant/eligibility-criteria)[NEET Eligibility](https://testbook.com/neet/eligibility-criteria)[MHT CET Eligibility](https://testbook.com/mht-cet/eligibility-criteria)[NCHMCT JEE Eligibility](https://testbook.com/nchmct-jee-exam/eligibility-criteria)[BPSC AE Eligibility](https://testbook.com/bpsc-ae/eligibility-criteria)[MPPSC AE Eligibility](https://testbook.com/mppsc-ae/eligibility-criteria)[TSGENCO AE Eligibility](https://testbook.com/tsgenco-ae/eligibility-criteria)[CMAT Eligibility](https://testbook.com/cmat-exam/eligibility-criteria)[ATMA 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Readable Markdown	A spring is a common object which almost everybody of us has seen. We know that when we stretch a spring we have to exert [energy](https://testbook.com/physics/energy) and when we release the stretched spring it coils back up again. Since we exert energy when stretching a spring, then that energy should go there. And since on releasing the stretched spring it coils back again without any additional force required, the general conclusion should be that the spring stores the energy exerted by us into itself, which it then uses to go back to its coiled position. This observation was quantified by Robert Hooke who gave [Hooke's Law](https://testbook.com/physics/hookes-law). This [Physics](https://testbook.com/physics) article will explain Hooke's Law Formula along with some solved examples. ## Hooke’s Law The Hooke’s law states that within the elastic limit, the stress applied on a body is directly proportional to the strain produced. This mean that the [force](https://testbook.com/physics/force) required to stretch or compress a spring over a certain distance is directly proportional to the distance through which the spring is stretched or compressed. The force is equal to the product of the spring constant and the distance over which the spring is stretched or compressed. Hooke’s law essentially defines elastic limit. In the stress-strain curve, Hooke’s law holds good up to the limit of proportionality. In simple words, it is applicable within the limit of proportionality. ## Hooke's Law Formula The formula for Hooke’s Law is mathematically defined as \\(F = -kx\\) The minus sign in the equation indicates that the force exerted by the spring is in the opposite direction to the displacement. In other words, if you stretch a spring, it will exert a force that tries to return it to its equilibrium position, and if you compress a spring, it will exert a force that tries to expand back to its equilibrium position. Where, F = Force required to change the linear dimension of the spring k = Spring Constant, in the units of N/m. x = Distance over which the spring is stretched or compressed. It is positive in sign when the Spring is stretched and negative when it is compressed. ## Limitations of Hooke’s Law Hooke’s law has some limitations that must be taken into consideration. - Hooke's Law is only valid up to a certain point, known as the [elastic limit](https://testbook.com/physics/elastic-limit). Beyond this limit, the material will start to deform permanently and the relationship between force and displacement will no longer be linear. - Some materials do not follow a linear relationship between force and displacement, and their behaviour cannot be accurately described by Hooke's Law. - Hooke's Law assumes that materials are isotropic. Therefore, anisotropic materials do not follow Hooke’s law. - When a material is subjected to a force beyond its elastic limit, it undergoes plastic deformation and does not return to its original shape. Hooke's Law does not apply in this case. - Temperature can affect the stiffness of a material and alter its behaviour, making it deviate from Hooke's Law. ## Application of Hooke’s Law Some common applications of Hooke’s law are as follows: - Hooke's Law is commonly used to design and analyze springs. - It helps in understanding the behaviour of pendulums, springs, etc. - It is used to study the elasticity and stiffness of a material. - It is also used to test the mechanical properties of a material such as tensile strength, modulus of elasticity, and compressive strength. ## Hooke's Law Formula Solved Examples Example 1. A spring with a spring constant of 2 N/m is stretched to a distance of 2 m. Calculate the force required. Solution 1: Since, k = 2 N/m x = 2 m Since, \\(F = -kx\\) Thus, \\(F = -2 \\times 2\\) \\(F = -4 N\\) Example 2. A spring with a spring constant of 2 N/m is stretched to a distance of 0.2 m. Calculate the force required. Solution 2: Since, k = 2 N/m x = 0.2 m Since, \\(F = -kx\\) Thus, \\(F = -2 \\times 0.2\\) \\(F = -0.4 N\\) Example 3. A spring with a spring constant of 4 N/m is stretched to a distance of 0.95 m. Calculate the force required. Solution 3: Since, k = 4 N/m x = 0.95 m Since, \\(F = -kx\\) Thus, \\(F = -4 \\times 0.95\\) \\(F = -3.8 N\\) Example 4. A spring with a spring constant of 4 N/m is stretched to a distance of 0.55 m. Calculate the force required. Solution 4: Since, k = 4 N/m x = 0.55 m Since, \\(F = -kx\\) Thus, \\(F = -4 \\times 0.55\\) \\(F = -2.2 N\\) Hope this article about the Hooke’s Law formula was able to get the concept of this topic in motion. There are many such interesting topics and their real-life applications to learn about, just download the [Testbook app](https://link.testbook.com/0DRQgVCiWyb) and start browsing to get insights on them which can clear all your concepts regarding them.
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