JEE Main 2022PhysicsMechanical Properties of SolidsEasyNumerical

JEE Main 2022 — Mechanical Properties of Solids Question with Solution

JEE Main 2022 (25 Jul Shift 1)

Question

A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F, its length increases by 5 cm. Another wire of the same material of length 4 L and radius 4r is pulled by a force 4 F under same conditions. The increase in length of this wire is _____ cm.

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Show full solutionCorrect answer: 5
Correct answer
5

Step-by-step explanation

Young's modulus is given by Y=FLA∆L, here, A is cross-section area and ∆L is change in length.

Now, when force F is applied, change in length ΔL1=FLAY=FLπr2Y=5 cm

Now, when force 4F is applied, change in length

ΔL2=4 F4Lπ16r2Y=FLπr2Y=5 cm

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About this question

This is a previous-year question from JEE Main 2022, covering the Mechanical Properties of Solids chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.