JEE Main 2023PhysicsMechanical Properties of SolidsMediumNumerical

JEE Main 2023 — Mechanical Properties of Solids Question with Solution

JEE Main 2023 (11 Apr Shift 1)

Question

The length of a wire becomes l1 and l2 when 100 N and 120 N tension are applied respectively. If 10l2=11l1, then the natural length of wire will be 1xl1. Here the value of x is

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Correct answer
2

Step-by-step explanation

Young's modulus is given by Y=FA∆ll

⇒FA=YΔll⇒Δl=FlAY

⇒l+Δl=l1⇒F1LAY+L=LF1AY+1=l1   ...(i)

Similarly,

l2=F2AY+1L

⇒10l2=11l1

It is given that 10l1=11l2

⇒10×LF2AY+1=11LF1AY+1

⇒10F2AY+10=11F1AY+11

Substituting F1=100 N, F2=120 N

⇒1200AY−1100AY=1⇒100AY=1

⇒1AY=1100

Using equation (i),

 L=l1F1AY+1=l1100100+1=l12

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About this question

This is a previous-year question from JEE Main 2023, 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.