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JEE Main 202229 JuneMorning Shift

Exam: JEE Main
Year: 2022
Date: 29 June
Shift: Morning Shift
Subject: Physics
Chapter: Mechanical Properties of Solids

JEE Main 2022 · 29 June · Morning Shift · Physics · Mechanical Properties of Solids

A wire of length L is hanging from a fixed support. The length...

A wire of length

L

is hanging from a fixed support. The length changes to

{L}_{1}

and

{L}_{2}

when masses

1kg

and

2kg

are suspended respectively from its free end. Then the value of

L

is equal to

Options

A $\sqrt{{L}_{1}{L}_{2}}$
B $\dfrac{{L}_{1} + {L}_{2}}{2}$
C $2{L}_{1} - {L}_{2}$
D $3{L}_{1} - {L}_{2}$

Correct answer

C. $2{L}_{1} - {L}_{2}$

Step-by-step solution

From Hooke's law, $∆ L = \dfrac{FL}{AY} ⇒ ∆ L ∝ F$ . Therefore,

$\dfrac{{L}_{2} - L}{{L}_{1} - L} = \dfrac{{m}_{2}g}{{m}_{1}g} = \dfrac{2}{1}$ $⇒ L = 2{L}_{1} - {L}_{2}$

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