JEE Main 202120 JulyEvening Shift

Exam: JEE Main
Year: 2021
Date: 20 July
Shift: Evening Shift
Subject: Physics
Chapter: Mechanical Properties of Solids

JEE Main 2021 · 20 July · Evening Shift · Physics · Mechanical Properties of Solids

The length of a metal wire is ℓ _ 1 , when the tension in it is T _...

The length of a metal wire is ${ℓ}_{1},$ when the tension in it is ${T}_{1}$ and is ${ℓ}_{2}$ when the tension is ${T}_{2} .$ The natural length of the wire is:

Options

A $\sqrt{{ℓ}_{1}{ℓ}_{2}}$
B $\dfrac{{ℓ}_{1}{T}_{2} - {ℓ}_{2}{T}_{1}}{{T}_{2} - {T}_{1}}$
C $\dfrac{{ℓ}_{1}{T}_{2} + {ℓ}_{2}{T}_{1}}{{T}_{2} + {T}_{1}}$
D $\dfrac{{ℓ}_{1} + {ℓ}_{2}}{2}$

Correct answer

B. $\dfrac{{ℓ}_{1}{T}_{2} - {ℓ}_{2}{T}_{1}}{{T}_{2} - {T}_{1}}$

Step-by-step solution

${T}_{1} = k\left({ℓ}_{1} - {ℓ}_{0}\right)$

${T}_{2} = k\left({ℓ}_{2} - {ℓ}_{0}\right)$

$\dfrac{{T}_{1}}{{T}_{2}} = \dfrac{{ℓ}_{1} - {ℓ}_{0}}{{ℓ}_{2} - {ℓ}_{0}}$

${T}_{1}{ℓ}_{2} - {T}_{1}{ℓ}_{0} = {T}_{2}{ℓ}_{1} - {T}_{2}{ℓ}_{0}$

$\dfrac{{T}_{2}{ℓ}_{1} - {T}_{1}{ℓ}_{2}}{{T}_{2} - {T}_{2}} = {ℓ}_{0}$

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