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 '$\ell$'. Another wire of same material of length '2L' and radius '2r' is pulled by a force '2f'. Then the increase in its length will be :

JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Elasticity & SHM

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 '

ℓ

'. Another wire of same material of length '2L' and radius '2r' is pulled by a force '2f'. Then the increase in its length will be :

Answer: (B)

The extension of a stretched wire is

Δ L = \frac{F L}{A Y} = \frac{F L}{π r ^{2} Y}

. For the first wire

ℓ = \frac{f L}{π r ^{2} Y}

. For the second, with force

2 f

, length

2 L

and radius

2 r

ℓ^{'} = \frac{( 2 f ) ( 2 L )}{π ( 2 r ) ^{2} Y} = \frac{4 f L}{4 π r ^{2} Y} = \frac{f L}{π r ^{2} Y}

. The increase in length is therefore

ℓ

JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Single correct option