Question

A wire of length and radius is clamped at one end. On stretching the other end of the wire with a force F, the increase in its length is If another wire of same material but of length 2L and radius is stretched with a force 2F, the increase in its length will be

• A. $\frac{l}{4}$
• B. $\frac{l}{2}$
• C. l
• D. 2l

Answer 1

Answer: (C)

l

Answer 2

: Let Y be the Young’s modulus of the material of the wire, Then

For the first wire

$Y = \frac{F/\pi r^{2}}{l/L} = \frac{FL}{\pi r^{2}l}$ ….(i)

As both the wires are made of the same material, so their young modulus is same.

Let the extension produced in second wire be $l'$. Then

$Y = \frac{2F/\pi(2r)^{2}}{l'/2L} = \frac{FL}{\pi r^{2}l'}$ ……(ii)

Equating (i) and (ii) we get

$\frac{FL}{\pi r^{2}l} = \frac{FL}{\pi r^{2}l'}$or $l' = l$