# A wire of length L and radius r is rigidly fixed at one end. One stretching the other end of the wire with a force F, the increase in the its length is l. If another wire of same material…..

Q: A wire of length L and radius r is rigidly fixed at one end. One stretching the other end of the wire with a force F, the increase in the its length is l. If another wire of same material but of length 2L and radius 2r is stretched with a force of 2F, the increase in its length will be

(a) l

(b) 2l

(c) l/2

(d) l/4

Sol: $\displaystyle \Delta L = \frac{F L}{A Y}$
$\displaystyle l = \frac{F L}{(\pi r^2) Y}$ ….(i)
$\displaystyle l’ = \frac{2 F (2L )}{(\pi (2r)^2) Y}$
$\displaystyle l’ = \frac{F L}{(\pi r^2) Y} = l$