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

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Ans: (a)
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 $