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

Question

Dr. Abubacker · Accepted Answer

(b) Young’s modulus $Y = \frac{FL}{Al}$
$= \frac{FL}{{\pi a}^{2}l}$
Since for same material Young’s modulus is same, $ie,$
$Y_{1} = Y_{2}$
or$\ \frac{FL}{\ \ \ \ \ {\pi a}^{2}l} = \frac{(2F)(2L)}{{\pi(2a)}^{2}lʹ}$
or $l^{'} = l$

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

Explanation

Reviewed by Dr. Abubacker

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