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Physics-

General

Easy

Question

A wire of length Land 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 $2 a$ is stretched with a force 2F, the increase in its length will be

$l / 4$
$l$
$l / 2$
$2 l$

The correct answer is: $l$

Young’s modulus $Y equals fraction numerator F L over denominator A l end fraction$
$equals fraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction$
Since for same material Young’s modulus is same, $i e comma$
$Y subscript 1 end subscript equals Y subscript 2 end subscript$
or $fraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction equals fraction numerator open parentheses 2 F close parentheses left parenthesis 2 L right parenthesis over denominator pi open parentheses 2 a close parentheses to the power of 2 end exponent l ʹ end fraction$
or $l to the power of ´ end exponent equals l$

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