A wire of length L and radius r is fixed at one end. When a stretching force ,F is applied at free end, the elongation in the wire is /. When another wire of same material but of length 2L and radius 2r,also fixed at one end is stretched by a force 2F applied at free end, then elongation in the second wire will be

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l/4

l/2

answer is B.

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Detailed Solution

$Y = \frac{F / A}{Δl / l} For the first wire, Y = \frac{F \times L}{{πr}^{2} \times l} For the second wire, Y = \frac{2 F \times 2 L}{π (2 r)^{2} \times l^{'}} From the above two equations, l^{'} = l$

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