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NEET Medium

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by l on applying a force F, how much force is needed to stretch the socond wire by the same amount?

A

4F

B

6F

C

9F

D

F

Step-by-Step Solution

For wire 1,

Δl=(FAY)3l…(i)\Delta l = \left(\frac{F}{AY}\right)3l \quad \dots(i)

For wire 2,

F′3A=YΔll\frac{F'}{3A} = Y \frac{\Delta l}{l}

⇒Δl=(F′3AY)l…(ii)\Rightarrow \Delta l = \left(\frac{F'}{3AY}\right)l \quad \dots(ii)

From equation (i) & (ii),

Δl=(FAY)3l=(F′3AY)l\Delta l = \left(\frac{F}{AY}\right)3l = \left(\frac{F'}{3AY}\right)l

⇒F′=9F\Rightarrow \boxed{F' = 9F}

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