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Question: Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional...

Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area A and wire 2 has cross-sectional area 3A. if the length of wire 1 increases by Dx on applying force F, how much force is needed to stretch wire 2 by the same amount ?

A

F

B

4 F

C

6 F

D

9 F

Answer

9 F

Explanation

Solution

∵\because Dx = F.LA.Y\frac{F.L}{A.Y}

∴\therefore F = Y.A.ΔxL\frac{Y.A.\Delta x}{L} ………..(1)

Volume = A.L. = A'L' = constant

̃ AL = 3AL'

̃ L' = L/3 ……… (2)

From equation (1)

F′F\frac{F'}{F}= A′A.LL′\frac{A'}{A}.\frac{L}{L'}

= 3 × 3

̃ F' = 9F

So option (4) is correct.