JEE Main · 2009 · 12 Apr 2009 · Offline · Elasticity & SHM

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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

Δ x

on applying force F, how much force is needed to stretch wire 2 by the same amount?

(A)F
(B)4F
(C)6F
(D)9F✓ Correct

Answer: (D)

Solution

Because the wires share the same material and the same volume,

A_{1} ℓ_{1} = A_{2} ℓ_{2}

, and with the second wire three times as thick its length is one third,

\frac{ℓ _{1}}{ℓ _{2}} = 3

. The extension is

Δ x = \frac{F ℓ}{A Y}

, and demanding equal extensions,

\frac{F _{2} ℓ _{2}}{3 A Y} = \frac{F _{1} ℓ _{1}}{A Y}

, gives

F_{2} = 3 F_{1} \frac{ℓ _{1}}{ℓ _{2}} = 3 F \times 3

, so a force of

9 F

is needed.

JEE Main · 2009 · 12 Apr 2009 · Offline · Single correct option

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