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Q.

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. lf the length of the first wire is increased by ∆l on applying a force F, how much force is needed to stretch the second wire by the same amount ?

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a

F

b

9F

c

4F

d

6F

answer is B.

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Detailed Solution

We know Y = StressStrain = FA∆ll⇒Y = F∆, lAl = FlA∆lFor 1st wire; Y =F1l1A.∆l------(i)For IInd wire; Y = F2l23A.∆l-----(ii)As volume of the wire is sameHence, Al1 = 3Al2or l1l2  = 3-----(iii)From (i) and (ii); F1F2 = l23l1-----------(iv)From (iii) and (iv); F1F2 = 19 or F2 = 9F1
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