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Mechanical Properties Of Solids

Question

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

9F

6F

F

4F

Solution

Wire 1 :

$∆ l = (\frac{F}{A Y}) 3 l . . . . . (i)$

Wire 2:

$∆ l = (\frac{F'}{3 A Y}) l . . . . (i i) F r o m e q u a t i o n (i) a n d (i i) ∆ l = (\frac{F}{A Y}) 3 l = (\frac{F'}{3 A Y}) l O r, F' = 9 F$