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If the work done by stretching a wire by 1 mm is 2 J, the work necessary for stretching another wire of the same material but with double the radius of cross section and half the length by 1 mm is

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a

14J

b

4 J

c

8 J

d

16 J

answer is D.

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Detailed Solution

W=12FΔlW=12×Yπr2ΔllΔl and Y=Flπr2Δl or W=Yπr2Δl22l and F=Yπr2Δll or W∝r2l,W′∝(2r)22lW′W=8 or W′=8×2J=16J

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