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Q.

Two wires A and B are of the same material. Their lengths are in the ratio 1 : 2 and the diameters are in the ratio 2 : 1. If they are pulled by the same force, their increase in length will be in the ratio

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a

2:1

b

1:4

c

1 :8

d

8: 1

answer is C.

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Detailed Solution

We know that Y=Fπr2×LlSince X Fare same for both the wires, we have1r12L1l1=1r22L2l2  or  l1l2=r22×L1r12×L2=D2/22×L1D1/22×L2or 4l2=D22×L1D12×L2=D222D22×L12L1=18So , h:l2=1:8
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Two wires A and B are of the same material. Their lengths are in the ratio 1 : 2 and the diameters are in the ratio 2 : 1. If they are pulled by the same force, their increase in length will be in the ratio