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Question

Two wires of copper having the length in the ratio 4 : 1 and their radii ratio as 1 : 4 are stretched by the same force. The ratio of longitudinal strain in the two will be:

A
1 : 16
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B
16 : 1
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C
1 : 64
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D
64 : 1
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Solution

The correct option is B 16 : 1

L1L2=41 and R1R2=14F1=F2Y1=Y2 (as they made up of same material)
now,Y= stress × strain Y= Young modulus strain = stress Y
so, ( strain )1( strain )2=( stress )1( stress )2
=F1πR22πR21F2 as F1=F2S1S2=161

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