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Question

Two wires of different material and radius have their length in ratio of 1:2. if these were stretched by the same force, the strain produced will be in the ratio.

A
4:1
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B
1:1
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C
2:1
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D
1:2
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Solution

The correct option is B 1:1
We know that the young's modulus is given by,
Y=stress/strain=(F/A)/strain
=>strain=F/AY
where,
F = force applied
A = area of cross section
since the wires are made of same material so there young's modulus will be same.
Also the force applied and the area of cross section is same (because radius is same)
Hence,
strain1/strain2=FAY/FAY=1
So, the ratio of strain will be 1:1 despite of the ratio of length.
Hence,
option (B) is correct answer.

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