A load of 4.0 kg is suspended from a ceiling through a steel wire of length 20 m and radius 2.0 mm. It is found that the length of the wire increases by 0.031 mm as equilibrium is achieved. Find Young modulus of steel. Take g=3.1πms−2.
A
1011N/m2
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B
2×1011N/m2
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C
3×1011N/m2
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D
4×1011N/m2
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Solution
The correct option is B2×1011N/m2 The longitudinal stress =(4.0kg)(3.1πms−2)π(2.0×10−3m)2 =3.1×106m)−2. The longitudinal strain =0.31×10−3m2.0m =0.0155×10−3 Thus Y=3.1×106Nm−20.0155×10−3=2.0×1011Nm−2.