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 0.31 mm as equilibrium is achieved. Find Young modulus of steel. Take g=3.1π ms−2.
2×1011N/m2
The longitudinal stress = ForceArea
Force = mg = 4.0×3.1π N
Area = πr2 = π(2.0×10−3)2 m2
The longitudinal stress =4×3.1ππ(2.0×10−3)2
=3.1×106N/m−2
The longitudinal strain = Change in lengthTotal length
The longitudinal strain =0.31×10−3m2.0m
=0.0155×10−3
Young,s modulus Y = StressStrain
Thus Y=3.1×106Nm−20.0155×10−3=2.0×1011N m−2.