A 5m long cylindrical steel wire with radius `2xx10^(-3)m` is suspended vertically from a rigid support and carries a bob of mass 100kg at the other end. If the bob gets snapped, calculate the change in temperature of the wire ignoring radiation losses.
(For the steel wire : Young's modulus `=2.1xx10^(11)Pa` ,Density `7860kg//m^(3)` , specific heat capacity `=420J//kg-K`)

Explanation

Energy stored per unit volume is given by `=(1)/(2)` stress `xx` strain
When the bob gets snapped, this stored energy is released, thereby raising temperature of wire, i.e., `=(1)/(2)` stress `xx` strain `xx` volume `=msDeltatheta`
or `((m)^(2)L)/(2AY)=(rhoLA)sDeltatheta` or `Deltatheta=((mg)^(2))/(2rhoA^(2)Ys)=0.00457K`