A 5 m long cylindrical steel wire radius `2 xx 10^(-3)` m is suspended vertically from a rigid support ad carries a bob of mass 100 kg at the orhte end. If the bob gets snapped, calculate the change in temperature of one wire ignoring radiation losses.
(For the steel wire : Young's modulus = `2.1 xx 10^(11)` Pa, Density 7860 `kg//m^(2)`, speific heat capacity = 420 j/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" = ms Delta theta`
or `((mg)^(2)L)/(2AY)=(rhoLA)sd theta`
or `Delta theta=((mg)^(2))/(2rhoA^(2)Ys)=0.00457k`