A 5m long cylinderical steel wire with radius ` 2 xx 10^(-3)` m is suspended from a rigid suppose and carries of bob of mass 100 kg at the other end. If the gets snapped, calculate the change in temperarture the wire igoring radiation losses.
(For the steel wire: Young's modulus `2.1 xx 10^(11)` Pa, Density `7860 kg//m^(2)` , specific heat capacity = 420 j/kg-K).

Explanation

Energy stroed 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)s Deltatheta`
or `Deltatheta=((mg)^(2))/(2 rho A^(2)Ys) = 0.00457K`