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Question

A $$5$$m long cylindrical steel wire with radius $$2\times 10^{-3}$$m is suspended vertically from a rigid support and carries a bob of mass $$100$$ kg at the other end. If the bob gets snapped, calculate the change in temperature of the wire ignoring radiation losses.
(For the steel wire: Youngs Modulus $$=2.1\times 10^{11}Pa$$; Density $$=7860 kg/m^3$$; Specific heat $$=420$$ J/kg-K).


Solution

$$ms\Delta \theta =\Delta U=(1/2)\times$$ stress $$\times$$strain $$\times$$ volume
$$(A.L.\rho)s\Delta \theta =(Mg)^2L/(2YA)$$ neglecting the strain due to the weight of wire
$$\Delta \theta =(Mg)^2/(2\rho AYs)=0.00457$$ K.

Physics

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