A load of 31 . 4 kg is suspended from a wire of radius 10 - 3 m and density 9 × 10 3 kg m - 3 . Calculate the change in temperature of the wire if 75 % of the stored elastic potential energy is converted into heat. The Young's modulus and heat capacity of the material of the wire is 9 . 8 × 10 10 N m - 2 and 490 J kg - 1 K - 1 respectively.

Step-by-step solution

As work done in stretching an elastic body per unit volume is given by W V = 1 2 stress × strain = 1 2 stress 2 Y as Y = stress strain ........ (1) So W = 1 2 Mg A 2 V Y as stress = F A = Mg A Now according to given problem heat produced H = (75/100) W = 3 4 . W ⇒ ms Δ θ = 3 4 × 1 2 Mg π r 2 2 V Y as H = ms Δ θ using equation (1) or ρ V s Δ θ = 3 4 × 1 2 Mg π r 2 2 V Y as m = ρ V ∴ Δ θ = 3 8 3 1 . 4 × 9 . 8 π × 1 0 - 6 2 1 9 . 8 × 1 0 1 0 × 1 9 × 1 0 3 × 4 9 0 i.e., Δ θ = 1 1 2 0 K = 8 . 3 3 × 1 0 - 3 K