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On loading a metal wire of cross section $10^{- 6} m^{2}$ and length 2m by a mass of 210 kg it extends by 16mm and suddenly broke from the point of support. If density of that metal is $8000 k g m^{- 3}$ and its specific heat is $420 J k g^{- 1} K^{- 1}$ the rise in temperature of wire is $(g = 10 m s^{- 2})$

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${2.5}^{0} C$

$10^{0} C$

$5^{0} C$

$6^{0} C$

answer is A.

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Detailed Solution

$Work done by gravity in stretching the wire$

$W = U = \frac{1}{2} \times Stress \times Strain \times Volume$

$When wire breaks from support, work done on it is converted to heat$

$Q = ms Δ T$

$W = \frac{1}{2} \times \frac{m g}{A} \times \frac{Δ ℓ}{ℓ} \times \frac{m}{ρ}$

$Δ T = \frac{mg Δ ℓ}{2 A ℓ ρ S}$

$Δ T = \frac{210 \times 9.8 \times (16 \times 10^{- 3})}{2 \times 10^{- 6} \times 2 \times 8000 \times 420} = 2.45 K$

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