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On loading a metal wire of cross section 10^–6 m² 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 kgm^–3 and its specific heat is 420 Jkg^–1 K^–1 the rise in temperature (in ⁰c) of wire is $_____$ × 10^–1 (g = 10 ms^-2).

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Detailed Solution

Given,

$Energy = \frac{1}{2} \times stress \times volume = \frac{1}{2} \times \frac{F}{A} \times \frac{∆ l}{l} \times \frac{m}{p}$

$= \frac{1}{2} \times \frac{2100}{10 - 6} \times \frac{16}{1000 \times 2} \times \frac{210}{8000}$

$specific heat \times temperature \times mass = energy$

$420 \times t \times 210 = \frac{1}{2} \times \frac{2100}{10 - 6} \times \frac{16}{1000 \times 2} \times \frac{210}{8000}$

$\Rightarrow t = \frac{1}{2 \times 420} \times \frac{2100}{10 - 6} \times \frac{16}{1000 \times 2} \times \frac{1}{8000} = 25 \times 10^{- 1}$

Hence the correct answer is 25.

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