Question

The length of a metal rod at $0^{\circ }$C is 0)5 m. When it is heated, its length increases by 2)7 mm. The final temperature of rod is (coeff. of linear expansion of metal $=$ 90$\times {10}^{-6}{/}^{\circ }$C )

• A. ${20}^{\circ }C$
• B. ${30}^{\circ }C$
• C. ${40}^{\circ }C$
• D. ${60}^{\circ }C$

Answer 1

Answer: (D)

${60}^{\circ }C$

In this case, $l=$ 0.5 m
$dl=2.7$ mm $=$ 27X ${10}^{-4}$ m
$\alpha =$90 X${10}^{-6}$
$dt=dl/(l$X $\alpha$) =(3/5) $\times {10}^2$
Since the initial temperature is 0 degree, the final temperature will be 60 degree centigrade.