Question

What should be the temperature rise of a brass rod , so as to increase its length by $1\%$? (Given: coefficient of linear expansion of glass rod, $\alpha =2\times {10}^{-5}{}^{\circ }{C}^{-1})$.

• A. 1000 ⁰C
• B. 500 ⁰C
• C. 200 ⁰C
• D. 100 ⁰C

Answer 1

The correct option is B

500 ⁰C

Let, coefficient of linear expansion $=\alpha =2\times {10}^{-5}{}^{\circ }{C}^{-1}$
Initial length $=l_0$
Final length $=l$
Change in temperature $=t$
Since, the length has to be increased by 1%, we have
change in length $=l-l_0=0.01l_0$
We know, $\alpha \times l_0\times t=l-l_0$
or, $\alpha \times l_0\times t=0.01l_0$
$\Rightarrow 2\times {10}^{-5}\times t=0.01$
$\Rightarrow t=\frac{0.01}{2}\times {10}^5={500}^{\circ }C$