Question

A brass rod is $1$m long at $0^{0}C$, if coefficient of expansion is $1.9\times {10}^{-5}$ $K^{-1}$ then length at ${30}^{0}C$ is

• A. 1.0057
• B. 15.7
• C. 1.00057
• D. 1.57

Answer 1

Answer: (C)

1.00057

The initial length at $0^{0}C$ is $l_1=1$m

Let the length at ${30}^{0}C$ be $l_2$

The coefficient of expansion is $\alpha =1.9\times {10}^{-5}$

So we have $\frac{l_2-l_1}{l_1}=\alpha \times △t$

$\Rightarrow l_2=l_1+l_1\times \alpha \times △t$

$\Rightarrow l_2=1(1+1.9\times {10}^{-5}(30-0\left)\right)$

$\Rightarrow l_2=1+0.00057=1.00057$

Therefore the correct option is $C$