Question

An iron rod and another of brass, both at ${27}^{\circ }C$ differ in length by ${10}^{-3}m$. The coefficient of linear expansion for iron is $1.1\times {10}^{-5}$${/}^{\circ }C$ and for brass is $1.9\times 10-5$${/}^{\circ }C$. The temperature at which both these rods will have the same length is

• A. 0°C
• B. 152°C
• C. 175°C
• D. Data is insufficient

Answer 1

The correct option is A

0°C

The given data is normally insufficient to determine the result. Either the length of one of the rods at $0^{\circ }C$ must be known or one has to assume that both the rods had the same length at $0^{\circ }C$ which is not possible if they have the same length again at another temperature. Suppose the two rods had the same length $L$ at $0^{\circ }C$. Then by the given problem,

$L[1+1.9\times {10}^{-5}\times 27]-L[1+1.1\times {10}^{-5}\times 27]$ = ${10}^{-3}$

$L\times 0.8\times 27\times {10}^{-5}$ = ${10}^{-3}$

Or $L$ = $\frac{{10}^{-3}}{0.8\times 27\times {10}^{-5}}m$ = $4.63m$

Hence $0^{\circ }C$ is a possible choice and the rods had equal length of $4.63m$ at $0^{\circ }C$