Question

A brass rod at ${30}^{\circ }C$ is observed to be 100 cm long when measured by a steel scale which is correct at $0^{\circ }C$. $\alpha$ for steel is $12\times {10}^{-6}{/}^{\circ }C$ and $\alpha$ for brass is $19\times {10}^{-6}{/}^{\circ }C$. The correct length of brass rod at $0^{\circ }C$ is :

• A. 100.021 cm
• B. 99.979 cm
• C. 100.042 cm
• D. 99.958 cm

Answer 1

Answer: (B)

99.979 cm

As steel scale is correct at 0℃.

Actual length measured by steel scale at 30℃.

$L=100(1+t\times \alpha )L=100(1+12\times {10}^{-6}\times 30)L=100\left(1.00036\right)cmL=100.036cm$

Brass rod has length 100.036cm at 30℃ let's assume length L' is length at 0℃

so -

$100.036=L^{\prime }(1+t\times \alpha )100.036=L^{\prime }(1+19\times {10}^{-6}\times 30)100.036=L^{\prime }\left(1.00057\right)L^{\prime }=99.979cm$