Question

A glass rod when measured with a zinc scale, both at ${30}^{\circ }C$ appears to be of length $100cm$. If the scale shows correct reading at $0^{\circ }$.(${\alpha }_z=26\times {10}^{-6}/{}^{0}C$ ${\alpha }_g=8\times {10}^{-6}/{}^{0}C$)

• A. $100.078cm$
• B. $100.054cm$
• C. $100.024cm$
• D. $100.027cm$

Answer 1

The correct option is B $100.054cm$

Given,

$l_0=100cm$

${\alpha }_z=26\times {10}^{-6}{/}^{0}C$

${\alpha }_g=8\times {10}^{-6}{/}^{0}C$

Length at ${30}^{0}C$ is

$l=l_0(1+{\alpha }_z\Delta T)$

$l=100(1+26\times {10}^{-6}\times 30)$

$l=100.078cm$

The true length at $0^{0}C$

$l_t=\frac{l_0(1+{\alpha }_z\Delta T)}{1+{\alpha }_g\Delta T}$

$l_t=\frac{100.078cm}{1+8\times {10}^{-6}\times 30}$

$l_t=100.054cm$

The correct option is B.