Question

Brass scale of a Barometer gives correct reading at $0^{\circ }C.$ coefficient of linear expansion of brass is $18\times {10}^{-6}{/}^{-6}C.$ If the barometer reads $76cm$ at ${20}^{\circ }C,$ the correct reading is $({\gamma }_{Hg}=18\times {10}^{-5}/0C)$

• A. $76.426cm$
• B. $75.7cm$
• C. $76.2736cm$
• D. $76.264cm$

Answer 1

The correct option is C $76.2736cm$

$L_0=75$cm

$\begin{array}{c}a=18\times {10}^{-6}{/}^{0}C\\ \Delta T=20-0={27}^{0}C\end{array}$

We know that the formula for the coefficient of linear expansion

$\begin{array}{c}L=L_0\left(1+\alpha \Delta T\right)\\ L=76\left(1+18\times {10}^{-6}\times 20\right)\\ =76\left(1+0.00036\right)\\ =76\times 1.00036\\ =76.2736\end{array}$

Atmospheric pressure at ${20}^{0}C$ is $76.2736$ cm of brass.