Question

A barometer having a metallic scale reads a height $H_0$ at temperature ${\theta }^{\circ }C$. The true scale is calibrated at $0^{\circ }C$. If $\alpha$ is the coefficient of linear expansion of the metal and $\gamma$ the coefficient of cubical expansion of mercury, the correct pressure $H_{corr}$ is:

• A. $H_0\frac{(1+\gamma \theta )}{(1+\alpha \theta )}$
• B. $H_0\frac{(1-3\alpha \theta )}{(1+\gamma \theta )}$
• C. $H_0\frac{(1+\alpha \theta )}{(1+\gamma \theta )}$
• D. $H_0\frac{(1-\gamma \theta )}{(1-3\alpha \theta )}$

Answer 1

The correct option is C $H_0\frac{(1+\alpha \theta )}{(1+\gamma \theta )}$

$Lengthofscaleuptoreadingat{\theta }^{0}C=H_o(1+\alpha \theta )$

$Lengthofmercuryat{\theta }^{o}C=H_{corr}(1+\gamma \theta )$

$\therefore H_o(1+\alpha \theta )=H_{corr}(1+\gamma \theta )$

$H_{corr}=H_o\frac{(1+\alpha \theta )}{(1+\gamma \theta )}$

This is the required solution.