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Two vertical glass tubes filled with a liquid are connected by a capillary tube as shown in the figure. The tube on the left is put in an ice bath at $0^o C$ while the tube on the right is kept at $30^o C$ in a water bath. The difference in the levels of the liquid in the two tubes is $4 \,\,cm$ while the height of the liquid column at $0^o C$ is $120\,\,cm$. The coefficient of volume expansion of liquid is (Ignore expansion of glass tube)
$22 × 10^{-4}/^o C$
$1.1 × 10^{-4}/^o C$
$11 × 10^{-4}/^o C$
$2.2 × 10^{-4}/^o C$
Solution
Pressure at the bottom of both the tubes must be same.
$h_{1} \rho_{1} g=h_{2} \rho_{2} g$
$\Longrightarrow h_{1} \rho_{1}=h_{2}\left(\frac{\rho_{1}}{1+\gamma t}\right)$
$\Longrightarrow a+\gamma t=\frac{124}{120}$
$\Longrightarrow \gamma \approx 11.11 \times 10^{-4} /^{\circ} \mathrm{C}$
