Question

Two vertical glass tubes fitted 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 $0^{\circ }C$ while the tube on the right is kept in a water bath at ${30}^{\circ }C$. The difference in the levels of the liquid in the two tubes is $4cm$ while the height of the liquid column at $0^{\circ }C$ is $120cm$. The coefficient of volume expansion of liquid is (Ignore expansion of glass tube)

• A. $22\times {10}^{-4}{/}^{\circ }C$
• B. $1.1\times {10}^{-4}{/}^{\circ }C$
• C. $11\times {10}^{-4}{/}^{\circ }C$
• D. $2.2\times {10}^{-4}{/}^{\circ }C$

Answer 1

The correct option is C $11\times {10}^{-4}{/}^{\circ }C$

Pressure at the bottom of both the tubes must be same.

$h_1{\rho }_{1}g=h_2{\rho }_{2}g$

$⟹h_1{\rho }_1=h_2\left(\frac{{\rho }_1}{1+\gamma t}\right)$

$⟹a+\gamma t=\frac{124}{120}$
$⟹\gamma \approx 11.11\times {10}^{-4}{/}^{\circ }C$