Question

A U-tube contains mercury with one limb at 0${}^0$C and the other at 100${}^0$C. The heights of the mercury columns are 60cm at 0${}^0$C and 62 cm at 100${}^0$C. The coefficient of volume expansion of mercury (in ${}^0{C}^{-1}$) is

• A. 2/100
• B. 2/60
• C. 2/62
• D. $3.33\times {10}^{-4}$

Answer 1

The correct option is D $3.33\times {10}^{-4}$

Pressure at the bottom of the first limb=$h_1{\rho }_{0}g$

Pressure at the bottom of the second limb=$h_2{\rho }_{100}g=h_2\frac{{\rho }_0}{1+\gamma \Delta t}g$

For the system to be at equilibrium, pressure at the bottom of both the limbs is equal.

$⟹\gamma =\frac{h_2-h_1}{h_1\Delta t}=3.33\times {10}^{-4}$