Question

The volume of an air bubble is doubled as it rises from the bottom of a lake to its surface. The atmospheric pressure is 75 cm of mercury and the ratio of the density of mercury to that of lake water is 40/3. The depth of the lake is:

• A. 15 m
• B. 10 m
• C. 20 m
• D. 25 m

Hint:

Boyle’s law helps relate the pressure and volume of a gas at constant temperature. The pressure and volume are inversely proportional.

Answer 1

The Correct Option is C

We can use Boyle’s Law for the air bubble: \[ P_1 V_1 = P_2 V_2 \] Since the volume is doubled, \( V_2 = 2V_1 \), and the pressures at the surface and at the depth are given by: \[ P_2 = P_{\text{atm}} + \rho_{\text{water}} g h \] The atmospheric pressure \( P_{\text{atm}} = 75 \, \text{cm of mercury} = 0.75 \, \text{m of mercury} \), and the depth \( h \) is related to the change in volume. Using the given ratio of densities, we calculate the depth to be \( 20 \, \text{m} \).