Question

A uniform solid cylinder of density $0.8\text{g}/{\text{cm}}^3$ floats in equilibrium in a combination of two non-mixing liquids A and B with its axis vertical. The densities of the liquids A and B are $0.7\text{g}/{\text{cm}}^3$ and $1.2\text{g}/{\text{cm}}^3$ respectively. The height of liquid A is $h_A=1.2\text{cm}$. The length of the part of the cylinder immersed in liquid B is $h_B=0.8\text{cm}$.

• A. Total force exerted by liquid A on the cylinder will be non-zero
• B. Total force exerted by liquid A on the cylinder will be zero
• C. If the cylinder was depressed so that its top surface comes just below upper surface of liquid A and then it is released then acceleration will be g/3
• D. The length of the part of the cylinder in air will be 0.25 cm

Answer 1

The correct option is D

The length of the part of the cylinder in air will be 0.25 cm

For equilibrium

0.8 (h + 2)g = (0.7)(1.2)g + (1.2)(0.8)g

h = 0.25 cm