A body is just floating on the surface of a liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. What will happen to the body

The correct option is It will sink.

To understand why the body will sink, let us analyze the physical principles acting on it step-by-step:

1. Initial Equilibrium State:
Initially, the body is just floating at the surface, meaning it is almost fully submerged, and its density (${\rho }_b$) is equal to the density of the liquid (${\rho }_l$). At this point, the upward buoyant force is equal to the downward gravitational force (weight of the body).

2. Increase in Hydrostatic Pressure:
When the body is pushed slightly down, it is submerged deeper into the liquid. The hydrostatic pressure ($P$) exerted by the liquid on the body increases with depth ($h$) according to the formula:

$P=P_0+{\rho }_{l}gh$

where $P_0$ is the atmospheric pressure and $g$ is the acceleration due to gravity.

3. Compression and Density Increase:
This increased hydrostatic pressure compresses the body, causing a slight decrease in its volume ($V$). Since the mass ($m$) of the body remains constant, a decrease in volume results in an increase in the density of the body (${\rho }_b$) because:

${\rho }_b=\frac{m}{V}$

As a result of this compression, the density of the body becomes greater than the density of the liquid (${\rho }_b>{\rho }_l$).

4. Conclusion:
Since the density of the body is now greater than the density of the liquid, the downward force of gravity (weight) exceeds the upward buoyant force. Therefore, the net force acts downwards, and the body will sink.