Question

A piece of wood is floating in water kept in a bottle. The bottle is connected to an air pump. Neglect the compressibility of water. When more air is pushed into the bottle from the pump, the piece of wood will float with

• A. larger part in the water
• B. lesser part in the water
• C. same part in the water
• D. None of the above, rather the piece of wood will sink to the bottom.

Answer 1

The correct option is C same part in the water

For any body submerged in water, buoyant force (equal to weight of the water displaced) balances the weight of the body.

If the submerged height of wood is $h$,
$B={\rho }_{w}gh=mg$ where $mg$ is the weight of the piece of wood.
Therefore the submerged height doesn't depend on the atmospheric pressure (pressure of air in bottle in this case). So the submerged height doesn't change when more air is pushed into the bottle.
Option (c) is correct.