Concepts Of Physics MCQ Edition [Volume 1]PhysicsFluid Mechanics
A piece of wood is floating in water kept inside a bottle. The bottle is connected to an air pump. Neglecting the compressibility of water, when additional air is pushed into the bottle using the pump, the piece of wood will float with
Options
- Athe same part in the water
- Ba larger part in the water
- Cit will sink
- Da lesser part in the water
Correct answer
D. a lesser part in the water
Step-by-step solution
Let V be the total volume of the wood, V_ in be the volume submerged in water, _w be the density of water, _a be the density of air, and be the density of wood. The weight of the wood is balanced by the buoyant force due to water and the buoyant force due to air. V g = V_ in _w g + (V - V_ in ) _a g V_ in ( _w - _a) = V ( - _a) V_ in = V - _a _w - _a When more air is pushed into the bottle, the pressure increases, which increases the density of air _a . Differentiating V_ in with respect to _a : dV_ in d _a = V -(