Question

A wooden block is floating partially immersed in a water tank. If the block is pressed slowly to bottom of the tank by a force $F$, work done by this $F$ is equal to:

• A. Work done against upthrust exerted by the water
• B. Work done against upthrust plus loss of gravitational potential energy of the block.
• C. Work done against upthrust minus loss of gravitational potential energy of the block.
• D. All of the above.

Answer 1

The correct option is C Work done against upthrust minus loss of gravitational potential energy of the block.

Initially the wooden block floats partially immersed in water. So, upthrust exerted by water is exactly equal to weight of the block.

But when it is pressed down the more water is displaced. Hence, upthrust exerted by water increases. The force required to press down the block is equal to $F=\text{upthrust}-mg$.
Hence, work done by the force $F$ will be equal to work against $\text{upthrust}-mg$.
It means that work done by the external force is equal to (work done against upthrust minus loss of gravitational potential energy of the block).
Hence, (c) alone is the correct answer.