Question

A wooden block is floating in a water tank. The block is pressed to the bottom during the process a work is done. Which of the following statements are incorrect?
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A. Work done is equal to work done against upthrust by the water.
B. Work done is equal to work done against upthrust plus loss of gravitational potential energy of the block.
C. Work done is equal to work done against upthrust minus loss of gravitational potential energy of the block.
D. Work done is equal to loss of gravitational potential energy of the block.

Answer 1

Any block floats in water due to the net effect of downward gravitational attraction force and upward upthrust force.
- If we have to press the block to the bottom, we have to apply a force along downward direction against the upthrust.
- And when the block is pressed to the bottom then it will move towards the ground. So, its potential energy will also decrease.

Complete step by step answer:
When any block floats in water then two forces act on it.

One is downward gravitational force ($mg$) and another one is upward thrust force ($\mathop F\nolimits_t$).

Now, as we can easily understand from the figure that these two forces are acting opposite to each other now if these two forces have equal magnitude.
Then, net resultant force along the vertical on the floating object will become zero.

So, now if we try to press the object to the bottom, we have to apply a force against the upthrust force and along the gravitational force.

Now according to the definition of work,

If any force causes a displacement along the direction of the force, then work done by the force will be positive.

And if any force causes a displacement along the opposite direction to the force, then the work done by the force is negative.

So, here we have to do negative work against the upthrust force and positive work along the gravitational force, I.e., weight of the object.

Now, if the object is pressed to the bottom, its height from the ground is decreased. And the height decreases by $h$ then its potential energy decreases by $mgh$ ($m$ is the mass of the object and $g$ is the gravitational acceleration of the object).
A. is an incorrect option. As, there should be change in potential energy also.
B. is an incorrect option. As gravitational potential energy is decreasing so we have to subtract that.
C. Is the correct option as it clearly states the answer.
D. Is an incorrect answer as there should be the work done against the upthrust also.

Here we have to choose the wrong or incorrect statements.

So, (A), (B) and (C) are the incorrect statements.

Note:
If any object moves along the direction of the applied force, then the work done by the applied force is positive.
- If any object moves opposite to the direction of the applied force, then the work done by the applied force is negative.
- Here we have considered the work energy theorem. Work done against gravitational force is the change in gravitational potential energy.
- To solve this kind of problem we should draw the force diagram of that object then we can easily solve it.