Question

Two 20kg flatworms climb over a very thin wall, 10cm high. One of the worms is 20cm long, the other is wider and only 10cm long. Which of the following statement is correct regarding them
A) $20cm$ worm has done more work against gravity
B) $10cm$ worm has done more work than gravity
C) Both worms have done equal work against gravity
D) The ratio of work done by both the worms is $4:5$.

Answer 1

Recall the concept of gravitational potential energy, as per which there is energy stored in an object if it is at some height above the Earth’s surface. Also, the concept of work done against gravity will be used here since earthworms are moving upwards.

Complete step by step solution:
Step I:
The earthworms are climbing over a very thin wall. Therefore, when an object or a body having mass is made to move at some height, then work is to be done against the force of gravity. This work is done so that the body can balance the downward effect of gravity and can move. The force applied by earthworms is the external force.
Step II:
The work done against gravity is calculated as the height increases from the center of mass. The center of mass is located in the middle of the worm if the worm is folded in half.
Step III:
As per the given condition, the center of mass of the narrow flatworm will be $5cm$ above the wall, but for the wider worm, it will be $7.5cm$.

Hence work done by the worm that is 10 cm long will be more. Therefore Option B is the right answer.

Note:
If an object moves at some height above the earth, then some energy is stored in the form of gravitational potential energy. This energy is later released as kinetic energy when the object starts moving. In such cases, the object moves in the opposite direction to which the force is applied.