Question

Two $20$g flatworms climb over a very thin wall, $10$cm high. One of the worm is $20$cm long, the other is wider and only $10$cm long. Which of the following statement is correct regarding them?

• A. $20$cm worm has done more work against gravity
• B. $10$cm worm has done more work against gravity
• C. Both worms have done equal work against gravity
• D. Ratio of work done by both the worms is $4:5$

Answer 1

Answer: (B)

$10$cm worm has done more work against gravity

The work done against gravity can be calculated from the increases in height of the centre of mass. The centre of mass of a worm folded in two is located at the middle of either half, i.e., at a point one-quarter of the worm's total length from one end, as given in the figure. Thus, the centre of mass of the narrow flat worm travels $5$cm up the wall; while that of the board one moves $7.5$cm. Hence, work done by $10$cm worm is more against gravity. Also, the ratio of the work done is $2:3$.