Two 20g flatworms climb over a veruy thin walll, 10 cm high.One of the wrom is 20 cm long, the other is wider and only 10 cm long. Which of the following statement is correct reagarding them?

Options

A. 20 cm wormk 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 donw by both the worms is 4:5

Answer

To solve the problem regarding the two flatworms climbing over a wall, we need to analyze the situation step by step.

### Step-by-Step Solution:

1. **Identify the Parameters**:
- Both flatworms have a mass of 20 g.
- The height of the wall is 10 cm.
- One worm is 20 cm long, and the other is 10 cm long.

2. **Understand the Concept of Center of Gravity**:
- The center of gravity (CG) is the point where the weight of the body can be considered to act.
- For uniform objects, the CG is located at the midpoint of the object.

3. **Determine the Center of Gravity for Each Worm**:
- For the 20 cm worm:
- The CG is at the midpoint, which is 10 cm from one end.
- When climbing over a 10 cm wall, the CG will be at a height of 10 cm (the height of the wall).
- For the 10 cm worm:
- The CG is at the midpoint, which is 5 cm from one end.
- When climbing over the wall, the CG will be at a height of 5 cm (the height of the wall).

4. **Calculate the Work Done Against Gravity**:
- The work done against gravity is given by the formula:
\[ \text{Work} = mgh \]
- Where:
- \( m \) = mass of the worm = 20 g = 0.02 kg (conversion to kg)
- \( g \) = acceleration due to gravity = 9.8 m/s²
- \( h \) = height of the center of gravity above the ground.

5. **Calculate Work for Each Worm**:
- For the 20 cm worm:
\[ h = 10 \text{ cm} = 0.1 \text{ m} \]
\[ \text{Work}_{20cm} = 0.02 \times 9.8 \times 0.1 = 0.0196 \text{ J} \]
- For the 10 cm worm:
\[ h = 5 \text{ cm} = 0.05 \text{ m} \]
\[ \text{Work}_{10cm} = 0.02 \times 9.8 \times 0.05 = 0.0098 \text{ J} \]

6. **Comparison of Work Done**:
- The work done by the 20 cm worm is greater than that done by the 10 cm worm.
- Therefore, the correct statement is that the 20 cm worm has done more work against gravity.

### Conclusion:
The correct statement regarding the two flatworms is that the 20 cm worm has done more work against gravity than the 10 cm worm.