A massless string passes around a frictionless pulley whose axis is horizontal. A monkey holds on to one end of the string and a body with the same mass as the monkey is attached to the other end. The monkey starts climbing upwards with an acceleration a. Then the other body moves 

Options

A. downward with an acceleration a
B. downward with a uniformly velocity
C. upward with an acceleration a
D. upward with an acceleration a/2

Answer

To solve the problem, we need to analyze the forces acting on both the monkey and the body attached to the other end of the string.

### Step-by-Step Solution:

1. **Identify the masses and accelerations**:
- Let the mass of the monkey be \( m \).
- The mass of the body attached to the other end of the string is also \( m \).
- The monkey is climbing upwards with an acceleration \( a \).

2. **Draw Free Body Diagrams (FBD)**:
- For the monkey:
- The forces acting on the monkey are the tension \( T \) in the string acting upwards and the weight \( mg \) acting downwards.
- For the body:
- The forces acting on the body are the tension \( T \) acting upwards and the weight \( mg \) acting downwards.

3. **Apply Newton's Second Law for the monkey**:
- For the monkey climbing upwards:
\[ T - mg = ma \]
- Rearranging gives:
\[ T = mg + ma \quad \text{(Equation 1)} \]

4. **Apply Newton's Second Law for the body**:
- For the body moving downwards:
\[ mg - T = ma' \]
- Here, \( a' \) is the acceleration of the body. Rearranging gives:
\[ T = mg - ma' \quad \text{(Equation 2)} \]

5. **Set the two expressions for tension equal**:
- From Equation 1 and Equation 2:
\[ mg + ma = mg - ma' \]

6. **Solve for \( a' \)**:
- Rearranging the equation gives:
\[ ma' = -ma \implies a' = -a \]
- This indicates that the body moves downwards with the same magnitude of acceleration as the monkey climbs upwards.

7. **Conclusion**:
- Since the monkey climbs upwards with an acceleration \( a \), the body moves downwards with an acceleration \( a \).

### Final Answer:
The body moves downwards with an acceleration \( a \).