A body of weight `w_1` is suspended from the ceiling of a room through as chain of weight `w_2`. The ceiling pulls the chain by a force

Options

A. `w_1`
B. `w_2`
C. `w_1+w_2`
D. `(w_1+w_2)/2`

Answer

To solve the problem of a body of weight \( w_1 \) suspended from the ceiling through a chain of weight \( w_2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Forces Acting on the System**:
- The body has a weight \( w_1 \) acting downwards.
- The chain has a weight \( w_2 \) also acting downwards.
- The ceiling exerts an upward force (normal force) on the chain.

2. **Draw a Free Body Diagram**:
- Draw the ceiling, the chain, and the body.
- Indicate the downward forces \( w_1 \) (weight of the body) and \( w_2 \) (weight of the chain).
- Indicate the upward force \( F \) (the force exerted by the ceiling on the chain).

3. **Write the Equation for Forces**:
- The total downward force acting on the system (body + chain) is the sum of their weights:
\[ F_{\text{down}} = w_1 + w_2 \]
- The upward force exerted by the ceiling is equal to the normal force \( N \):
\[ F_{\text{up}} = N \]

4. **Apply Newton's First Law**:
- Since the system is in equilibrium (not accelerating), the total upward force must equal the total downward force:
\[ N = w_1 + w_2 \]

5. **Conclusion**:
- Therefore, the force exerted by the ceiling on the chain is:
\[ F = w_1 + w_2 \]

### Final Answer:
The force exerted by the ceiling on the chain is \( F = w_1 + w_2 \).

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