Gravel is dropped on a conveyor belt at the rate of 2 kg/s. The extra force required to keep the belt moving at `3 ms^(-1)` is

Options

A. 1 N
B. 3 N
C. 4 N
D. 6 N

Answer

To solve the problem, we need to determine the extra force required to keep the conveyor belt moving at a constant velocity of 3 m/s when gravel is being dropped onto it at a rate of 2 kg/s.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Rate of mass flow (dm/dt) = 2 kg/s
- Velocity of the conveyor belt (v) = 3 m/s

2. **Understand the Concept:**
- When gravel is dropped onto the conveyor belt, it adds mass to the system. To maintain the constant velocity of the belt, an additional force is required to account for the change in momentum due to the incoming gravel.

3. **Apply the Formula for Force:**
- The extra force (F) required can be calculated using the formula:
\[ F = v \cdot \frac{dm}{dt} \]
- Here, \( \frac{dm}{dt} \) is the rate of change of mass (2 kg/s) and v is the velocity of the conveyor belt (3 m/s).

4. **Substitute the Values:**
- Substitute the values into the equation:
\[ F = 3 \, \text{m/s} \cdot 2 \, \text{kg/s} \]

5. **Calculate the Force:**
- Perform the multiplication:
\[ F = 6 \, \text{N} \]

6. **Conclusion:**
- The extra force required to keep the conveyor belt moving at 3 m/s while gravel is dropped onto it at a rate of 2 kg/s is 6 Newtons.

### Final Answer:
The extra force required is **6 N**.

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