On the horizontal surface of plank a block of mass 1 kg is placed `(mu=0.6)` which is stationary w.r.t. plank. Plank is moving with acceleration `5 m//s^(2)`, then the frictional force on the block will be

Options

A. 5N
B. 6N
C. 5.88N
D. 8N

Answer

To solve the problem of finding the frictional force on a block of mass 1 kg placed on a plank that is accelerating at 5 m/s², we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the block, \( m = 1 \, \text{kg} \)
- Coefficient of friction, \( \mu = 0.6 \)
- Acceleration of the plank, \( a = 5 \, \text{m/s}^2 \)

2. **Calculate the Normal Force (N):**
- The normal force acting on the block is equal to its weight since it is on a horizontal surface.
- \( N = mg \)
- Assuming \( g \approx 10 \, \text{m/s}^2 \):
\[ N = 1 \, \text{kg} \times 10 \, \text{m/s}^2 = 10 \, \text{N} \]

3. **Calculate the Maximum Frictional Force (F_max):**
- The maximum frictional force can be calculated using the formula:
\[ F_{\text{max}} = \mu N \]
- Substituting the values:
\[ F_{\text{max}} = 0.6 \times 10 \, \text{N} = 6 \, \text{N} \]

4. **Determine the Required Frictional Force (F):**
- Since the block is stationary with respect to the plank, it must accelerate with the same acceleration as the plank.
- The frictional force required to keep the block moving with the plank is given by:
\[ F = ma \]
- Substituting the values:
\[ F = 1 \, \text{kg} \times 5 \, \text{m/s}^2 = 5 \, \text{N} \]

5. **Compare the Required Frictional Force with Maximum Frictional Force:**
- We found that the required frictional force \( F = 5 \, \text{N} \) is less than the maximum frictional force \( F_{\text{max}} = 6 \, \text{N} \).
- This means the frictional force will be sufficient to prevent relative motion between the block and the plank.

6. **Conclusion:**
- The frictional force acting on the block is equal to the required frictional force:
\[ F_{\text{friction}} = 5 \, \text{N} \]

### Final Answer:
The frictional force on the block will be **5 N**.

---