A block of mass 10 kg is kept over a rough surface and a force F=4t is applied on it. At what value of t the block will start moving :-

Options

A. `gt10` s
B. `lt8` s
C. `=9` s
D. None

Answer

To solve the problem, we need to determine the time \( t \) at which the block will start moving when a force \( F = 4t \) is applied to it. The block is on a rough surface, which means that friction will play a role in determining when the block starts to move.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the block, \( m = 10 \, \text{kg} \)
- Coefficient of friction, \( \mu = 0.4 \)
- Force applied, \( F = 4t \)

2. **Calculate the Weight of the Block:**
The weight \( W \) of the block can be calculated using the formula:
\[ W = mg \]
where \( g \) (acceleration due to gravity) is approximately \( 10 \, \text{m/s}^2 \).
\[ W = 10 \, \text{kg} \times 10 \, \text{m/s}^2 = 100 \, \text{N} \]

3. **Calculate the Maximum Static Friction Force:**
The maximum static friction force \( f_{\text{max}} \) can be calculated using the formula:
\[ f_{\text{max}} = \mu \times N \]
where \( N \) is the normal force, which is equal to the weight of the block in this case.
\[ f_{\text{max}} = 0.4 \times 100 \, \text{N} = 40 \, \text{N} \]

4. **Set Up the Equation for Motion:**
The block will start moving when the applied force \( F \) exceeds the maximum static friction force \( f_{\text{max}} \):
\[ F > f_{\text{max}} \]
Substituting the expressions we have:
\[ 4t > 40 \]

5. **Solve for \( t \):**
To find the value of \( t \) when the block starts moving, we can rearrange the inequality:
\[ t > \frac{40}{4} \]
\[ t > 10 \]

6. **Conclusion:**
The block will start moving when \( t \) is greater than 10 seconds.

### Final Answer:
The block will start moving at \( t > 10 \, \text{seconds} \).