A ball of mass 150 g starts moving at 20 m/s and its hits by a force which acts on it for 0.1 sec. Then the impulsive force is:

Options

A. 75 N
B. 300 N
C. 3 N
D. 30 N

Explanation

To find the impulsive force acting on the ball, we can use the impulse-momentum theorem, which states that the impulse (force multiplied by the time duration) is equal to the change in momentum of the object.

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass of the ball, \( m = 150 \, \text{g} = 0.150 \, \text{kg} \) (since 1 g = 0.001 kg)
- Initial velocity, \( u = 20 \, \text{m/s} \)
- Time duration of the force, \( \Delta t = 0.1 \, \text{s} \)

2. **Calculate the change in momentum:**
- The change in momentum (\( \Delta p \)) can be expressed as:
\[ \Delta p = m \Delta v \]
- However, we need to find the change in velocity (\( \Delta v \)). Since the final velocity is not given, we will assume that the force acts to stop the ball (final velocity \( v = 0 \, \text{m/s} \)).
- Therefore, the change in velocity is:
\[ \Delta v = v - u = 0 - 20 = -20 \, \text{m/s} \]

3. **Calculate the change in momentum:**
- Now substituting the values into the change in momentum formula:
\[ \Delta p = m \Delta v = 0.150 \, \text{kg} \times (-20 \, \text{m/s}) = -3 \, \text{kg m/s} \]

4. **Use the impulse-momentum theorem to find the impulsive force:**
- According to the impulse-momentum theorem:
\[ F \Delta t = \Delta p \]
- Rearranging for \( F \):
\[ F = \frac{\Delta p}{\Delta t} \]
- Substituting the values:
\[ F = \frac{-3 \, \text{kg m/s}}{0.1 \, \text{s}} = -30 \, \text{N} \]

5. **Conclusion:**
- The impulsive force experienced by the ball is \( 30 \, \text{N} \) (the negative sign indicates the direction of the force is opposite to the motion of the ball).

### Final Answer:
The impulsive force is \( 30 \, \text{N} \).