A cricket ball of mass 150 kg is moving with a velocity of `12 m//s` and is hit by a bat so that ball is turned back with a velocity of `20 m//s` . The force of the blow acts for 0.01 s on the ball . Find the average force exerted by the bat on the ball.

Options

A. the change in momentum of the ball is 48 kg-m/s.
B. the average force exerted by the bat on the ball is 480 N.
C. the change in momentum of the ball is 1.2 kg-m/s
D. the average force exerted by the bat on the ball is 120 N.

Answer

To solve the problem, we need to find the average force exerted by the bat on the cricket ball. We will use the concept of momentum and the formula for average force.

### Step-by-step Solution:

1. **Identify the Given Data:**
- Mass of the cricket ball, \( m = 150 \, \text{grams} = 0.15 \, \text{kg} \) (since 1 kg = 1000 grams)
- Initial velocity of the ball, \( u = 12 \, \text{m/s} \)
- Final velocity of the ball after being hit, \( v = -20 \, \text{m/s} \) (the negative sign indicates that the ball is moving in the opposite direction)
- Time duration of the force acting on the ball, \( \Delta t = 0.01 \, \text{s} \)

2. **Calculate the Change in Momentum:**
- The change in momentum (\( \Delta p \)) is given by the formula:
\[ \Delta p = m(v - u) \]
- Substituting the values:
\[ \Delta p = 0.15 \, \text{kg} \times (-20 \, \text{m/s} - 12 \, \text{m/s}) = 0.15 \, \text{kg} \times (-32 \, \text{m/s}) \]
- This simplifies to:
\[ \Delta p = 0.15 \times -32 = -4.8 \, \text{kg m/s} \]

3. **Calculate the Average Force:**
- The average force (\( F \)) can be calculated using the formula:
\[ F = \frac{\Delta p}{\Delta t} \]
- Substituting the values:
\[ F = \frac{-4.8 \, \text{kg m/s}}{0.01 \, \text{s}} = -480 \, \text{N} \]
- The negative sign indicates the direction of the force is opposite to the initial motion of the ball. Therefore, the magnitude of the average force is:
\[ |F| = 480 \, \text{N} \]

4. **Conclusion:**
- The average force exerted by the bat on the ball is \( 480 \, \text{N} \).