A 150 g ball, moving horizontally at 20m/s was hit straight back to bowler at 12m/s. If contact with bat lasted for 0.04 sec, then average force exerted by the bat on the ball is:-

Options

A. 100N
B. 120N
C. 150N
D. 200N

Explanation

To solve the problem of finding the average force exerted by the bat on the ball, we can follow these steps:

### Step 1: Identify the given values
- Mass of the ball (m) = 150 g = 0.150 kg (since 1 g = 0.001 kg)
- Initial velocity of the ball (u) = 20 m/s (moving towards the bowler)
- Final velocity of the ball (v) = -12 m/s (moving back towards the bowler, hence the negative sign)
- Time of contact (Δt) = 0.04 s

### Step 2: Calculate the initial momentum (P_initial)
The initial momentum (P_initial) can be calculated using the formula:
\[ P_{\text{initial}} = m \cdot u \]
Substituting the values:
\[ P_{\text{initial}} = 0.150 \, \text{kg} \cdot 20 \, \text{m/s} = 3.0 \, \text{kg m/s} \]

### Step 3: Calculate the final momentum (P_final)
The final momentum (P_final) can be calculated using the formula:
\[ P_{\text{final}} = m \cdot v \]
Substituting the values:
\[ P_{\text{final}} = 0.150 \, \text{kg} \cdot (-12 \, \text{m/s}) = -1.8 \, \text{kg m/s} \]

### Step 4: Calculate the change in momentum (ΔP)
The change in momentum (ΔP) is given by:
\[ \Delta P = P_{\text{final}} - P_{\text{initial}} \]
Substituting the values:
\[ \Delta P = -1.8 \, \text{kg m/s} - 3.0 \, \text{kg m/s} = -4.8 \, \text{kg m/s} \]

### Step 5: Calculate the average force (F)
The average force can be calculated using the formula:
\[ F = \frac{\Delta P}{\Delta t} \]
Substituting the values:
\[ F = \frac{-4.8 \, \text{kg m/s}}{0.04 \, \text{s}} = -120 \, \text{N} \]

### Step 6: Interpret the result
Since we are interested in the magnitude of the force, we can say:
\[ |F| = 120 \, \text{N} \]

Thus, the average force exerted by the bat on the ball is **120 N** in the direction opposite to the ball's initial motion.

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