A cricket baal of mass 0.25 kg with speed 10 m/s collides with a bat and returns with same speed with in `0.01` s. The force acted on bat is

Options

A. 25 N
B. 50 N
C. 250 N
D. 500 N

Answer

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

### Step 1: Identify the given values
- Mass of the cricket ball (m) = 0.25 kg
- Initial speed of the ball (u) = -10 m/s (taking the direction towards the bat as negative)
- Final speed of the ball (v) = +10 m/s (after collision, the ball returns in the opposite direction)
- Time of collision (t) = 0.01 s

### Step 2: Calculate the change in velocity (Δv)
The change in velocity can be calculated using the formula:
\[ \Delta v = v - u \]
Substituting the values:
\[ \Delta v = 10 - (-10) = 10 + 10 = 20 \, \text{m/s} \]

### Step 3: Use the formula for force
The force (F) can be calculated using Newton's second law, which states:
\[ F = m \cdot \frac{\Delta v}{t} \]
Substituting the known values:
\[ F = 0.25 \cdot \frac{20}{0.01} \]

### Step 4: Simplify the expression
Calculating the right side:
\[ F = 0.25 \cdot 2000 = 500 \, \text{N} \]

### Conclusion
The force exerted on the bat by the cricket ball is **500 N**.