A ball of mass 0.2 kg moves with a velocity of `20m//sec` and it stops in `0.1` sec , then the force on the ball is

Options

A. 40 N
B. 20 N
C. 4 N
D. 2 N

Answer

To solve the problem of finding the force on a ball of mass 0.2 kg that moves with a velocity of 20 m/s and stops in 0.1 seconds, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the ball (m) = 0.2 kg
- Initial velocity (u) = 20 m/s
- Final velocity (v) = 0 m/s (since the ball stops)
- Time taken (t) = 0.1 seconds

2. **Calculate the Change in Momentum (Δp):**
- The change in momentum (Δp) can be calculated using the formula:
\[ \Delta p = m(v - u) \]
- Substituting the values:
\[ \Delta p = 0.2 \, \text{kg} \times (0 \, \text{m/s} - 20 \, \text{m/s}) \]
- This simplifies to:
\[ \Delta p = 0.2 \, \text{kg} \times (-20 \, \text{m/s}) = -4 \, \text{kg m/s} \]

3. **Calculate the Force (F):**
- According to Newton's second law, force is the rate of change of momentum:
\[ F = \frac{\Delta p}{t} \]
- Substituting the values:
\[ F = \frac{-4 \, \text{kg m/s}}{0.1 \, \text{s}} = -40 \, \text{N} \]

4. **Determine the Magnitude of the Force:**
- The magnitude of the force is:
\[ |F| = 40 \, \text{N} \]
- The negative sign indicates that the force is acting in the opposite direction of the ball's initial motion.

### Final Answer:
The magnitude of the force on the ball is **40 N**.