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 step by step, we will use Newton's laws of motion, particularly the second law which states that Force (F) is equal to mass (m) times acceleration (a).

### 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 to stop (t) = 0.1 s

2. **Calculate Acceleration (a):**
We can use the first equation of motion:
\[ v = u + at \]
Rearranging the equation to solve for acceleration (a):
\[ a = \frac{v - u}{t} \]
Substituting the known values:
\[ a = \frac{0 - 20}{0.1} = \frac{-20}{0.1} = -200 \, \text{m/s}^2 \]
The negative sign indicates that the acceleration is in the opposite direction of the initial velocity (deceleration).

3. **Calculate the Force (F):**
Using Newton's second law:
\[ F = m \cdot a \]
Substituting the mass and acceleration:
\[ F = 0.2 \, \text{kg} \cdot (-200 \, \text{m/s}^2) = -40 \, \text{N} \]
The negative sign indicates that the force is acting in the opposite direction of the motion.

4. **Final Answer:**
The magnitude of the force acting on the ball is 40 N, and it acts in the direction opposite to the motion of the ball.

### Summary:
The force on the ball is **40 N** in the direction opposite to its initial motion.

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