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. (a)40 N
B. (b)20 N
C. (c)4 N
D. (d)2 N

Answer

To solve the problem step by step, we will use the concepts of mass, velocity, time, and force.

### Step 1: Identify the given values
- Mass of the ball (m) = 0.2 kg
- Initial velocity (u) = 20 m/s (since the ball is moving)
- Final velocity (v) = 0 m/s (since the ball stops)
- Time taken to stop (t) = 0.1 s

### Step 2: Calculate the acceleration
To find the force acting on the ball, we first need to calculate the acceleration. Acceleration (a) is defined as the change in velocity (Δv) over time (t).

\[ a = \frac{v - u}{t} \]

Substituting the values:

\[ a = \frac{0 - 20}{0.1} = \frac{-20}{0.1} = -200 \, \text{m/s}^2 \]

### Step 3: Calculate the force
Now, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a):

\[ F = m \cdot a \]

Substituting the values:

\[ F = 0.2 \, \text{kg} \cdot (-200 \, \text{m/s}^2) \]

Calculating this gives:

\[ F = -40 \, \text{N} \]

The negative sign indicates that the force is acting in the opposite direction of the motion (which is expected since the ball is stopping).

### Step 4: Conclusion
The magnitude of the force acting on the ball is 40 N.

### Final Answer:
The force on the ball is 40 N (in the direction opposite to the motion).

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