A 0.5 kg ball moves in a circle of radius 0.4 m at a velocity of 4 m/s. The centripetal force on the ball is

Options

A. (a)10N
B. (b)20N
C. (c)40N
D. (d)80N

Answer

To find the centripetal force acting on a ball moving in a circular path, we can use the formula for centripetal force:

\[ F = \frac{mv^2}{r} \]

Where:
- \( F \) is the centripetal force,
- \( m \) is the mass of the object,
- \( v \) is the velocity of the object,
- \( r \) is the radius of the circular path.

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass of the ball, \( m = 0.5 \, \text{kg} \)
- Velocity of the ball, \( v = 4 \, \text{m/s} \)
- Radius of the circular path, \( r = 0.4 \, \text{m} \)

2. **Substitute the values into the formula:**
\[ F = \frac{mv^2}{r} \]
Plugging in the values:
\[ F = \frac{0.5 \, \text{kg} \times (4 \, \text{m/s})^2}{0.4 \, \text{m}} \]

3. **Calculate \( v^2 \):**
\[ (4 \, \text{m/s})^2 = 16 \, \text{m}^2/\text{s}^2 \]

4. **Substitute \( v^2 \) back into the equation:**
\[ F = \frac{0.5 \, \text{kg} \times 16 \, \text{m}^2/\text{s}^2}{0.4 \, \text{m}} \]

5. **Multiply the mass and \( v^2 \):**
\[ 0.5 \, \text{kg} \times 16 \, \text{m}^2/\text{s}^2 = 8 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \]

6. **Now divide by the radius:**
\[ F = \frac{8 \, \text{kg} \cdot \text{m}^2/\text{s}^2}{0.4 \, \text{m}} = 20 \, \text{N} \]

7. **Conclusion:**
The centripetal force acting on the ball is \( 20 \, \text{N} \).

### Final Answer:
The centripetal force on the ball is **20 Newtons**.

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