A vehicle of mass `200kg` is moving along a levelled curved road of radius `70`mwith angular velocity of `0.2 rad/s` The centripetal force action on thevehicle is :

Options

A. `560 N`
B. `2240 N`
C. `2800 N`
D. `14 N`

Answer

To find the centripetal force acting on a vehicle moving along a curved road, we can use the formula for centripetal force:

\[ F_c = m \cdot \omega^2 \cdot r \]

where:
- \( F_c \) is the centripetal force,
- \( m \) is the mass of the vehicle,
- \( \omega \) is the angular velocity, and
- \( r \) is the radius of the curved path.

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass of the vehicle, \( m = 200 \, \text{kg} \)
- Radius of the curved road, \( r = 70 \, \text{m} \)
- Angular velocity, \( \omega = 0.2 \, \text{rad/s} \)

2. **Substitute the values into the formula:**
\[ F_c = m \cdot \omega^2 \cdot r \]
\[ F_c = 200 \cdot (0.2)^2 \cdot 70 \]

3. **Calculate \( \omega^2 \):**
\[ (0.2)^2 = 0.04 \]

4. **Substitute \( \omega^2 \) back into the equation:**
\[ F_c = 200 \cdot 0.04 \cdot 70 \]

5. **Calculate \( 200 \cdot 0.04 \):**
\[ 200 \cdot 0.04 = 8 \]

6. **Now multiply by the radius \( r \):**
\[ F_c = 8 \cdot 70 \]

7. **Calculate \( 8 \cdot 70 \):**
\[ 8 \cdot 70 = 560 \]

8. **Final Result:**
\[ F_c = 560 \, \text{N} \]

### Conclusion:
The centripetal force acting on the vehicle is \( 560 \, \text{N} \).