A car of mass 1000 kg moves on a circular path with constant speed of 16 m/s. It is turned by 90º after travelling 628 m on the road. The centripetal force acting on the car is-

Options

A. 160 N
B. 320 N
C. 640 N
D. 1280 N

Answer

To solve the problem, we need to find the centripetal force acting on a car of mass 1000 kg that is moving in a circular path with a constant speed of 16 m/s after it has turned 90 degrees while traveling a distance of 628 m.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the car (m) = 1000 kg
- Speed of the car (v) = 16 m/s
- Distance traveled on the road (l) = 628 m
- Angle turned (θ) = 90 degrees = π/2 radians

2. **Determine the Radius of the Circular Path:**
- The arc length (l) for a circular path can be expressed as:
\[ l = r \cdot \theta \]
- Rearranging this formula to find the radius (r):
\[ r = \frac{l}{\theta} \]
- Substitute the values:
\[ r = \frac{628 \, \text{m}}{\frac{\pi}{2}} = \frac{628 \times 2}{\pi} = \frac{1256}{\pi} \]
- Using \(\pi \approx 3.14\):
\[ r \approx \frac{1256}{3.14} \approx 400 \, \text{m} \]

3. **Calculate the Centripetal Force:**
- The formula for centripetal force (F_c) is given by:
\[ F_c = \frac{mv^2}{r} \]
- Substitute the known values:
\[ F_c = \frac{1000 \, \text{kg} \cdot (16 \, \text{m/s})^2}{400 \, \text{m}} \]
- Calculate \(v^2\):
\[ v^2 = 16^2 = 256 \, \text{m}^2/\text{s}^2 \]
- Now substitute this value back into the centripetal force equation:
\[ F_c = \frac{1000 \cdot 256}{400} \]
- Simplifying the expression:
\[ F_c = \frac{256000}{400} = 640 \, \text{N} \]

4. **Conclusion:**
- The centripetal force acting on the car is **640 N**.