A car is moving along a horizontal curve of radius 20 m , and coefficient of friction between the road and wheels of the car is `0.25` . If acceleration due to gravity is `(9.8 m//s^(2))`, then its maximum speed is

Options

A. `3 m//s`
B. `5 m//s`
C. `7 m//s`
D. `9 m//s`

Explanation

To find the maximum speed of a car moving along a horizontal curve, we can use the formula derived from the concepts of circular motion and friction. The maximum speed \( V_{max} \) can be calculated using the equation:

\[ V_{max} = \sqrt{\mu g r} \]

Where:
- \( \mu \) is the coefficient of friction (0.25 in this case),
- \( g \) is the acceleration due to gravity (9.8 m/s²),
- \( r \) is the radius of the curve (20 m).

### Step-by-step solution:

1. **Identify the given values**:
- Coefficient of friction, \( \mu = 0.25 \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)
- Radius of the curve, \( r = 20 \, \text{m} \)

2. **Substitute the values into the formula**:
\[ V_{max} = \sqrt{0.25 \times 9.8 \times 20} \]

3. **Calculate the product inside the square root**:
- First, calculate \( 0.25 \times 9.8 \):
\[ 0.25 \times 9.8 = 2.45 \]
- Next, multiply by the radius \( r \):
\[ 2.45 \times 20 = 49 \]

4. **Take the square root of the result**:
\[ V_{max} = \sqrt{49} = 7 \, \text{m/s} \]

5. **Conclusion**:
The maximum speed of the car while navigating the curve is \( 7 \, \text{m/s} \).