The minimum velocity (in ms^(-1))` with which a car driver must traverse a flat curve of radius 150m and coefficient of friction 0.6 to avoid skidding is

Options

A. (a)60
B. (b)30
C. (c)15
D. (d)25

Explanation

To find the minimum velocity with which a car driver must traverse a flat curve of radius 150 m and a coefficient of friction of 0.6 to avoid skidding, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Car:**
- The forces acting on the car include the gravitational force (weight), the normal force, and the frictional force. The gravitational force acts downwards, while the normal force acts upwards. The frictional force provides the necessary centripetal force to keep the car moving in a circular path.

2. **Understand the Condition for Skidding:**
- For the car to avoid skidding, the frictional force must be equal to or greater than the centripetal force required to keep the car moving in a circle. The centripetal force \( F_c \) required is given by:
\[ F_c = \frac{mv^2}{r} \]
- Where \( m \) is the mass of the car, \( v \) is the velocity, and \( r \) is the radius of the curve.

3. **Frictional Force:**
- The maximum frictional force \( F_f \) that can act on the car is given by:
\[ F_f = \mu N \]
- Where \( \mu \) is the coefficient of friction and \( N \) is the normal force. For a flat surface, the normal force \( N \) is equal to the weight of the car, which is \( mg \). Therefore:
\[ F_f = \mu mg \]

4. **Setting Up the Inequality:**
- To avoid skidding, we set the centripetal force equal to the maximum frictional force:
\[ \frac{mv^2}{r} \leq \mu mg \]

5. **Canceling Mass and Rearranging:**
- We can cancel the mass \( m \) from both sides (assuming \( m \neq 0 \)):
\[ \frac{v^2}{r} \leq \mu g \]
- Rearranging gives:
\[ v^2 \leq \mu g r \]

6. **Substituting Values:**
- We know:
- \( \mu = 0.6 \)
- \( g = 10 \, \text{m/s}^2 \) (approximately)
- \( r = 150 \, \text{m} \)
- Substituting these values into the equation:
\[ v^2 \leq 0.6 \times 10 \times 150 \]
\[ v^2 \leq 900 \]

7. **Calculating the Velocity:**
- Taking the square root of both sides:
\[ v \leq \sqrt{900} \]
\[ v \leq 30 \, \text{m/s} \]

### Final Answer:
The minimum velocity with which a car driver must traverse the curve to avoid skidding is **30 m/s**.