A car is moving in a horizontal level of circular track with uniform speed of `10 m/s`. If radius of circular path is 50 m then the minimum coefficient of friction to avoid over turning is

Options

A. 0.3
B. 0.5
C. 0.1
D. 0.2

Answer

To solve the problem of finding the minimum coefficient of friction required to avoid overturning for a car moving on a circular track, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Speed of the car, \( v = 10 \, \text{m/s} \)
- Radius of the circular path, \( R = 50 \, \text{m} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \) (standard value)

2. **Understand the Forces Acting on the Car:**
- When the car is moving in a circular path, it experiences a centripetal force directed towards the center of the circle.
- The frictional force provides the necessary centripetal force to keep the car moving in a circle.

3. **Centripetal Force Equation:**
- The formula for centripetal force is given by:
\[ F_c = \frac{mv^2}{R} \]
- Here, \( m \) is the mass of the car, \( v \) is the speed, and \( R \) is the radius of the circular path.

4. **Frictional Force:**
- The maximum frictional force 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 level surface, \( N = mg \).

5. **Setting Up the Equation:**
- To avoid skidding, the frictional force must be equal to the required centripetal force:
\[ \mu mg = \frac{mv^2}{R} \]
- Here, we can cancel \( m \) from both sides since it appears in both terms:
\[ \mu g = \frac{v^2}{R} \]

6. **Solving for the Coefficient of Friction:**
- Rearranging the equation gives:
\[ \mu = \frac{v^2}{gR} \]

7. **Substituting the Values:**
- Now substituting the known values into the equation:
\[ \mu = \frac{(10)^2}{10 \times 50} \]
- This simplifies to:
\[ \mu = \frac{100}{500} = \frac{1}{5} = 0.2 \]

8. **Conclusion:**
- Therefore, the minimum coefficient of friction required to avoid overturning is:
\[ \mu = 0.2 \]

### Final Answer:
The minimum coefficient of friction to avoid overturning is **0.2**.

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