If the road is horizontal (no banking), what should be the minimum friction coefficeint so that a scooter going at 18 km/hr does not skid for r=10m ?

Options

A. 0.25
B. 0.18
C. 0.3
D. 0.4

Explanation

To solve the problem of determining the minimum friction coefficient required for a scooter traveling at 18 km/hr on a horizontal road with a radius of 10 m, we can follow these steps:

### Step-by-Step Solution:

1. **Convert the Speed from km/hr to m/s**:
The speed of the scooter is given as 18 km/hr. To convert this to meters per second (m/s), we use the conversion factor:
\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]
Therefore,
\[ V = 18 \times \frac{5}{18} = 5 \text{ m/s} \]

2. **Identify the Given Values**:
- Radius of the turn, \( r = 10 \text{ m} \)
- Speed of the scooter, \( V = 5 \text{ m/s} \)
- Acceleration due to gravity, \( g = 10 \text{ m/s}^2 \) (approximate value)

3. **Apply the Concept of Centripetal Force**:
For an object moving in a circular path, the required centripetal force \( F_c \) is given by:
\[ F_c = \frac{mV^2}{r} \]
where \( m \) is the mass of the scooter.

4. **Frictional Force**:
The frictional force \( F_f \) that prevents the scooter from skidding is given by:
\[ F_f = \mu mg \]
where \( \mu \) is the coefficient of friction and \( g \) is the acceleration due to gravity.

5. **Set Up the Equation**:
For the scooter not to skid, the frictional force must be equal to the centripetal force:
\[ \frac{mV^2}{r} = \mu mg \]

6. **Cancel the Mass**:
Since mass \( m \) appears on both sides of the equation, we can cancel it out:
\[ \frac{V^2}{r} = \mu g \]

7. **Solve for the Coefficient of Friction \( \mu \)**:
Rearranging the equation gives us:
\[ \mu = \frac{V^2}{rg} \]

8. **Substitute the Known Values**:
Now substitute \( V = 5 \text{ m/s} \), \( r = 10 \text{ m} \), and \( g = 10 \text{ m/s}^2 \):
\[ \mu = \frac{5^2}{10 \times 10} = \frac{25}{100} = 0.25 \]

9. **Conclusion**:
The minimum coefficient of friction required so that the scooter does not skid is:
\[ \mu = 0.25 \]

### Final Answer:
The minimum friction coefficient required is \( \mu = 0.25 \).

---