A motor cyclist riding at `36kmh^(-1)` has turn a corner. Find the least radius of the curve, he should follow for safe travelling, if the coefficient of friction between the tyres and the road is `0.2`.

Options

A. 10 m
B. 25 m
C. 50 m
D. 100 m

Explanation

To solve the problem of finding the least radius of the curve that a motorcyclist should follow for safe traveling, we can use the formula derived from the principles of circular motion and friction.

### Step-by-Step Solution:

1. **Convert Speed to SI Units**:
The speed of the motorcyclist is given as \( 36 \, \text{km/h} \). We need to convert this to meters per second (m/s).
\[ \text{Speed} = 36 \, \text{km/h} \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{h}}{3600 \, \text{s}} = 10 \, \text{m/s} \]

**Hint**: Remember to convert the speed from km/h to m/s by using the conversion factor \( \frac{1000}{3600} \).

2. **Identify Given Values**:
- Coefficient of friction (\( \mu \)) = 0.2
- Acceleration due to gravity (\( g \)) = \( 10 \, \text{m/s}^2 \) (approximately)

3. **Use the Formula for Safe Turning**:
The formula for the least radius of the curve for safe turning is given by:
\[ R = \frac{v^2}{\mu g} \]

4. **Substitute the Values**:
Now, substitute the values of \( v \), \( \mu \), and \( g \) into the formula:
\[ R = \frac{(10 \, \text{m/s})^2}{0.2 \times 10 \, \text{m/s}^2} \]
\[ R = \frac{100 \, \text{m}^2/\text{s}^2}{2 \, \text{m/s}^2} = 50 \, \text{m} \]

5. **Conclusion**:
The least radius of the curve that the motorcyclist should follow for safe traveling is \( 50 \, \text{m} \).

### Final Answer:
The least radius of the curve is \( 50 \, \text{m} \).

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