Question

What will be the maximum speed of a car on a circular road of radius $12 \text{ m}$ if the coefficient of friction between the tyres and the road is $0.3$? $g = 10 \text{ms}^{-2}$}

• A. $3.6 \text{ ms}^{-1}$
• B. $36 \text{ ms}^{-1}$
• C. $60 \text{ ms}^{-1}$
• D. $10 \text{ ms}^{-1}$
• E. $6 \text{ ms}^{-1}$

Hint:

For flat circular roads, the maximum safe speed is independent of the mass of the vehicle. It only depends on the friction, radius, and gravity.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
When a car moves on a circular flat road, the necessary centripetal force is provided by the static friction between the tyres and the road. The maximum speed is reached when the centripetal force equals the maximum static frictional force.
Key Formula or Approach:
The maximum speed \( v_{max} \) is given by the formula:
\[ v_{max} = \sqrt{\mu r g} \]

Step 2: Detailed Explanation:
Given parameters:
Radius \( r = 12 \text{ m} \)
Coefficient of friction \( \mu = 0.3 \)
Acceleration due to gravity \( g = 10 \text{ ms}^{-2} \)
Substituting the values into the formula:
\[ v_{max} = \sqrt{0.3 \times 12 \times 10} \]
\[ v_{max} = \sqrt{3 \times 12} \]
\[ v_{max} = \sqrt{36} = 6 \text{ ms}^{-1} \]

Step 3: Final Answer:
The maximum speed of the car is $6 \text{ ms}^{-1}$.