Question

A car turns on a road of radius \(300\,m\). Coefficient of friction = 0.3. Find maximum speed. (Take \(g=10\,m/s^2\))

• A. \(10\,m/s\)
• B. \(30\,m/s\)
• C. \(40\,m/s\)
• D. \(50\,m/s\)

Hint:

On flat roads, friction alone provides centripetal force. Always use \(v_{max} = \sqrt{\mu rg}\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
For a turn on a road where only friction is specified (or banking angle is not provided), the maximum speed is limited by the maximum static friction providing the centripetal force.
Step 2: Key Formula or Approach:
The maximum speed on a level circular road is given by:
\[ v = \sqrt{\mu rg} \]
: Detailed Explanation:
Given values:
Radius \(r = 300\text{ m}\)
Coefficient of friction \(\mu = 0.3\)
Acceleration due to gravity \(g = 10\text{ m/s}^{2}\)
Substituting the values:
\[ v = \sqrt{0.3 \times 300 \times 10} \]
\[ v = \sqrt{3 \times 300} = \sqrt{900} \]
\[ v = 30\text{ m/s} \]
Step 3: Final Answer:
The maximum speed is \(30\text{ m/s}\).