Question

A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0.34. [Take \( g = 10 \) ms\(^{-2}\)]

• A. 3.4 ms\(^{-1}\)
• B. 22.4 ms\(^{-1}\)
• C. 13 ms\(^{-1}\)
• D. 17 ms\(^{-1}\)

Hint:

If the speed exceeds this limit, the required centripetal force \( (\frac{mv^2}{r}) \) becomes greater than the maximum available friction \( (\mu mg) \), causing the car to skid outwards.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
When a car takes a turn on a horizontal road, the necessary centripetal force is provided entirely by the static friction between the tires and the road surface.

Step 2: Key Formula or Approach:
The maximum speed \( v_{max} \) to avoid skidding on a flat circular path is given by: \[ v_{max} = \sqrt{\mu rg} \] where \( \mu = 0.34 \), \( r = 50\text{ m} \), and \( g = 10\text{ ms}^{-2} \).

Step 3: Detailed Explanation:
Substitute the given values into the formula: \[ v_{max} = \sqrt{0.34 \times 50 \times 10} \] \[ v_{max} = \sqrt{0.34 \times 500} \] \[ v_{max} = \sqrt{170} \] Now, find the approximate square root: Since \( 13^2 = 169 \), then \( \sqrt{170} \approx 13.04\text{ ms}^{-1} \).

Step 4: Final Answer
The approximate maximum speed is 13 ms\(^{-1}\).