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

To determine the maximum speed of a car moving on a horizontal curved road, we need to understand the role of friction between the tires and the road surface. The key formula for calculating this speed involves the coefficient of friction, the radius of the curve, and gravitational acceleration.

The formula to find the maximum speed \( v \) of a car moving on a curved path without skidding is:

\(v = \sqrt{\mu \times g \times r}\)

where:

• \(\mu\) is the coefficient of friction between the tires and the road.
• \(g\) is the acceleration due to gravity.
• \(r\) is the radius of the curved path.

Given data:

• \(\mu = 0.34\)
• \(g = 10 \, \text{ms}^{-2}\)
• \(r = 50 \, \text{m}\)

Substitute these values into the formula:

\(v = \sqrt{0.34 \times 10 \times 50}\)

Calculate the intermediate value:

\(v = \sqrt{170}\)

Calculate the square root:

\(v \approx 13.038 \, \text{ms}^{-1}\)

Upon rounding to one decimal place, the maximum speed is approximately 13 ms\(^{-1}\).

Therefore, the correct answer is 13 ms\(^{-1}\).

This calculation shows why the correct answer is 13 ms\(^{-1}\), as per the given options.