Question

A car is moving on a horizontal curved road of radius 50 m. If the friction coefficient between tyres and road is 0.34, the approximate maximum speed of the car will be nearly:

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

Hint:

For circular motion, the friction between the road and tyres provides the centripetal force. The maximum speed is calculated using \( v_{{max}} = \sqrt{R \cdot g \cdot \mu} \), where \( \mu \) is the coefficient of friction and \( R \) is the radius.

Answer 1

The Correct Option is C

The maximum speed \( v_{{max}} \) in a circular motion, where friction provides the centripetal force, is given by: \[ v_{{max}} = \sqrt{R \cdot g \cdot \mu} \] where: - \( R = 50 \, {m} \) is the radius of the curve, - \( g = 9.8 \, {m/s}^2 \) is the acceleration due to gravity, - \( \mu = 0.34 \) is the coefficient of friction. Substitute the given values into the formula: \[ v_{{max}} = \sqrt{50 \times 9.8 \times 0.34} \] \[ v_{{max}} = \sqrt{166.6} \approx 12.91 \, {m/s} \] Thus, the approximate maximum speed of the car is \( 13 \, {m/s} \).