Question

A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of the car will be, if the friction coefficient between tyres and road is 0.34. (Take g = 10 m/s²):

• A. 13.4m/s
• B. 13m/s
• C. 22.4m/s
• D. 17m/s

Hint:

 For motion on curved roads:
• Use the formula vmax = \(\sqrt{µgr}\) for safe turning.
• Ensure all values are in consistent units for accurate results.

Answer 1

The Correct Option is B

To determine the maximum speed of a car moving on a horizontal curved road, we use the formula for maximum speed in terms of friction.

The formula for the maximum speed v_{\text{max}} on a flat, curved road is given by:

v_{\text{max}} = \sqrt{\mu g R}

Where:

• \mu is the coefficient of friction,
• g is the acceleration due to gravity (10 m/s²),
• R is the radius of the curvature (50 m).

Substitute the given values into the formula:

v_{\text{max}} = \sqrt{0.34 \times 10 \times 50}

Calculate the product inside the square root:

= \sqrt{170}

Using a calculator, find the square root of 170:

v_{\text{max}} \approx 13 \, \text{m/s}

Thus, the maximum speed of the car is approximately 13 m/s.

Therefore, the correct answer is 13 m/s.