Question

A car goes around a curve of radius 48 m. If the road is banked at an angle of 15° with the horizontal, the maximum speed in kilometers per hour at which the car can travel if there is to be no tendency to skid even on very slippery pavement (tan 15° = 0.27 approximately) is:

• A. 30.6 km/h
• B. 40.6 km/h
• C. 20.6 km/h
• D. None

Hint:

For banking curves, the maximum speed is determined by the radius of the curve, gravitational acceleration, and the banking angle of the road.

Answer 1

The Correct Option is A

The maximum speed \( v_{\text{max}} \) can be calculated using the formula for the banking of curves: \[ v_{\text{max}} = \sqrt{r g \tan \theta} \] Substituting the values: \[ v_{\text{max}} = \sqrt{48 \times 9.8 \times 0.27} \approx 8.53 \, \text{m/s} \] Converting to km/h: \[ v_{\text{max}} = 8.53 \times 3.6 \approx 30.6 \, \text{km/h} \]