Question

A motor vehicle of mass 1000 kg is moving on a circular road having banking angle \( 30^\circ \) and coefficient of friction 0.2. Then the normal reaction force on the motor vehicle is about:
(Acceleration due to gravity = \( 10 \, \text{ms}^{-2} \))

• A. \( 6750 \, \text{N} \)
• B. \( 9060 \, \text{N} \)
• C. \( 1070 \, \text{N} \)
• D. \( 13055 \, \text{N} \)

Hint:

On banked roads, normal force accounts for both component of weight and effects of friction depending on angle and direction.

Answer 1

The Correct Option is D

Resolving forces on a banked curve, total normal force increases due to centripetal acceleration and friction. Approximate combined effect leads to: \[ N \approx \frac{mg}{\cos \theta - \mu \sin \theta} = \frac{1000 \cdot 10}{\cos 30^\circ - 0.2 \cdot \sin 30^\circ} = \frac{10000}{\frac{\sqrt{3}}{2} - 0.2 \cdot \frac{1}{2}} \approx 13055 \, \text{N} \]