Question

A motorcycle racer takes a round with speed 20 m/s on a curved road of radius 40 m. The leaning angle of the motorcycle with vertical for safe turn is

• A. 75°
• B. 45°
• C. 60°
• D. 30°

Hint:

For safe turns, the leaning angle of the motorcycle can be found using the formula \( \tan \theta = \frac{v^2}{rg} \), where \( v \) is the speed, \( r \) is the radius, and \( g \) is the acceleration due to gravity.

Answer 1

The Correct Option is B

Step 1: Understanding the centripetal force.
The motorcycle moves along a curved path, so the centrifugal force must be balanced by the component of gravitational force. The relation for the leaning angle \( \theta \) is: \[ \tan \theta = \frac{v^2}{rg} \] where \( v = 20 \, \text{m/s} \) is the speed, \( r = 40 \, \text{m} \) is the radius, and \( g = 10 \, \text{m/s}^2 \) is the acceleration due to gravity. Substituting these values: \[ \tan \theta = \frac{(20)^2}{40 \times 10} = \frac{400}{400} = 1 \] Step 2: Finding the angle.
Thus, \( \theta = \tan^{-1} 1 = 45^\circ \).
Step 3: Conclusion.
Therefore, the leaning angle is 45°, corresponding to option (B).