Question

A wheel of radius \( R \) rolls on the ground with a uniform velocity \( v \). The relative acceleration of topmost point of the wheel with respect to the bottom most point is: 

• A. \( \frac{v^2}{R} \)
• B. \( \frac{v^2}{2R} \)
• C. \( \frac{4v^2}{R} \)
• D. \( \frac{v^2}{R} \)

Hint:

In rolling motion, the relative acceleration of the topmost point with respect to the bottommost point is half of the value obtained for a point on the wheel.

Answer 1

The Correct Option is B

Step 1: Relative acceleration definition.
For rolling motion, the acceleration at the topmost point with respect to the bottommost point is \( \frac{v^2}{2R} \). This is derived from the relationship between linear velocity and rotational motion.
Thus, the correct answer is (2).