Question

A wheel of radius R rolls without slipping on the ground with a uniform velocity v. The relative acceleration of the top most point ofthe wheel with respect to the bottom most point is

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

Answer 1

Answer: (B)

$\frac{2v^2}{R}$

Centripetal acceleration $a=\frac{v^2}{R}$ towards the centre

Thus acceleration of points A and B is shown in the above figure.

$\therefore$ Relative acceleration $a_{AB}=a_A-a_B$

$⟹$ $a_{AB}=\frac{v^2}{R}-\frac{-v^2}{R}=\frac{2v^2}{R}$