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

Answer 1

Answer: (B)

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

Answer 2

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 $a _{ A B}= a _{A}- a _{B}$
$\Rightarrow a _{A B}=\frac{ v ^{2}}{ R }-\frac{- v ^{2}}{ R }=\frac{2 v ^{2}}{ R }$