Question

A wheel of radius $R$ rolls on the ground with a uniform velocity $v$ . The relative acceleration of the topmost point of the wheel with respect to the bottommost point is

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

Answer 1

Answer: (B)

As it is rolling
$\Rightarrow \, \omega =\frac{V}{R}$
$V_{Q}=0$
$\Rightarrow V_{P / Q}=\omega \left(\right. 2 R \left.\right)=2V$
$\Rightarrow a_{P / Q}=\frac{V_{P / Q} ^{2}}{2 R}=\frac{\left(\right. 2 V \left.\right)^{2}}{2 R}=\frac{2 V^{2}}{R}$