Question

A wheel of radius $R$ as shown in figure, is set in pure rolling. Point $P$ represents the point on the wheel, in contact with a point $Q$ on the ground. Which of the following statement(s) is/are correct?

• A. There is no relative motion at the point of contact between wheel and ground.
• B. Wheel will perform pure rolling if velocity of point $P$ is zero.
• C. $V_{\text{cm}}=\omega R$
• D. None of these

Answer 1

Answer: (A), (B), (C)

The correct options are
A There is no relative motion at the point of contact between wheel and ground.
B Wheel will perform pure rolling if velocity of point $P$ is zero.
C $V_{\text{cm}}=\omega R$

Since the point $Q$ on the ground is always at rest, hence for rolling without slipping,
$V_P=0...\left(i\right)$


$V_P=V_O+V_{PO}$
$\Rightarrow V_P=V_{cm}-\omega R...\left(ii\right)$
From both equations,
$V_{\text{cm}}-\omega R=0$
$\therefore V_{\text{cm}}=\omega R$
If the point of contact $\left(P\right)$ is has the same velocity as that of the ground, then there will be no relative motion between wheel and ground.
Thus, options (a), (b), (c) are correct.