Question

A wheel rolls without slipping on a level road as shown in figure.


Choose the correct option(s):

• A. The speed of point $B$ is $2V$
• B. The speed of points $C,A$ and $D$ is equal to $V$
• C. The speed of point $A$ is zero and speed of point $C$ is $\sqrt{2}V$
• D. The speed of point $O$ is less than the speed of $C$.

Answer 1

Answer: (A), (C), (D)

The correct options are
A The speed of point $B$ is $2V$
C The speed of point $A$ is zero and speed of point $C$ is $\sqrt{2}V$
D The speed of point $O$ is less than the speed of $C$.

For pure rolling,
$\text{Velocity of point A on wheel}=\text{Velocity of surface in contact}$
Here, surface is the ground at rest
$\Rightarrow V_A=0$
$\Rightarrow V-\omega r=0$
$\therefore V=\omega r...\left(i\right)$


From the shown figure, the magnitude of velocity (speed) of points on the wheel are,
$V_B=V+\omega r=V+V=2V$
$V_C=\sqrt{V^2+(\omega r{)}^2}$
$=\sqrt{V^2+V^2}=\sqrt{2}V$
$V_D=\sqrt{V^2+(\omega r{)}^2}$
$=\sqrt{V^2+V^2}=\sqrt{2}V$
Therefore, options (a), (c), (d) are correct.