Question

A plank is moving with a velocity $4\text{m/s}$. A disc of radius $1\text{m}$ rolls on it without slipping with an angular velocity of $3\text{rad/s}$ as shown in figure. Then, the velocity of the centre of the disc $\left(V_{\text{cm}}\right)$ is

• A. $4\text{m/s}$
• B. $1\text{m/s}$
• C. $3\text{m/s}$
• D. $7\text{m/s}$

Answer 1

The correct option is D $7\text{m/s}$

In pure rolling (rolling without slipping) velocity of contact points $\left(P\&Q\right)$ will be same.


i.e $\text{Velocity of disc at contact point}=\text{Velocity of plank}$
$\Rightarrow V_P=V_Q...\left(i\right)$
$\because$ Tangential velocity $\left(\omega R\right)$ and translational velocity at $P$ are in opposite direction.
$\Rightarrow V_P=V_{cm}-\omega R\&V_Q=4\text{m/s}$
From Eq $\left(i\right)$,
$V_{\text{cm}}-\omega R=4$
$V_{\text{cm}}=4+(3\times 1)$
$\therefore V_{\text{cm}}=7\text{m/s}$