Question

Velocity of centre of mass of the ring when it starts rolling motion is

• A. $V_0/4$
• B. $V_0/2$
• C. $V_0/3$
• D. $2V_0/3$

Answer 1

The correct option is B $V_0/2$

$v$ and $w$ be the velocity and angular velocity when pure rolling starts.

$⟹v=Rw$

$fR=I\alpha$

$fR=\left(M{R}^2\right)\alpha ⟹f=MR\alpha$

$w=0+\alpha t=\frac{f}{MR}t$ ..................(1)

Also, $f=Ma$ and $v=V_o-at$

$v=V_o-\frac{f}{M}t$ ..................(2)

Thus using (1) : $v=V_o-wR⟹v=\frac{V_o}{2}$ [as$(v=Rw)$]