Question

A ring of mass M and radius R sliding with a velocity $v_0$ suddenly enters into rough surface where coefficient of friction is $\mu$, as shown

• A. The ring starts motion when centre of mass becomes stationary
• B. The ring starts rolling motion when the point of contact becomes stationary
• C. The time after which the ring starts rolling is $\frac{v_0}{2\mu g}$
• D. The rolling velocity is $\frac{v_0}{2}$

Answer 1

Answer: (B), (C), (D)

The correct options are
B The ring starts rolling motion when the point of contact becomes stationary
C The time after which the ring starts rolling is $\frac{v_0}{2\mu g}$
D The rolling velocity is $\frac{v_0}{2}$

Let rolling velocity is v and angular velocity is $\omega$ then,

$v=v_0-\mu gt$ ......(1)

and $\omega =\frac{\mu g}{r}t$ .....(2)

Also, $v=r\omega$

$\mu gt=v_0-\mu gt\Rightarrow t=\frac{v_0}{2mug}$

and $v=\frac{v_0}{2}$