Question

A uniform circular disc placed on a rough horizontal surface is initially given a velocity $v_{0}$ and angular velocity $\omega _{0}$ as shown in figure. The disc comes to rest after moving some distance in the direction of motion. Then $\frac{v_{0}}{r \omega _{0}}$ is:

• A. $\frac{1}{2}$
• B. $2$
• C. $\frac{1}{3}$
• D. $3$

Answer 1

Answer: (A)

From conservation of angular momentum about a point on the surface,
Initial angular momentum = final angular momentum:
$Mv_{0}r-\frac{1}{2}Mr^{2}\omega _{0}=0$
Therefore $\frac{v_{0}}{r \omega _{0}}=\frac{1}{2}$