Question

A uniform circular disc of radius $r$ is placed on a rough horizontal surface and given a linear velocity $v_o$ and angular velocity ${\omega }_o$ as shown. The disc comes to rest after moving some distance to the right. It follows that:

• A. $3v_o=2{\omega }_{o}r$
• B. $2v_o={\omega }_{o}r$
• C. $v_o={\omega }_{o}r$
• D. $2v_o=3{\omega }_{o}r$

Answer 1

The correct option is B $2v_o={\omega }_{o}r$

as ther is slipping friction acts

now , $a=\frac{F}{m}\alpha =\frac{2FR}{M{R}^2}=\frac{2F}{MR}nowv-at=0\Rightarrow t_1=\frac{v}{a}\omega -\alpha t=0\Rightarrow t_2=\frac{\omega }{\alpha }asdisccomestorest{t}_1=t_2\frac{v}{a}=\frac{\omega }{\alpha }\Rightarrow \frac{mv}{F}=\frac{m\omega r}{2F}\Rightarrow \omega r=2v_0$