Question

A solid sphere and a hollow sphere of equal mass and radius are placed over a rough horizontal surface after rotating it about its masss centre with same angular velocity ${\omega }_0$. Once the pure rolling starts let $v_1$ and $v_2$ be the linear speeds of their centres of mass. Then

• A. $v_1=v_2$
• B. $v_1>v_2$
• C. $v_1<v_2$
• D. data insufficient

Answer 1

Answer: (C)

$v_1<v_2$

$ma=f⟹a=\frac{f}{m}$

Also, $fr=I\alpha ⟹a=\frac{I\alpha }{mr}$

Now, $v=0+at=\frac{I\alpha }{mr}t$ .................(1)

$w=w_o-\alpha t$

$\frac{v}{r}=w_o-\frac{mvr}{I}$ (using (1) and $v=rw$)

$⟹v=\frac{w_{o}r}{1+\frac{m{r}^2}{I}}$

As $I_{hollowsphere}>I_{solidsphere}⟹v_2>v_1$