Question

A system of identical cylinder and plates is shown in figure. All the cylinders are identical and there is no slipping at any contact. The velocity of lower and the upper plates are $v$ and $2v$, respectively, as shown. Then the ratio of angular speeds of the upper cylinders to lower cylinder is:

• A. $\frac{1}{3}$
• B. $3$
• C. $1$
• D. None of these

Answer 1

The correct option is B $3$

Angular velocity of the upper cylinder can be given as:

${\omega }_{up}=\frac{2v-(-v)}{2R}=\frac{3v}{2R}$;

and for the lower cylinder, it can be given as:

${\omega }_{lower}=\frac{v-0}{2R}=\frac{v}{2R}$

Hence, ratio, $\frac{{\omega }_{up}}{{\omega }_{lower}}=\frac{\frac{3v}{2R}}{\frac{v}{2R}}$

$\Rightarrow \frac{{\omega }_{up}}{{\omega }_{lower}}=\frac{3v}{v}=3$

Hence, the correct option is $\left(B\right)$