Question

A system of uniform cylinders and plates is shown in the figure. All the cylinders are identical and there is no slipping at any contact. Velocity of lower and upper plate is $v_0$ and 2$v_0$ respectively as shown in the figure. Then the ratio of angular speed of upper cylinder to lower cylinder is

• A. $1:3$
• B. $3$
• C. $1:2$
• D. $2:1$

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 $\left(B\right)$