Question

The velocity of the centre of a smaller cylinder is $ v$. There is no slipping anywhere. The velocity of the center center of a larger cylinder is

• A. $v$
• B. $2v$
• C. $\frac{3v}{2}$
• D. none of the above

Answer 1

The correct option is A

$v$

Step 1:Given:

The velocity of the center of a smaller cylinder $v_s=v$.

Step 2:To Find:

The velocity of the center of the larger cylinder.

Step 3:Calculate Velocity of the center of the larger cylinder:

1. In figure $C_1$ and $C_2$are the instantaneous center of rotation the of the two cylinders.
2. The cylinder can be considered as rotation about $C_1$and $C_2$.
3. In the absence of slipping between the plank and the cylinders, point $A_1$and $A_2$ have the same velocity.
4. Angular velocity of the larger cylinder is ${\omega }_L=\frac{2v}{4R}=\frac{v}{2R}$.
5. Velocity of the center of larger cylinder is

$$\begin{gathered} v_L={\omega }_L\times 2R \\ =\frac{v}{2R}\times 2R \\ =v \end{gathered}$$

Hence, Option (A) is correct.