Question

A cylinder is placed between two planks as shown in figure. There is no sliding anywhere between planks and cylinder, then velocity of cylinder with respect to ground is

• A. zero
• B. $\frac{V}{2}$ towards right
• C. $\frac{V}{2}$ towards left
• D. $\frac{3V}{2}$ towards right

Answer 1

The correct option is B $\frac{V}{2}$ towards right


$\omega =\frac{V_A-V_B}{AB}$
$\omega =\frac{2V-(-V)}{2R}$
$\omega =\frac{3V}{2R}$
${\overrightarrow{V}}_{CB}=R\omega =\frac{3}{2}V\hat{i}$
${\overrightarrow{V}}_{CG}={\overrightarrow{V}}_{CB}+{\overrightarrow{V}}_{BG}=\frac{3}{2}V\hat{i}-V\hat{i}=\frac{V}{2}\hat{i}$