Question

A cylinder of radius $R$ is to roll without slipping between two planks as shown in the figure, Then

• A. angular velocity of the cylinder is $\frac{v}{R}$ counter clockwise
• B. angular velocity of the cylinder is $\frac{2v}{R}$ clockwise
• C. velocity of centre of mass of the cylinder is v towards left
• D. velocity of centre of mass of the cylinder is $2v$ towards right

Answer 1

Answer: (A), (D)

The correct options are
A angular velocity of the cylinder is $\frac{v}{R}$ counter clockwise
D velocity of centre of mass of the cylinder is $2v$ towards right

$v_0+R{\omega }_0=v.....\left(i\right)$
$v_0-R{\omega }_0=3v.....\left(ii\right)$
Solving these two equations, we get
$v_0=2v$ and ${\omega }_0=-\frac{v}{R}$