Question

On the cylinder of radius R in the figure, which is rolling with velocity of centre of mass $v=\frac{\omega R}{4}$ towards right ($\omega$ is clockwise), find the velocities (magnitude) at points A, B, C, D.

• A. $5v,\sqrt{17}v,3v,\sqrt{17}v$
• B. $5v,\sqrt{2}v,3v,\sqrt{2}v$
• C. $2v,\sqrt{2}v,0,\sqrt{2}v$
• D. $2v,\sqrt{17}v,0,\sqrt{17}v$

Answer 1

The correct option is A

$5v,\sqrt{17}v,3v,\sqrt{17}v$

At A and C the relative velocity $\omega$R and V are parallel and antiparallel respectively

$\therefore$Velocity at A = v+ $\omega$ R = 5V towards right

Velocity at C = $\omega$ R - V = 3v towards left

At B and D the $\omega$ R and v components are perpendicular.

$=\sqrt{(\omega R{)}^2+v^2}=\sqrt{(4v{)}^2+v^2}=\sqrt{17}v$

$\therefore$ Magnitude of velocities at B and D are equal