Question

A circular disk of a radius R rolls without slipping at a velocity V. The magnitude of the velocity at point P (see figure) is:

• A. $\sqrt{3}V$
• B. $\sqrt{3}\frac{V}{2}$
• C. $\frac{V}{2}$
• D. $\frac{2V}{\sqrt{3}}$

Answer 1

The correct option is A $\sqrt{3}V$


Magnitude of velocity at Point P
$=\sqrt{V^2+V^2+2V^2\cos {60}^{\circ }}$
$=\sqrt{2V^2+2V^2\cos {60}^{\circ }}$
$=V\sqrt{2+2\cos {60}^{\circ }}$
$=\sqrt{3}V$