Question

The bob of a simple pendulum at rest position is given minimum velocity in horizontal direction, so that it describes vertical circle of radius equal to length of simple pendulum. If velocity of the bob at the highest point is $V$, then velocity is at an angular displacement $60$ from lowest point is:

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

Answer 1

The correct option is C $2V$

Velocities are critical:
$V=\sqrt{gR}$

$H=R(1-cos{60}^0)$

$=\frac{3R}{2}$

Apply Work Energy Theorem between A and B,
$\frac{3}{2}mgR=\frac{m{V}_0^2}{2}-\frac{m(\sqrt{gR}{)}^2}{2}$

$⟹2\sqrt{gR}=V_0$

$V_0=2V$