First slide

Vertical circular motion

Question

A simple pendulum consists of light string from which a spherical bob of mass m is suspended. The distance between the point of suspension and the centre of the bob is l. The bob is given a tangential velocity v at the position of equilibrium (bottom). What can be maximum value of V so that the pendulum oscillates without the string becoming slack?

Moderate

A

$\sqrt{gl}$
B

$\sqrt{2 gl}$
C

$\sqrt{4 g l}$
D

$\sqrt{5 g l}$

Solution

The pendulum can oscillate without string becoming slack, when the bob describes semicircle. Hence
$\frac{1}{2} {mv}^{2} = mgl or v = \sqrt{(2 gl)}$

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