First slide

Vertical circular motion

Question

A simple pendulum of length I has a maximum angular displacement $θ$ . The maximum kinetic energy of the bob of mass m will be

Moderate

A

$m g l (1 - \cos θ)$
B

$m g l \cos θ$
C

$m g l \sin θ$
D

None of these

Solution

Height, $h = l (1 - \cos θ)$
$v_{m}^{2} = 2 g h = 2 g l (1 - \cos θ)$
$∴$ Maximum kinetic energy, $K_{m} = \frac{1}{2} m v_{m}^{2} = m g l (1 - \cos θ)$

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