First slide

Vertical circular motion

Question

One end of a light string of length l is tied to a small sphere and the other end is attached to a fixed point O at the ceiling of a room. The sphere is gently released from rest when the string is horizontal. When the string is vertical, acceleration of the sphere is

Moderate

A

2g
B

zero
C

g
D

g/2

Solution

(1)
The sphere will follow a vertical circular path.
At its lowest position, is speed is V.
Conserving energy, $\frac{1}{2} m V^{2} = m g l \Rightarrow V = \sqrt{2 g l}$
$∴ A c c e l e r a t i o n a t B, a_{n} = \frac{V^{2}}{l} = \frac{2 g l}{l} = 2 g$

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