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Friction and Vertical Circular Motion Problems

A smooth ring...

Question

A smooth ring of mass m can slide on a fixed horizontal rod. A string tied to the ring passes over a fixed pulley B and carries a block C of mass as shown below. As the ring starts sliding.

A

The acceleration of the ring is

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B

The acceleration of the ring is

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C

The acceleration of the ring is

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D

The acceleration of the ring is

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Solution

The correct option is A
The acceleration of the ring is

$T c o s θ = m a 2 m g - T = 2 m A a c o s θ = A a = \frac{2 g c o s θ}{1 + 2 c o s^{2} θ}$

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