Question

A bead of mass m is released from rest at A to move along the fixed smooth circular track as shown in figure. The ratio of magnitudes of centripetal force and normal reaction by the track on the bead at any point P0 described by the angle θ ( ≠ 0 ) would

• A. Increase with θ
• B. Decrease with θ
• C. Remain constant
• D. First increase with θ and then decrease

Answer 1

Answer: (C)

Remain constant

Answer 2

The correct answer is option C) Remain constant

Applying the law of conservation of energy at point P0 we get

1/2 mv2 = mgR sinθ

⇒ mv2 / R = 2mg sinθ

But mv2 / R = centripetal force FC

⇒ FC = 2mg sinθ

Also, N - mg sinθ = FC

⇒ N - mg sinθ = 2mg sinθ

⇒ N = 3mg sinθ

Therefore, the ratio of centripetal force to the normal reaction is given by

FC / N = (2mg sinθ) / (3mg sinθ)

⇒ FC / N = 2/3 that represents a constant value.