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

The Correct Option is C

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 F_C

⇒ F_C = 2mg sinθ

Also, N - mg sinθ = F_C

⇒ N - mg sinθ = 2mg sinθ

⇒ N = 3mg sinθ

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

F_C / N = (2mg sinθ) / (3mg sinθ)

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