A small block of mass m is released from rest from point A inside a smooth hemisphere bowl of radius R , which is fixed on ground such that OA is horizontal. The ratio (x) of magnitude of centripetal force and normal reaction on the block at any point B varies with θ as:

Question

A small block of mass m is released from rest from point A inside a smooth hemisphere bowl of radius R , which is fixed on ground such that OA is horizontal. The ratio (x) of magnitude of centripetal force and normal reaction on the block at any point B varies with θ as:, , , ,

MARKS App · Accepted Answer

m v 2 R = N - m g sin ⁡ θ N = m v 2 R + m g sin ⁡ θ By energy conservation, m g R s i n θ = 1 2 m v 2 m v 2 R = 2 m g sin ⁡ θ N = 3 m g sin ⁡ θ R a t i o = m v 2 R N = 2 3 (constant) x = 2 3

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