Circular Motion #5

Classical Mechanics Level 3

A sphere of mass m m , radius r r moves in a circle with constant speed v v , always touching the inner surface of a fixed hollow cylinder with radius R R . The top view of the system is shown. All surfaces are smooth. If the magnitude of the normal reaction (in Newtons) exerted by the cylinder on the sphere is A B \frac{ A } { B } where A A and B B are co-prime positive integers, what is A + B A + B ?

  • m = 0.1 kg m = 0.1 \text{ kg}
  • v = 1 m s − 1 v = 1 \text{ m s}^{-1}
  • r = 0.1 m r = 0.1 \text{ m}
  • R = 1 m R = 1 \text{ m}

This problem is part of the set - Circular Motion Practice


The answer is 10.

Pranshu Gaba by Pranshu Gaba , 22, India

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1 solution

Kalash Pai
Nov 4, 2015

Drawing free body diagram, (in the frame of moving sphere), Forces acting on the sphere are Normal reaction perpendicular to the circle at the point of contact (passing through centre) and Centrifugal pseudoforce mv^2/(R-r) (We are considering motion of centre of mass) Equate the forces, we get the answer

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Hmm.. This is not quite right. You are drawing the free body diagram in the frame of hollow cylinder, which is an inertial frame. Pseudo forces do not appear in inertial frames.

Pranshu Gaba - 5 years, 7 months ago

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Sorry, correction made.

Kalash Pai - 5 years, 7 months ago

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