A particle of mass m oscillates along the horizontal diameter A B inside a smooth spherical shell of the radius R . At any instant the kinetic energy of the particle is K . Then the force applied by particle on the shell at this instant is

Question

A particle of mass m oscillates along the horizontal diameter A B inside a smooth spherical shell of the radius R . At any instant the kinetic energy of the particle is K . Then the force applied by particle on the shell at this instant is, K R, 2 K R, 3 K R, K 2 R

MARKS App · Accepted Answer

Let the velocity of the particle at the point P is v . From the conservation of mechanical energy 1 2 m v 2 = K = m g h Let N be the normal reaction between the particle and the shell at this instant. Then N - m g sin ⁡ θ = m v 2 R m v 2 R = 2 K R or N = m g h R + 2 K R = K R + 2 K R m g h = K ∴ N = 3 K R = f o r c e o n s h e l l

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