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 p

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

TestHub · Accepted Answer

Let the velocity of the particle at the point $P$ is $v$ .

From the conservation of mechanical energy

$\frac{1}{2} m v^{2} = K = m g h$

Let $N$ be the normal reaction between the particle and the shell at this instant. Then

$N - m g \sin θ = \frac{m v^{2}}{R} (\frac{m v^{2}}{R} = \frac{2 K}{R})$

or $N = m g (\frac{h}{R}) + \frac{2 K}{R} = \frac{K}{R} + \frac{2 K}{R} (m g h = K)$

$∴ N = \frac{3 K}{R} = f o r c e o n s h e l l$

Physics - Circular Motion Question with Solution | TestHub

Options:

Doubts & Discussion