Question

A particle of mass, $m$, oscillates along a semi-circular path ACB inside a fixed smooth spherical shell of radius, $R$. It is released from point A. If at any instant KE of the particle is $K$, then the force applied by particle on the shell at this instant is:

• A. $\frac{K}{R}$
• B. $\frac{2K}{R}$
• C. $\frac{3K}{R}$
• D. $\frac{K}{2R}$

Answer 1

Answer: (C)

$\frac{3K}{R}$

From the conservation of energy principle:

$mgR\sin \theta =\frac{1}{2}m{v}^2$

And, from the equation of motion:

$2mg\sin \theta =\frac{m{v}^2}{R}$

So, using the given condition:

$mgR\sin \theta =K$
and, $mg\sin \theta =\frac{K}{R}$

Force applied by the particle on the shell:

$N=\frac{m{v}^2}{R}+mg\sin \theta$
or, $N=2mg\sin \theta +mg\sin \theta$

or, $N=3mg\sin \theta$

or, $N=\frac{3K}{R}$