Question

A particle of mass $‘m^{\prime }$ oscillates along the horizontal diameter $AB$ inside a smooth spherical shell of radius $R$. At any instant $K.E.$ of the particle is $K$. Then force applied by particle on the shell at this instant is:

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

Answer 1

The correct option is B $\frac{3K}{R}$

Energy conservation at B and particle position,
$mgR\sin \theta =\frac{1}{2}m{v}^2=K\dots \left(i\right)$
$mg\sin \theta =KR$
From the $FBD$ of the particle, $N=mg\sin \theta +\frac{m{v}^2}{R}$
Using $\left(i\right)$,
$N=3mg\sin \theta$
$=\frac{3K}{R}$

Final Answer: (c)