Question

A particle of mass $m$ oscillates between $P_1$ and $P_2$ inside a fixed smooth spherical shell of radius $R$. At any instant the kinetic energy of the particle is $E$. Then the force exerted by the particle on the shell at this instant is:

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

Answer 1

The correct option is D $\frac{3E}{R}$


Let $\theta$ be the angle formed by the particle with line $P_1{P}_2$.
From the figure we say that
$N-mgsin\theta =\frac{m{v}^2}{R}$ ...........(i)
By applying conservation of energy at this instant we get
$mgR=mg(R-h)+\frac{1}{2}m{v}^2$
$⟹\frac{1}{2}m{v}^2=mgh$ .............(ii)
By using equ (i) and (ii)
$N=mg\left(\frac{h}{R}\right)+\frac{2E}{R}$
$=\frac{E}{R}+\frac{2E}{R}=\frac{3E}{R}$