First slide

Gravitaional potential energy

Question

A particle of mass ‘m’ moves on the axis of a ring of radius ‘R’ and mass M. If particle at rest is released from ‘P’ then its kinetic energy at centre c will be

Moderate

A

$\frac{G m M}{R}$
B

$\frac{G M m}{2 R}$
C

$\frac{G m M}{\sqrt{3 R}} (\sqrt{3} - 1)$
D

$\frac{\sqrt{3} G M m}{R}$

Solution

distance of the mass m from the ring is $\sqrt{{(\sqrt{3} R)}^{2} + R^{2}} = 2 R$ initial potential energy = - $\frac{G M m}{2 R}$ and final potential energy when at the center is $- \frac{G M m}{R}$
kinetic energy is the difference in potential energy

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