Question

A point $P(\sqrt3R,0,0)$ lies on the axis of a ring of a mass 'M' and radius 'R'. The ring is located in y-z plane with its centre at origin 'O'. A small particle of mass 'm' starts from 'P' and reaches 'O' under gravitational attraction only. Its speed at 'O' will be

• A. $\sqrt\frac{GM}{R}$
• B. $\sqrt\frac{Gm}{R}$
• C. $\sqrt\frac{GM}{\sqrt2R}$
• D. $\sqrt\frac{GM}{\sqrt {R}}$

Answer 1

The Correct Option is A

According to law of conservation of energy $\frac{1}{2} m V^2 = m(\Delta V)$ $\Rightarrow \frac{1}{2} mV^2 = m \left[ \frac{-GM}{2R} - \left( - \frac{GM}{R}\right) \right]$ $\Rightarrow \frac{1}{2} m V^2 = m \left(\frac{GM}{2R}\right) \, \Rightarrow V = \sqrt{\frac{GM}{R}}$