question_answer

  A point particle is held on the axis of a ring of mass m and radius r at a distance r from its centre C. When released, it reaches C under the gravitational attraction of the ring. Its speed at C will be         [JEE ONLINE 26-05-2012]

A) \[\sqrt{\frac{2Gm}{r}\left( \sqrt{2}-1 \right)}\]

B)      \[\sqrt{\frac{Gm}{r}}\]

C) \[\sqrt{\frac{2Gm}{r}\left( 1-\frac{1}{\sqrt{2}} \right)}\]

D)      \[\sqrt{\frac{2Gm}{r}}\]

Correct Answer: C

Solution :

[c] Let 'M' be the mass of the particle

Now,

i.e.

or

or