BITSAT2021PhysicsGravitationActual
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
Options
- A2 G m r ( 2 -1)
- BG m r
- C2 G m r (1- 1 2 )
- D2 G m r
Correct answer
C. 2 G m r (1- 1 2 )
Step-by-step solution
Let ' M ' be the mass of the particle Now, E_ initial =E_ final i.e. GMm 2 r +0= GM m r + 1 2 MV ² or, 1 2 MV ²= GM m r [1- 1 2 ] 1 2 ~V ²= G m r [1- 1 2 ] or, V = 2 Gm r (1- 1 2 )