A point `P` lies on the axis of a fixed ring of mass `M` and radius `a`, at a distance `a` from its centre `C`. A small particle starts from `P` and reaches `C` under gravitational attraction only. Its speed at `C` will be.

Options

A. zero
B. `sqrt((2GM)/R)`
C. `sqrt((2GM)/R(sqrt(5)-1))`
D. `sqrt((2GM)/R(1-1/(sqrt(5))))`

Answer

D

Explanation

Gravitational potential at `P`
`v_(p)=(-GM)/sqrt((5R)`
Gravitational potential at `O`
`v_(0)=-(GM)/R`
Using work energy theorem,
`W=/_\Kimpliesm[v_(P)-v_(O)]=1/2mv^(2)`
`m=[(GM)/r-(GM)/sqrt(5R)]=V`