A point `P` lies on the axis of a fixed ring of mass `M` and radius `R`, at a distance `2R` from its centre `O`. A small particle starts from `P` and reaches `O` under gravitational attraction only. Its speed at `O` will be

Options

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

Answer

A

Explanation

`-(GMm)/(sqrt(R^(2)+4R^(2)))=-(GMm)/(sqrt(R^(2)))+1/2mv^(2)`
`rArr v^(2)=(2GM)/R[1-1/(sqrt(5))]`