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A point P lies on the axis of a fixed ri...

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

A

zero

B

`sqrt((2GM)/R)`

C

`sqrt((2GM)/R(sqrt(5)-1))`

D

`sqrt((2GM)/R(1-1/(sqrt(5))))`

Text Solution

Verified by Experts

The correct Answer is:
D
`W=Deltak=m[V_(P)-V_(Q)]=1/2mv^(2)`
`m[(-GM)/(sqrt(5)R)+(GM)/R]=1/2mv^(2)`
`v=sqrt((2GM)/R(1=1/(sqrt(5)))`
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