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A body moving radially away from a plane...

A body moving radially away from a planet of mass `M`, when at distance `r` from planet, explodes in such a way that two of its many fragments move in mutually perpendicular circular orbits around the planet. What will be

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The correct Answer is:
`(a) sqrt((GM)/r); (b) rsqrt(2); (c) sqrt((2GM)/r)`
(i) Centripetal force is provided by gravitational field.
`(m_(1)v^(2))/r=(GMm_(1))/(r^(2))`
`v=sqrt((GM)/r)`
(ii) Maximum distance `=sqrt(2)r`
(iii) Relative velocity just before collision maximum distance `=sqrt(2)v`
maximum distance `=sqrt((2GM)/r)`
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