A Body moving radially away from a planet of mas M, when at distance r from planet, explodes in such a way that two of its many fragments move in mutually prependicular circular orbits around the planet what will be
(i). Then velocity in circular orbits?
(ii). Maximum distance between the two fragments before collision and
(iii). Magnitude of their relative velocity just before they collide?

Answer

(a) `sqrt((GM)/(r ))` ; (b) `rsqrt(2)`; (c ) `sqrt((2GM)/(r ))`

Explanation

(i) Centripetal force is provided by gravitational field.
`(m_(1)v^(2))/(r )=(GMm)/(r^(2)) rArr v = sqrt((GM)/(r ))`

(ii) Maximum distance `= sqrt(2)r`
(iii) Relative velocity just before collision
Mag. of relative velocity `= sqrt(2)v = sqrt((2GM)/(r ))`