(a) Applying conservation of angular momentum
`m upsilon_(1) (2R) = m upsilon_(2) (4R)`
`upsilon_(1) = 2 upsilon_(2)` ..(i)
From conservation of energy
`(1)/(2) m upsilon_(1)^(2) - (GMm)/(2R) = (1)/(2) m upsilon_(2)^(2) - (GMm)/(4R)` ..(ii)
Solving Eqs. (i) and (ii), we get
`upsilon_(2) = sqrt((GM)/(6R)), upsilon_(1) = sqrt((2Gm)/(3R))`
(b) If `r` is the radius of curvature at point `A`
`(m upsilon_(1)^(2))/(r) = (GMm)/((2R)^(2))`
`r = (4 upsilon_(1)^(2)R^(2))/(GM) = (8R)/(3)` (putting value of `upsilon_(1)`)