In an isolated asteroid of radius R and uniform density $$\rho$$, a spherical cavity of diameter AC = R is excavated, where C is centre of asteroid. Choose correct alternative (s)

A

A ball just dropped from A will strike C with speed $$v = 2R\sqrt{\frac{\pi\rho G}{3}}$$

B

A ball dropped from A will reach C after time $$t = \sqrt{\frac{3}{\pi\rho G}}$$

C

Acceleration of ball dropped from A varies as its distance from O (centre of cavity)

D

Weight of a body placed at B (diametrically opposite to A) on surface of asteroid decreases by a factor $$\frac{7}{8}$$ due to excavation of cavity