In an isolated asteroid of radius R and uniform density , a...

In an isolated asteroid of radius

R

and uniform density

\rho

, a spherical cavity of diameter

A C=R

is excavated, where

C

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

In an isolated asteroid of radius R and uniform density , a spherical cavity of diameter A C=R is excavated, where C is

Options

AA ball just dropped from A will strike C with speed $v=2 R \sqrt{\frac{\pi \rho G}{3}}$
BA ball dropped from A will reach C after time $t=\sqrt{\frac{3}{\pi \rho G}}$
CAcceleration of ball dropped from A varies as its distance from O (centre of cavity)
DWeight 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.

Correct answer

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

Step-by-step solution

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