A spherical hole of radius `R//2` is excavated from the asteroid of mass M as shown in the figure the gravitational acceleration at a point on the surface of the asteroid just above the excavation is

Options

A. `(GM)/R^(2)`
B. `(GM)/(2R^(2))`
C. `(GM)/(8k^(2))`
D. `(7GM)/(8R^(2))`

Answer

B

Explanation

`m' = m/((4piR^(3))/3)xx(4pi)/3 R^(3)/8=m/8`
`g=(Gm)/R^(2)-(Gm^(4))/(8R^(2))= (Gm)/(2piR^(2))`