Consider `a` thin spherical shell of uniform density of mass `M` and radius `R`:

Options

A. The gravitational field inside the shell will be zero
B. The gravitational self energy of shell is `(GM^(2))/(2R)`
C. Attractive force experience by unit area of the shell pull the other half is `(GM^(2))/(2R^(2))`
D. Net gravitational force with which one hemisphere of the shell arracts other, is `(GM^(2))/(8R^(2))`

Answer

A, B, D

Explanation

`F=(-GMm)/(R^(3))x`
`a=(-GM)/(R^(3))x`
`a=-omega^(2)x`
`omega=sqrt((GM)/R^(3))`
`V=Romega=Rxxsqrt((GM)/(R^(3)))=sqrt((GM)/R)`
After collision, velocity of ball towards 'A'
`V_(C)=esqrt((GM)/R)=0.2sqrt((GM)/R)`
`V_(C)=1/5sqrt((GM)/R)`
`A^(1)=(V_(c))/(omega)=(1/5sqrt((GM)/R))/(sqrt((GM)/(R^(3))))=R/5`
`:.` Net distance `=R+R/5+R/5`