In the figure shown there is a hollow hemisphere of radius 'R'. It has a uniform mass distribution having total mass m. The gravitational potential at points A, D and B are` V_A` , `V_D` and `V_B` respectively. Distance of D and B from centre C are R/2 and 2R respectively. The points C, D and B are lying on radial line of the hollow hemisphere

Options

A. `V_(A)=-(Gm)/(R)`
B. `V_(D)=-(Gm)/(R)`
C. `V_(B)=-(Gm)/(2R)`
D. `V_(A)=V_(D)ltV_(B)`

Explanation

Consider another identical hemisphere to complete a hollow spherical shell the potential at a point D due to half shell
`V_(D)=(1)/(2)xx` potantial due to complete shell at D (due to symmetry) `=(1)/(2)xx(-(G.2m)/(R))=-(Gm)/(R)`
`V_(A)=(1)/(2)xx` potential due to complete shell at `A=(1)/(2)xx(-G.2m)/(R))=-(Gm)/(R)`
`V_(B)=(1)/(2)xx` potential due to complete shell ab B (again due to symmetry) `=(1)/(2)xx-(Gxx2m)/(2R)=-(Gm)/(2R)`
`V_(A)=V_(D)=-(Gm)/(R),V_(B)=-(Gm)/(2R)`