From a solid sphere of mass M and radius R, a spherical portion of radius R/2 is removed, as shown in the figure Taking gravitational potential `V =0at r = oo,` the potential at (G = gravitational constatn)

Options

A. `(-2GM)/(3R)`
B. `(-2GM)/(R )`
C. `(-GM)/(2R)`
D. `(-GM)/(R )`

Answer

D

Explanation

(d) Due to complete solid sphere, potential at point P
`V_(sphere) = (-GM)/(2R^3)[(3R^2 - ((R )/(2))^2))]`
`(-Gm)/(2R^3)((11R^2)/(4)) = - 11(kGM)/(8R)`

Due to cavity part potential at point P
`V_(cavity) =-(3)/(2) (8)/(R)/(2) =-(3GM)/(8R)`
So potential at the centre of cavity
`=V_(sphere) - V_(cavity) =-(11GM)/(8R) - (-(3)/(8) (GM)/(R )) = (-GM)/(R )`