From a solid sphere of mass m and radius R, a spherical portion of raidus R/2 is removed, as shown in the figure. Taking gravtitational potential V=0 at `r=0`, the potential at the centre of the cavity thus formed is (G=Gravitational constant).

Options

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

Answer

B

Explanation

Potential at internal point sphere at a distance r is
`v=(-GM)/R[3/2-(r^(2))/(2R^(2))]` at `r=R/2`
`v_(1)=(-11)/8(GM)/R`
For the removed part
`v_(2)=3/2(G M/8)/(R/2)=3/8(GM)/R`
`v=v_(1)+v_(2)=(-GM)/2`