Calculate the gravitational potential at the centre of base of a solid hemisphere of mass `M`, radius `R`.

Explanation

Consider a hemispherical shell of radius r and thickness dr. Its mass is given by
`dm=M/(2/3piR^(3))(2pir^(2)dr)=(3Mr^(2)dr)/(R^(3))`

Since all point of this hemispherical shell are at the same distance r form centre O, potential at O due to it is
`dV=(-Gdm)/r=(-3GMrdr)/(R^(3))`
`:.V=int_(0)^(R)dV=(-3GM)/(2R)`