From a solid sphere of mass M and radius `R/2` aspherical portion of radius ž is romoved as shown in figure. Taking gravitational potential V = 0 and `r = oo` , the potential at the centre of the cavity thus form is ......... . (G = Gravitational constant)

Options

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

Answer

B

Explanation

`implies` Gravitational potential of earth (sphere) is `V_1 = - (GM)/(2R^3) [ 3R^2 -R^2/4] " "...(1)`
and Gravitational potenital of portion `R/2`
`V_2 =-((3GM)/8)/(2(R/2))`
Now , `V = V_1 -V_2`
`=-(3GM)/(2R) +(GM)/(8R) +(3GM)/(8R)`
`=- (12GM + GM + 3GM)/(8R)`
` = - (8GM)/ (8R)`
`= - (GM)/R`