A Level Physics - Gravitation

The answer is option B

Potential = -G(V1).(rho)/2R - G(V2).(2 x rho)/(R + R/2)
where (rho) is the density of the large sphere
V1 is the volume of the large sphere (= (4/3).pi.R^3, pi = 3.14159...)
V2 is the volume of the small sphere (= (4/3).pi.(R/2)^3 )

substitiute the values of V1 and V2 into the equation and simplify.

2010-07-04 16:06:19 補充：
The whole large sphere, of density (rho), has already taken one (rho). Leaving two (rho) for the small sphere. In other words, you could regard the arrangement as a large sphere of uniform density (rho) with a small sphere of density 2 x (rho) added to it....

2010-07-04 16:06:31 補充：
.... Thus the "dark region" has an overall density of 3 x (rho).