A solid sphere of uniform density and radius 4 units is located with its centre at the origin O of coordinates. Two sphere of equal radii 1 unit, with their centres at A(-2,0 ,0) and B(2,0,0) respectively, are taken out of the solid leaving behind spherical cavities as shown if fig Then:

Answer

D

Explanation

Let `rho`=density of sphere, `R`=radius of sphere, `r`=radius of spherical cavity. Mass of complete sphere`=4/3piR^(3)rho=M`
Here, `m=(Mr^(3))/(R^(3))=(M(1)^(3))/((4)^(3))=M/64`.
Now, `vec(I)_(R)=vec(I)+vec(I)_(P)+vec(I)_(Q)`, Here, `vec(I)_(R)=0`, also `vec(I)_(P)=-vec(I)_(Q)`.