A solid sphere of uniform density and radius `4` units is located with its centre at the origin `O` of coordinates. Two spheres of equal radii `I` 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 in the figure.

Then

Options

A. `(31GM)/1024`
B. `(Gm)/1024`
C. `31GM`
D. zero

Answer

D

Explanation

Let `rho=` density of sphere `R=`radius of sphere, `r=`radius of the spherical cavities.
Mass of the complete sphere `=4/3piR^(3)rho=M`
Mass of the removed sphere `=4/3pir^(3)rho=m`
Here `m=(Mr^(3))/(R^(3))=(M(1)^(3))/((4)^(3))=M/64`
Now `vecI_(r)=vecI+vecI_(P)+vecI_(Q)`
Here `I=0, also vecI_(P)=-vecI_(Q)impliesI_(R)=0`