Question

If a cube of side r/2 is removed from a uniform sphere of radius r as shown in the figure the shift in centre mass is

Answer 1

Explanation:

The formula for calculting the shift in centre of mass is ;

Shift = Removed mass / (original mass - removed mass) x D

Here is D is the diameter of the object being removed.

Now the volume of sphere having radius R is given as;

V = 4/3 pi x r^3

Mass of sphere would be ;

m = V x d

m =  4/3 pi x r^3

Similarly mass of cube removed

m' = 1/8 r^3 d

The shift in centre of mass = 1/8 r^3 d / (4/3 pi x r^3  - 1/8 r^3 d) x r/2