Question

The moment of inertia of a solid sphere of density rho and radius r about its diameter is

Answer 1

Answer:

The answer will be  176/105 x r^5rho

Explanation:

According to the problem the density of the sphere and the radius of the sphere is given

Now we know that for a solid sphere the moment of inertia is (2/5)mr^2

Again we know that density = mass/volume = m/v

Therefore rho = m/v

               => m = rho x v

               =>   m = rho x (4/3)πr^3

Therefore the moment of inertia =

                      (2/5) x rho x (4/3)πr^3 x r^2 = (8 / 15)πr^5rho = 176/105 x r^5rho