Question

At any angular speed, a uniform solid sphere of diameter D has the same rotational kinetic energy as a uniform hollow sphere of the same diameter when both are spinning about an axis through their centers. The moment of inertia of a solid sphere is :

Answer 1

m = (3/5)*M

Step-by-step explanation:

Given:-

- The angular speed of both hollow and solid sphere = w

- The diameter of solid & hollow sphere = D

- The mass of the solid sphere = M

- Both rotate about their common axis with similar rotational kinetic energy.

Find:-

The mass of hollow sphere (m) ?

Solution:-

- The formula for rotational kinetic energy (K.E) of any rigid body is:

K.E = 0.5*I*w^2

Where,

I : Moment of inertia of rigid body

- The rotational kinetic energies of both hollow sphere and solid sphere are same:

0.5*I_solid*w^2 = 0.5*I_shell*w^2

I_solid = I_shell

0.4*M*D^2 / 4 = (2/3)*m*D^2 / 4

(2/5)*M = (2/3)*m

m = (3/5)*M