Question

Two metallic spheres of equal outer radii are found to have same moment of inertia about their respective diameters. Then which of the following statement(s) is/are true ?

• A. Two spheres have equal mass
• B. The ratio of masses is nearly 1.67 : 1
• C. The spheres are made of different materials
• D. Their rotational kinetic energies will be equal when rotated with equal uniform angular speed about their respective diameters

Answer 1

The correct option is D Their rotational kinetic energies will be equal when rotated with equal uniform angular speed about their respective diameters

$K.E=\frac{1}{2}I{\omega }^2$
Since in option d, $\omega$ is given same and as already mentioned moment of inertia about their respective diameters is also same, therefore $K.E$ is constant.

Although, moment of inertia of sphere contains term of mass as well as terms of outer radius and inner radius of sphere. As, only outer radius is given same, so masses need not be equal as change in inner radius can cancel out effect of change in mass to maintain same moment of inertia of both spheres.

Also, we can't determine ratio of mass untill information about inner radius is also given.

Even to comment on density of sphere (material they are made up of), information about inner radius is needed.