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(D) The moment of inertia $(I)$ of a sphere about its diameter is given by $I = \frac{2}{5}MR^2$, where $M$ is the mass and $R$ is the radius.Since th

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Their rotational kinetic energies will be equal when rotated with equal uniform angular speed about their respective diameters.

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(D) The moment of inertia $(I)$ of a sphere about its diameter is given by $I = \frac{2}{5}MR^2$, where $M$ is the mass and $R$ is the radius.Since the spheres have equal outer radii $(R_1 = R_2 = R)$ and equal moments of inertia $(I_1 = I_2)$, it follows that $\frac{2}{5}M_1R^2 = \frac{2}{5}M_2R^2$, which implies $M_1 = M_2$.However, if the spheres are hollow or have different internal structures, they could have the same moment of inertia despite different masses if their mass distributions differ.Given the problem states they have the same moment of inertia, the rotational kinetic energy $(K_r)$ is defined as $K_r = \frac{1}{2}I\omega^2$.Since $I_1 = I_2$ and both are rotated with the same angular speed $(\omega_1 = \omega_2 = \omega)$, their rotational kinetic energies must be equal $(K_{r1} = K_{r2} = \frac{1}{2}I\omega^2)$.Thus, option $(D)$ is the correct statement.

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

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