A spherical shell and a solid sphere (both of the same total mass)are rotating about a diameter at the same angular frequency and with the same rotational kinetic energy.What is the ratio of the spherical shell radius to the solid sphere (i.e.,R_{spherical shell}/R_{solid sphere})? A)(2/5)^1/2 B)(3/10)^1/2 C)(1/2)^1/2 D)(3/5)^1/2 E)(2/3)^1/2

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Quizplus · Accepted Answer

The rotational kinetic energy of a solid sphere is (2/5)MR^2ω^2, while that of a spherical shell is (1/2)MR^2ω^2. Since the two spheres have the same total mass and rotational kinetic energy, we have (2/5)MR^2ω^2 = (1/2)MR^2ω^2, which gives R_spherical shell/R_solid sphere = (3/5)^1/2.

A Spherical Shell and a Solid Sphere (Both of the Same