A hollow cylinder, a solid cylinder, and a solid sphere all have equal mass M an

Question

A hollow cylinder, a solid cylinder, and a solid sphere all have equal mass M and equal radius R. They all rotate with equal angular speed italic omega . For the cylinders the axis of rotation is the symmetry axis through the center, for the sphere the axis of rotation goes through the center of the sphere. Which of the following statements is true?

A. The kinetic energy of the rotation of the hollow cylinder is larger than that of the solid cylinder.

B. The kinetic energy of the rotation of the hollow cylinder is smaller than that of the solid cylinder.

C. The kinetic energy of the rotation of the sphere is larger than that of the solid cylinder.

D. Both A and C are correct.

Explanation / Answer

A only true.

here is the explanation.

Rotational kinetic energy, KE = (1/2)*I*w^2

we know, I_hallowCylliner = M*R^2

I_solidCyllinder = 0.5*M*R^2

I_solidsphere = (2/5)*M*R^2 = 0.4*M*R^2

clealry,

I_solidsphere < I_solidCyllinder < I_hallowCylliner

KE_solidsphere < KE_solid Cyllinder < KE_hallowcyllinder

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