Question

Two balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down an frictionless incline. They start together from rest at the top.

a) Which one will have more K.E.?

b) Which one will reach the bottom first or in other words which one has greater velocity?

(Hint: KR = ½ I ω2 and KT = ½ m v2 and v=rω and I=2/5 mr2 ; K.E. = KR + KT and K.E. = P.E.) Please show calculations for each part and clearly explain.

Answer #1

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(c) Which has the greater total kinetic energy at the
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Two spheres have the same radius (R) and same mass (M). One
sphere is solid, and the other is hollow and made of a denser
material. They start from rest at the top of an incline (rolls
without slipping).
(a) Which has greater moment of inertia?
(b) Which has the greater rotational kinetic energy?
(c) Which has the greater total kinetic energy at the
bottom?
(d) Which has the greater speed at the bottom?
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