A solid cylinder, a solid sphere, and a hollow sphere are released from the top

Question

A solid cylinder, a solid sphere, and a hollow sphere are released from the top of an inclined plane. Once released, they all roll down without slipping. If the radii of all three objects are the same, which one of the three objects will have the greatest speed when reaching the bottom of the slope? The moment of inertia (I) of each object is given by Icylinder=1 2 mr2 , ISolidSphere=2 5 mr2 and IHollowSphere=2 3 mr2 . m and r are the mass and the radius respectively.
(a) Solid Cylinder

(b) Solid Sphere

(c) Hollow Sphere

(d) They all reach the bottom at the same time

Explanation / Answer

v = sqrt(2gh/1+c)

here c is the constant for respective bodies

for cylinder v = sqrt(2gh/1+1/2) = sqrt(4gh/3)

for sphere v = sqrt(2gh/1+2/5) = sqrt(10gh/7)

for hallo sphere v = sqrt(2gh/1+2/3) = sqrt(6gh/5)

v sphere> v cylindr>v hallo sphere

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