A sphere and a cylinder have the same radius and the same mass. They start from rest at the top of an incline, (a) Which reaches the bottom first? (b) Which has the greater speed at the bottom? (c) Which has the greater total kinetic energy at the bottom? (d) Which has the greater rotational kinetic energy? Explain your answers.

Step-by-step solution

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A sphere and cylinder are of the same mass = M and same radius = R.

The Moment of Inertia of the sphere

The Moment of Inertia of the cylinder I2 = MR2

Applying the conservation of Energy at the top and bottom of the incline, we get:

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