A hollow cylinder and a solid cylinder having the same mass and diameter are rel

Question

A hollow cylinder and a solid cylinder having the same mass and diameter are released from rest simultaneously at the top of an inclined plane. Which reaches the bottom first? Explain. Animals that depend on being able to run fast have slender lower legs with flesh and muscle concentrated higher up near the shoulder. Why is this distribution of mass advantageous? Why is it that a child playing tightrope on a railroad track rail finds it easier to maintain her balance when her arms are fully outstretched to the sides? A diatomic molecule can be thought of as something like a weight lifting barbell with most of the mass of the molecule concentrated in two spherical (radius r) mass separated by a distance d>>r.. About what axis through the center of mass of the molecule would the moment of inertia be the least? About what axis through the center of mass of the molecule would the moment of inertia be the greatest?

Explanation / Answer

Solving 1st question

Let us compare moment of inertia .Comparing the moments of inertia should give you the correct ordering, with the given conditions that the masses and radii of the objects are the same.

acceleration = g*sin(theta)/(1+I/(M*R^2))

where g is the acceleration due to gravity, 9.81 m/s^2, theta is the angle the incline makes with respect to the horizontal, I is the moment of inertia of the rolling object, M is the mass of the rolling object, and R is the radius of the rolling object.

for solid cylinder ,I=0.5MR^2

for hollow cylinder I=MR^2

by putting value

acceleration for solid cylinder=gsin(theta/1.5 ,for hollow cylinder =gsin(theta)/2

so the acceleration of solid cylinder will be more so it will reach first

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