Question

For a hollow cylinder & a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier on the ground :

Answer 1

i think

hollow cylinder

Answer 2

Answer:

Hollow cylinder

Explanation:

It is to be assumed that each object has a uniform density and that they all will roll without slipping. Thus,

Let mass = m

The initial height = h

Gravity = g

Final velocity = v

Radius = r

Angular velocity = ω = v/r

Moment of inertia = I = kmr² (where k is a measure how close to the edge the mass is, on average)

Thus, using the equation for conservation of energy -

mgh = 1/2mv²+1/2Iω²

= 2gh = v²+kv²

v = √2gh/ 1+k

Thus, to maximize v, k needs to be minimized. Therefore the slowest object will be the hollow cylinder and the fastest will be the solid sphere. Thus, the hollow cylinder will reach earlier on the ground.