Question

A coin and a ring of same mass and diameter r allowed to roll smoothly from the top of a inclined plane. which one reaches the bottom first

Answer 1

When it comes to rolling, we look for moment of inertia. Moment of Inertia may be very simply defined as the resistance to rolling motion. So lesser the moment of Inertia, the more acceleration it will have. Here Moment of inertia of Coin is less than that of Ring.

Here this answer comes as they have same mass and same diametr.If they are different calculate with the help of these formulae and see which has smaller moment of inertia.

I (Moment of inertia) = M(R^2) for a ring

I = M(R^2)/2 for a disc.

Now consider another situation, when this plane is frictionless. When it is frictionless no body can roll they can only slide. If that happens which will reach first think yourself..

Answer 2

THE COIN WILL REACH FIRST.Because if they are with same mass and diameter,the ring has a hollow part in it and it will lay down or it will reaches slowly than coin. so we can conclude that coin will reaches first.