1) A Spherical Shell, Solid Sphere and Cylinder starting from the same height roll without slipping down an incline plane. They all have the same radius and same mass. Which object arrives at the bottom first? (Ispherical shell = 2/3 MR2 , Icylinder = ½ MR2 , Isphere = 2/5 MR2 )

The solid sphere will arrive at the bottom first.

Explanation:

From the question, the 3 objects start from the same height and roll without slipping down the same incline plane. We are also told that they have the same mass and radius. So, we can say they will have same torque.

Thus,

The solid sphere (I_s) has the moment of inertia of 2MR²/5 = 0.4MR²

That of the spherical shell (Isp) is 2MR²/3 = 0.67MR²

That of the cylinder is ½•MR² =0.5 MR²

Inspecting the values of the moment of inertia, The moment of inertia for spherical shell is the largest thereby having a greater resistance to motion. While the moment of inertia of the solid sphere is the least thereby having least resistance. Thus, least resistance would lead to faster speed and thus the solid sphere will have the greater speed and will arrive first.