A hoop, a uniform solid cylinder, a spherical shell, and a uniform solid sphere are released from rest at the top of an incline. What is the order in which they arrive at the bottom of the incline? Does it matter whether or not the masses and radii of the objects are all the same? Explain.

Solution 18DQ Step 1: We need to assume that all the objects have the same mass.consequently,the bodies have different densities. Given that,let's start our analysis.for any process energy is conserved.for this case there are 3 different types of energy: 1.Translational kinetic energy:because it moving forward. 2. otational kinetic energy:due to rotation. 3.Potential energy. We can write as: 2 2 E = mgh + 1/2mv + 1/2Iw Another assumption is made here is that the objects are rolling without slipping. Then v = rw E = mgh + 1/2mv + Iv /2r2 2