A ball (thin spherical shell)of mass m and radius Rand a very small lead marble (much smaller radius thanthe ball, so it can be treated as a point particle) of massM rolls moothly down an incline. The angle of the incline is µ. Note that theirinitial and ¯nal contact points have the samedi®erence in height,h.Rotational inertia of a spherical shell is Icom = 2/3 mR2 =betamR2.
a) Which object will come¯rst to the bottom of the incline and why?
b) Find the di®erence intheir speeds at the bottom of the incline, in terms of m;M; h; µ; g, and numerical constants as needed.
c) Find the di®erence intime when they reach the bottom, in terms of m;M; h; µ;g, and numerical constants as needed.