really hard abstract physics problem, i need an equation no values for the variables?

Question

A uniform spherical shell of mass M and radius R rotates about a vertical axis on frictionless bearings(the rotation is along an axis in the venter of the sphere) . A massless cord passes around the equator of the shell, over a pulley of rotational inertia I and radius r, and is attached to a small object of mass m. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object after it falls a distance h from rest? Use energy considerations. (Use g for acceleration due to gravity, and M, R, I, r and m, as appropriate.)

Answer 1

If you say shell, does it mean a hollow sphere? If yes then instead of (2/5) in Fernando’s formulas there must be (2/3). Click me if you have to prove it.

Answer 2

Potential energy of m = m*g*h.
Kinetic energy of sphere = (2/5)*Mv^2/2 (since rotational inertia of a sphere of mass M radius R is (2/5)*M*R^2).
Kinetic energy of a pulley = I*v^2/(2*r^2).
Kinetic energy of mass m = m*v^2/2.

By energy conservation law it follows:
(2/5)*Mv^2/2 + I*v^2/(2*r^2) + m*v^2/2 = m*g*h,
from where you can find v (the speed of the falling mass m after distance h).