Answer
The cannonball's translational kinetic energy at the bottom is greater than the marble's translational kinetic energy.
Work Step by Step
We can write an expression for the rotational inertia of a solid sphere:
$I = \frac{2}{5}MR^2$
We can use Equation (11-10) to find the acceleration of a solid sphere down the incline:
$a = \frac{g~sin~\theta}{1+I/MR^2}$
$a = \frac{g~sin~\theta}{1+\frac{2}{5}MR^2/MR^2}$
$a = \frac{g~sin~\theta}{1+\frac{2}{5}}$
$a = \frac{5}{7}~g~sin~\theta$
Since the acceleration of the marble and the cannonball is the same, the speed at the bottom is the same for both the marble and the cannonball.
We can write an expression for the translational kinetic energy:
$K = \frac{1}{2}Mv^2$
Since the cannonball's mass is greater than the marble's mass, the cannonball's translational kinetic energy at the bottom is greater than the marble's translational kinetic energy.
