Answer
The brass cylinder and the wood cylinder tie.
Work Step by Step
We can write an expression for the rotational inertia of a solid sphere:
$I = \frac{1}{2}MR^2$
We can use Equation (11-10) to find the acceleration of a solid cylinder down the incline:
$a = \frac{g~sin~\theta}{1+I/MR^2}$
$a = \frac{g~sin~\theta}{1+\frac{1}{2}MR^2/MR^2}$
$a = \frac{g~sin~\theta}{1+\frac{1}{2}}$
$a = \frac{2}{3}~g~sin~\theta$
Since the acceleration of the brass cylinder and the wood cylinder is the same, the time to reach the bottom is the same for both cylinders.
The brass cylinder and the wood cylinder tie.
