More Physics Homework Help at LeiAcademy.

Part1: If the pulley is uniform, then it can be considered as a uniform disk, which has ||I=\frac {1}{2}mR^2||.

Part2: Based on the time and distance it falls, you can find its actual acceleration as: $$\Delta y=V_{y0} \Delta t+\frac 1 2 a\Delta t^2.$$

Plug in the given distance, time and mass, etc., one can find ||a||.

With the rotational and linear motion, one can also find the linear acceleration in terms of the moment of inertia — here you would leave ||I|| in the equation as an unknown variable.

Solving the equations, you will get $$a=\frac {m_1}{\frac {I}{R^2}+m_1}.$$

Plug in the ||a|| found with the falling distance and time, you can find the numerical value of ||I||. Compare this ||I|| with the ||I|| calculated in the first part to determine if the disk is uniform or not.