Hey JayDilla, I get 1/3. Here's how:
Kinetic energy due to linear motion is:

where

giving

The rotational part requires the moment of inertia of a solid cylinder

Then the rotational kinetic energy is

Adding the two types of energy and factoring out common terms gives

Here the "1" in the parenthesis is due to linear motion and the "1/2" is due to the rotational part. Since this gives a total of 3/2 altogether, and the rotational part is due to a third of this (1/2), I say it's 1/3.
1) Current in each bulb: 0.1 A
The two light bulbs are connected in series, this means that their equivalent resistance is just the sum of the two resistances:

And so, the current through the circuit is (using Ohm's law):

And since the two bulbs are connected in series, the current through each bulb is the same.
2) 4 W and 8 W
The power dissipated by each bulb is given by the formula:

where I is the current and R is the resistance.
For the first bulb:

For the second bulb:

3) 12 W
The total power dissipated in both bulbs is simply the sum of the power dissipated by each bulb, so:

Answer: D. 292,338 J
This is the correct answer :)