Work and Rotational Kinetic Energy

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Homework Statement


(a) If R = 12 cm, M = 360 g, and m = 20 g (below), find the speed of the block after it has descended 50 cm starting from rest. Solve the problem using energy conservation principles. (Treat the pulley as a uniform disk.)


Homework Equations


KEi + PEi = KEf + PEf



The Attempt at a Solution


0 + mgh = (1/2)mv^2 + (1/2)Iw^2 + 0

mgh = (1/2)mv^2 + [(1/2)(1/2)mr^2](v/r)^2

mgh = (1/2)mv^2 + [(1/4)mr^2](v/r)^2

4mgh = 2mv^2 + mr^2(v/r)^2

but I don't this has got to be wrong somewhere because the r's will cancel out and I know that they need to be in the equation for velocity..can anyone help? I would greatly appreciate it!
 

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