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An object with mass $m$ hangs from a cylindrical pulley (with mass $M$ and radius $R$) at the end of a massless string. The rotational inertia for a cylinder is $I = \cfrac {MR^2}{2}$.

If the system starts from rest, what is the angular momentum of the pulley after a period of time, $t$?

A

$\cfrac {mgRt}{2}$

B

$\cfrac {mgRt}{M}$

C

$mgRt$

D

$\cfrac {mMgRt}{(M+2m)}$

E

$\cfrac {mMgRt}{2}$

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