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Two masses initially at rest are connected by a string passed over a massless pulley. Initially, the smaller mass $m$ is height $h$ lower than the bigger mass, $M$. $M$ falls through height $h$ while pulling mass $m$ up by the same amount. Take the system to be operating under ideal conditions. The speed $v$ of the smaller mass after this transition has taken place is

A

$v = \sqrt{2gh}$

B

$v = \sqrt{2gh \frac {M} {M+m}}$

C

$v = \sqrt{2gh \frac {M-m} {M}}$

D

$v = \sqrt{2gh \frac {M+m} {M-m}}$

E

$v = \sqrt{2gh \frac {M-m} {M+m}}$

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