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# Atwood's with Variables

APPH12-XVJ50W

A box of mass $M$ is attached to another smaller box of mass $m$ by a lightweight cord and hung over opposite sides of a lightweight pulley. The whole system is released from rest and accelerates at a rate of $a$.

Which of the following is a correct expression for the mass $m$ of the smaller box?

A

$$\frac { M\left( a-g \right) }{ a+g }$$

B

$$\frac { M\left( a+g \right) }{ a+g }$$

C

$$\frac { M\left( a+g \right) }{ g-a }$$

D

$$\frac { M\left( g-a \right) }{ a+g }$$