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# Center of Mass (CoM): Dumbbell with One Unknown Mass

APPHMC-H3@NO3

A dumbbell is composed of two spheres that are connected by a rod whose mass is negligible. The distance between the centers of each sphere is $d$. One of the spheres has a mass of $2M$ and the mass of the other sphere is unknown, as shown.

If the dumbbell can balance when supported at a point $2d/3$ from the center of the $2M$ sphere, what is the mass of the second sphere?

A

$2M$

B

$3M$

C

$2 \sqrt { 2 } M$

D

$4M$

E

$5M$