Answer
The speed of the 100-g ball is 2.5 m/s
Work Step by Step
Let the 100-g ball be at the position x = 0. Let the 200-g ball be at the position x = 30 cm.
We can find the center of mass $x_{com}$ of the system.
$x_{com} = \frac{(100~g)(0)+(200~g)(30~cm)}{100~g+200~g}$
$x_{cm} = 20~cm$
We can find the angular velocity of the system. The system rotates at 120 rpm which is 2 rev/s which is $4\pi ~rad/s$. Therefore, $\omega = 4\pi ~rad/s$
We can find the speed of the 100-g ball. Note that its radius of rotation is 20 cm.
$v = \omega ~r$
$v = (4\pi~rad/s)(0.20~m)$
$v = 2.5~m/s$
The speed of the 100-g ball is 2.5 m/s.
