disc of mass $2M$ and radius $R,$ on the frictionless table. The center of mass of the first disc has an initial velocity $v_0$ and rotates with an angular velocity ${}_0$ as indicated, while the second disc is initially stationary. When the first disc contacts the second $($a "glancing" collision$),$ they instantly stick to each other and move as a single object.

$I_{cm}=\frac{1}{2}M{R}^2$

What is the new center of mass after the collision relative to the contact point of the discs?

a$)\frac{1}{3}R$

b$)-\frac{2}{3}R$

c$)-\frac{1}{3}R$

d$)R$

e$)\frac{2}{3}R$

What is the velocity of the new center of the mass of the combined system after the collision?

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