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Two pendulums are allowed to rotate frictionlessly and without air resistance around the same point of rotation as shown in the figure (it is two balls suspended side by side at the top of a pendulum by rods). Both consist of balls of the same size, on ends of frictionless Ã‚ rods of length r (the rods have negligible mass). One ball has mass m and the other 3m. They are at rest, in contact, immediately above the point of rotation.

1. Where do the masses collide? What are their velocities at this position (relative to your defined coordinate system)?

2. If they collide perfectly inelastically, what is the velocity of the pair immediately after the collision?

3. How far back up (as a fraction of r) do they swing? Does this result make sense?

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