Aditya's challenges in Mechanics 5

Classical Mechanics Level 4

There is a fixed hemispherical cup of radius $R=1 \text{ m}$ . There are 5 point sized balls each of mass $m=1 \text{ kg}$ randomly placed inside the cup and held there. At time zero, the balls are set free.

What is the maximum possible heat (in Joules) that can be produced by an arrangement of this system via collisions?

Details and Assumptions:

$g=10 \text{ ms}^{-2}$ .
Coefficient of restitution for each collision $e=0$ .
This is a theoretical problem.

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