Swinging Dumble

Classical Mechanics Level pending

A little sphere of mass M M hangs at the end of a very long thread; to that sphere is, with a weightless rod, attached another little sphere of mass m m . The length of the rod is l l . Initially the system is in equilibrium. What horizontal velocity needs to be given to the bottom sphere for it to ascend the same height with the upper sphere? The sizes of the spheres are negligible compared to the length of the rod.

G i v e n I n f o r m a t i o n : Given Information :

m = 2 M m = 2M

l = 15 m l = 15m

g = 10 m s 2 g = 10\frac{m}{s^{2}}


The answer is 30.

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