# Getting back to the old things #4

Consider a hypothetical planet which is a very long solid cylinder of radius $$R$$ and has uniform density $$\rho$$. There is no atmosphere above the surface of the planet.

Now, somewhere from its curved surface, a small object is projected radially outward such that it reaches up to a maximum distance of $$3R$$ from the axis.

If the speed of projection can be represented as $$a R\sqrt{\pi \rho G \ln b}$$, where $$a$$ and $$b$$ are positive integers and $$G$$ is the universal gravitational constant, then find $$a+b$$.

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