# Falling charges, how many will succeed?

A horizontal conducting cylindrical hollow pipe of radius $$R = 54\text{ mm}$$ and length $$L = 100 \text{ cm} (R<<L)$$ has a small hole $$P$$ at its top, at the middle of the length as shown in the figure. Drops of mass $$M = 231 \text{ mg}$$ and charge $$q = 1 \text{ nC}$$ are falling into the hole from point $$A$$, at height $$2R$$ measured from the axis of the cylinder. Assume that the charge in the fallen drop gets uniformly distributed over the surface of the cylinder and charge distributed on cylinder remains uniform throughout. If the number of drops that will be able to enter the cylinder is given as $$n = x \times10^y$$ in scientific notation. Find the value of $$x + y$$.

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