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A frictionless circular piston of area $10^{-2} \: m^2$ and mass $100 \: kg$ sinks into a cylindrical container of the same area filled with water of density $1000 \: kg/m^3$ as shown in the figure. The container has a hole of area $10^{-3} \: m^2$ at the bottom that is open to the atmosphere. Assuming there is no leakage from the edges of the piston and considering water to be incompressible, the magnitude of the piston velocity (in $m/s$) at the instant shown is _____ (correct to three decimal places).
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