Two matchsticks are laid side-by-side on the surfaces of water. When a drop of light oil on the end of a third match stick is touched to the surface film between the two floating sticks, the two match sticks :

A metallic shpere of radius $1.0\times 10^{-3}m$ and density $1.0\times 10^{4}kg/m^3$ enters a tank of water after a free fall, falling through a distance of h in the earth's gravitational field. If its velocity remains unchanged after entering water, determine the value of h.

[Given : coefficient of viscosity of water = $1.0\times 10^{-3}N-s/m^2,g=10m/s^2$ and density of water = $1.0\times 10^{3}kg/m^3$]