A small spherical ball of radius 0.1mm and density 10⁴kgm^-3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity inside water, then the value of h will be_________ m.

(Given g = 10 ms^-2, viscosity of water = 1.0 × 10^-5 N-sm^-2).

mg = F_B + F_v $\Rightarrow \frac{4\pi }{3}{r}^3\rho g=\frac{4\pi }{3}{r}^3\sigma g+6\pi \eta rv$

$\Rightarrow v=\frac{2r^2\left(\rho -\sigma \right)g}{9\eta }=\frac{2\times 0.1\times 0.1\times 10^{-6}\times \left(10^4-10^3\right)\times 10}{9\times 1.0\times 10^{-5}}$

$\Rightarrow h=\frac{400}{2g}=20m$

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