Fluid Mechanics

JEE Main level, single correct, medium

184 of 192

Question 184 of 192

The terminal velocity (vt)\left({v}_{t}\right) of the spherical rain drop depends on the radius (r)\left(r\right) of the spherical rain drop as

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Answer: (B) r2{r}^{2}

The terminal velocity of a sphere of radius rr and density ρ\rho, immersed in a liquid of density σ\sigma and viscosity η\eta is given by vT=29(ρ−σ)r2gη{v}_{T}=\dfrac{2}{9}\dfrac{\left(\rho -\sigma \right){r}^{2}g}{\eta }
Hence, for spherical raindrop, vT∝r2{v}_{T}\propto {r}^{2}.

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