A spherical solid ball of volume V is made of a material of density ρ ₁ . It is falling through a

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9-1.Fluid Mechanics

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A spherical solid ball of volume $V$ is made of a material of density $\rho _1$ . It is falling through a liquid of density $\rho _2(\rho _2 < \rho _1)$ . Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$ , i.e., $F_{viscous} =\, -kv^2 (k > 0)$ . Then terminal speed of the ball is

A

$\sqrt {\frac{{Vg({\rho _1} - {\rho _2})}}{k}} $

B

$\frac{{Vg{\rho _1}}}{k}$

C

$\sqrt {\frac{{Vg{\rho _1}}}{k}} $

D

$\frac{{Vg({\rho _1} - {\rho _2})}}{k}$

Solution

Weight – upthrust $=\mathrm{F}_{\mathrm{vis}}$

$\Rightarrow \mathrm{V} \rho_{1} \mathrm{g}-\mathrm{V} \rho_{2} \mathrm{g}=\mathrm{kv}_{t}^{2}$

$\Rightarrow \mathrm{V}_{\mathrm{t}}=\sqrt{\frac{\mathrm{vg}\left(\rho_{1}-\rho_{2}\right)}{\mathrm{k}}}$

Standard 11

Physics

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