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., $F_{viscous}= -kv^2 (k >0 )$,The terminal speed of the ball is
AIEEE 2008,AIIMS 2013, Diffcult
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The condition for terminal speed $\left( {{V_t}} \right)$ is $Weight=Buoyant\,force+Viscous\,force$
$\therefore \,V{\rho _1}g = V{\rho _2}g + kv_t^2$
$\therefore {V_t} = \sqrt {\frac{{Vg\left( {{\rho _1} - {\rho _2}} \right)}}{k}} $
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