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A small spherical body of radius r and density rhomoves with the terminal velocity v in a fluid of coefficient of viscosity etaand density sigma . What will be the net force on the body? |
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Answer» `(4pi )/(3) r^3 (rho - sigma) g ` Now, when the spherical body moves DOWNWARDS in the fluid medium, with terminal velocity (say, `V_("terminal")`) then, sum of the viscous drag and upthrust will be EQUAL to the weight of the spherical body. ` therefore F_v + F_T -W` ` rArr 6pi eta r v_("terminal") + 4/3 pi r^3 sigma g = 4/3 pi r^3 rho g ` ` rArr 6pi eta r v_("terminal") = 4/3 pi r^3 (rho - sigma) g ` ` rArr v_("terminal") = (2r^2 (rho - sigma))/(9 eta) g ` `rArr F_("net") = 0` |
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