A metal sphere of radius 1 mm and mass 50 mg falls vertically in glycerine. Find (a) the viscous force exerted by the glycerine on the sphere when the speed of the sphere is 1 cm s-1, (b) the hydrostatic force exerted by the glycerine on the sphere and (c) the terminal velocity with which the sphere will move down without acceleration. Density of glycerine `=1260kgm^-3` and its coefficient of viscosity at room temperature = 8.0 poise.

A metal sphere of radius 1 mm and mass 50 mg falls vertically in glyce

1.	A metal sphere of radius 1 mm and mass 50 mg falls vertically in glycerine. Find (a) the viscous force exerted by the glycerine on the sphere when the speed of the sphere is 1 cm s-1, (b) the hydrostatic force exerted by the glycerine on the sphere and (c) the terminal velocity with which the sphere will move down without acceleration. Density of glycerine `=1260kgm^-3` and its coefficient of viscosity at room temperature = 8.0 poise.
Answer» Correct Answer - A::B::C (a) `F_(r)=6pietarv` `=6 pi (0.8)(10^(-3))(10^(-2))` `=1.5xx10^(-4)N` (b) Hydrostatic force= upthrust `=((4)/(3) pir^(3))rho g=(4)/(3) pi (10^(-3))^(3)xx1260xx9.8` `=5.2xx10^(-5) N` (c ) At terminal velocity `w=`Upthrust+viscous force or, `(50xx10^(-3)xx9.8)=(5.2xx10^(5)` `+6pi (0.8)(10^(3))v_(T)` Solving we get `v_(T)=32.5 m//s`.

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