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

A, B, C

Explanation

(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`.