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, D

Explanation

`r=1mm=10^-3m`
`v=10^-2m/s`
`eta=8 poise =0.8` decapoise
`=m=50mg=50x10^-3kg`
`sigma=1260kg/m^3`
a. viscous force `=6pieta rv`
`=6xx(3.14)x(0.8)xx(10^-3xx(10^-2)`
`=1.50xx10^-4N`
h. Hydrostatic force `=B=(4/3)pir^2sigmag`
`=(4*3)xx(3.14)xx(10^-9)xx1260xx10`
`=5.275xx10^-5N`
c. `pi eta rv+(4/3)pir^3 rho=mg`
`rarr v=(mg-4/3pi^r^2sigma g)/(6pietar)`
`=(50xx10^-34/3xx3.14xx10^-6xx1260x10)/(6xx3.14xx0.8xx10^-3)`
`=500-43xx3.14xx10^-3xx1260xx10)/(6xx3.14xx0.8)`
`=2.3cm/sec`