Question

The velocity of a small ball of mass 10 g and density `7.8 g//c c`. When dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is `1.3 g//c c`. What is the viscous force acting on the ball?

Answer 1

Here, `m=10g , rho_(1) = 7.8 g//c c`
`rho_(2)=1.3 g// c c`
Weight of the ball = `mg = 10 xx 980 dyn e`
Volume of the ball , `V=m/(rho_1) = 10/7.8 c c`
Buoyant force on the ball
= weight of liquid displaced
`m/(rho_1) xx rho_(2) xx g = 10/7.8 xx 1.3 xx 980 dyn e`.
Viscous force acting on the ball
= net weight of the ball
`10 xx 980 - 10//7.8 xx 1.3 xx 980`
`=8.166 xx 10^(3) dyn e`.