A spherical ball of radius 3.0xx10^(-4) m and density 10^(4) kg//m^(3) falls freely under gravity through a distance h before entering a tank of water. If after entering the water the velocity of the ball does not change, find h. Viscosity of water is 9.8xx10^(6) N-s//m^(2).

A spherical ball of radius 3.0xx10^(-4) m and density 10^(4) kg//m^(3)

1.	A spherical ball of radius 3.0xx10^(-4) m and density 10^(4) kg//m^(3) falls freely under gravity through a distance h before entering a tank of water. If after entering the water the velocity of the ball does not change, find h. Viscosity of water is 9.8xx10^(6) N-s//m^(2).
Answer» Solution :Before entering the water the velocity of ball is `sqrt(2g)`. If after entering the water this velocity does not CHANGE then this value should be equal to the terminal velocity. Therefore, `sqrt(2gh)=2/9 (R^(2)(rho-sigma)g)/(eta)` `:. h={(2)/(9) (r^(2)(rho-sigma)g)/(eta)}^(2)` `=(2)/(81) XX(r^(4)(rho-sigma)^(2)g)/(eta^(2))` `=(2)/(81)xx((3xx10^(-4))^(4)(10^(4)-10^(3))^(2)xx9.8)/(9.8xx10^(-6))^(2)` `=1.65xx10^(3)m`.