A metallic sphere of radius enter a tank of water, after a free fall through a distance of h in the earth's gravitational field, if its velocity remains unchanged after entering water, determine the value of h. Given: coefficient of viscosity of water =
The velocity attained by the sphere in falling freely from a height h is
v =
This is the terminal velocity of the sphere in water. Hence by Stoke's law, we have
v =
where r is the radius of the sphere, is the density of the material of the sphere
is the density of water and is coefficient of viscosity of water.
v =
= 20 m/s
from equation (i), we have
h =