Question

When a ball is released from rest in a very long column of viscous liquid its downwards acceleration is $a$ just after the release. Then its acceleration has acquired two thirds of the maximum velocity.

Answer 1

We know that a viscous force is the force which opposes the movement of a body in the fluid. The property of a fluid to oppose the motion of the body through it is called the viscosity of the body. We can answer this using the definition of coefficient of viscosity.

Formula used:
$f\propto v$

Complete step-by-step answer:
We know that viscosity of a given fluid is the ability of the fluid to resist the motion of any object which might be forced into it. For example, honey which is sticky and has restriction in motion has more viscosity as compared to water, which can flow easily.
Thus, let us assume that we are dropping a ball from rest into a long tube containing the viscous medium like that of honey. Then due to the viscosity of the honey, the ball will experience a resistive force, which is equal to the viscous force.
Consider the acceleration of the ball to be $a$, and viscous force experienced by it as $f$.
Then the net force in the downward direction will be
$F=ma$
Since $f\propto v$ where $v$ is the max velocity of the ball.
Then when the max velocity $v$ is achieved, we have $f=ma$
When two third of $v$ is achieved,
$f=\dfrac{2}{3}ma$
Thus the net force is $F=ma-\dfrac{2}{3}ma$
$\implies F=\dfrac{ma}{3}$
Clearly, on comparison we get that the acceleration of the ball is reduced to $\dfrac{a}{3}$

Note: Clearly, the viscous force can also be called the fluid friction, as it resists the motion of the body in a fluid. It was observed that more the molecules per unit area, less is the coefficient of viscosity. Which is to say that, if the medium is denser than the movement of the body in that fluid is slower.