Question

After terminal velocity is reached the acceleration of a body falling through a viscous fluid is:
A) zero
B) equal to g
C) less than g
D) greater than g

Answer 1

Hint The terminal velocity of a body is reached when the viscous drag force faced by the body matches the force due to gravitational acceleration. At this point, there is no net force on the body and we can use Newton’s second law to determine the acceleration.

Complete step by step answer
When an object is falling in a liquid, it experiences a viscous drag force due to the friction experienced by the object with the interaction with the liquid. The viscous force $F$ experienced by the particle of mass $m$ increases linearly with the velocity $v$ of the object $F = bv$ where $b$ is a constant.
When an object Is falling, it is accelerated due to gravity according to the relation $F = mg$ where $g$ is the gravitational acceleration on Earth. However, as its velocity rises, it will also experience more viscous force, and eventually, at one point the friction force and the buoyancy of the object will balance the force due to gravity and the object can be said to have reached the terminal velocity.
When the object reaches terminal velocity, the gravitational force will be balanced by the frictional force and the force due to the buoyancy of the object, so there will be no net force acting on the object. So, from Newton’s second law
$F = ma$ where $a$ is the acceleration,
As the net force $F$ is zero, the net acceleration of the object is also zero which corresponds to option (A).

Note
Another way of solving this question can also be as one of the interferences we can make from Newton’s first law which tells us that a body at rest or moving with constant velocity will continue being in that state unless a force acts on it. Since at terminal velocity, the object is travelling with constant terminal velocity, we can say that there is no force acting on the body.