
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
463.5k+ views
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.
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.
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Glucose when reduced with HI and red Phosphorus gives class 11 chemistry CBSE

The highest possible oxidation states of Uranium and class 11 chemistry CBSE

Find the value of x if the mode of the following data class 11 maths CBSE

Which of the following can be used in the Friedel Crafts class 11 chemistry CBSE

A sphere of mass 40 kg is attracted by a second sphere class 11 physics CBSE

Trending doubts
Define least count of vernier callipers How do you class 11 physics CBSE

The combining capacity of an element is known as i class 11 chemistry CBSE

Proton was discovered by A Thomson B Rutherford C Chadwick class 11 chemistry CBSE

Find the image of the point 38 about the line x+3y class 11 maths CBSE

Can anyone list 10 advantages and disadvantages of friction

Distinguish between Mitosis and Meiosis class 11 biology CBSE
