CBSE Class 11 Physics Chapter 9: Mechanical Properties of Fluids NCERT Solutions

Reviewed by NCERT Help Editorial Team · Updated on 29 Jul 2026

NCERT Solutions PDF Class 11 PDF

This resource provides detailed NCERT Solutions for Class 11 Physics, Chapter 9: Mechanical Properties of Fluids. It covers multiple-choice questions (MCQs) that test understanding of fluid dynamics concepts like streamline flow, viscosity, and terminal velocity. The solutions offer step-by-step explanations, clarifying the principles behind fluid behavior in various scenarios. This guide is designed to help students grasp complex topics, solve problems accurately, and prepare effectively for their CBSE examinations by reinforcing key concepts and problem-solving techniques related to fluid mechanics.

Home

Quick info

Board	CBSE
Class	Class 11
Subject	Physics Exemplar
Session	2026
Language	English
Type	NCERT Solutions
Chapter	Chapter 9

Chapter summary

This chapter focuses on the Mechanical Properties of Fluids, covering essential concepts like viscosity, streamline flow, and terminal velocity. The NCERT Solutions provide detailed answers to MCQs, explaining the underlying physics principles. Students will learn to analyze fluid motion, understand the factors affecting fluid flow, and apply concepts like the law of continuity and Bernoulli's principle. These solutions are crucial for mastering fluid mechanics topics relevant to the CBSE curriculum.

Learning outcomes

Understand the concept of streamline flow and its characteristics.
Analyze the factors affecting fluid velocity in pipes of varying cross-sections.
Explain the phenomenon of terminal velocity for a falling object in a viscous fluid.
Differentiate between streamline and turbulent flow.
Apply the law of continuity to solve problems related to fluid flow.

Topics covered

Paper topics

Mechanical Properties of Fluids
Viscosity
Streamline Flow
Turbulent Flow
Terminal Velocity
Law of Continuity
Fluid Dynamics
Fluid Velocity
Cross-sectional Area
Ideal Fluid

Important topics

Streamline Flow Characteristics
Law of Continuity Application
Factors Affecting Fluid Velocity
Concept of Terminal Velocity
Distinction between Streamline and Turbulent Flow

PDF preview

Read page by page below. PDF is streamed from the official NCERT website — no download button on this page.

Loading document …

Page of

Loading page …

Questions and Solutions

Question 1

A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in figure, indicate the one that represents the velocity (v) of the pebble as a function of time (t).

Figure shows four plots of velocity (v) versus time (t).

Solution: When the pebble is dropped into the viscous oil, it experiences two main forces: gravity pulling it downwards and viscous drag force acting upwards. Initially, when the velocity is zero, the viscous force is zero. As the pebble starts falling, its velocity increases, and consequently, the upward viscous force (

F = 6\pi \eta r v

, where

\eta

is the coefficient of viscosity,

r

is the radius of the pebble, and

v

is its instantaneous velocity) also increases. The net force on the pebble is the difference between the gravitational force and the viscous force. Since the viscous force increases with velocity, the net downward force and hence the acceleration decrease. This means the velocity does not increase linearly with time. Eventually, the viscous force becomes equal in magnitude to the gravitational force. At this point, the net force becomes zero, and the pebble stops accelerating, reaching a constant velocity known as the terminal velocity. Therefore, the velocity-time graph starts from zero, increases non-linearly, and then becomes constant. This is represented by plot (c).

Question 2

Which of the following diagrams does not represent a streamline flow?

Diagrams (a), (b), (c), and (d) show different flow patterns.

Solution: A streamline flow is characterized by smooth, orderly motion of fluid particles. In a streamline flow, the velocity of each fluid particle at any given point remains constant over time (for steady flow). Streamlines represent the paths taken by fluid particles. A fundamental property of streamlines is that they cannot cross each other. If two streamlines were to cross, it would imply that a fluid particle at the point of intersection has two different velocities simultaneously, which is impossible. Diagram (d) shows streamlines crossing each other, indicating that it does not represent a streamline flow; it likely represents turbulent flow.

Question 3

Along a streamline,

the velocity of a fluid particle remains constant
the velocity of all fluid particles crossing a given position is constant
the velocity of all fluid particles at a given instant is constant
the speed of a fluid particle remains constant

Solution: A streamline is defined as a curve traced by a fluid particle in motion such that the tangent to the curve at any point gives the direction of the fluid velocity at that point. For a steady flow, the velocity of every fluid particle passing through a particular point in the fluid remains constant. This means that if you observe a fixed point in the fluid, all particles that pass through that point will have the same velocity. However, the velocity of a single fluid particle may change as it moves along its path if the flow is not uniform. Therefore, option (b) correctly describes the condition along a streamline in a steady flow.

Question 4

An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters 2.5 cm and 3.75 cm. The ratio of the velocities in the two pipes is

Solution: For the flow of an ideal fluid through a pipe, the law of continuity applies. This law states that the volume flow rate must be constant throughout the pipe, assuming the fluid is incompressible and there are no leaks. Mathematically, this is expressed as

A_1 V_1 = A_2 V_2

, where

A_1

and

A_2

are the cross-sectional areas of the pipe at two different points, and

V_1

and

V_2

are the corresponding fluid velocities.

Given the diameters of the two sections are $d_1 = 2.5$ cm and $d_2 = 3.75$ cm.

The radii are $r_1 = d_1 / 2 = 1.25$ cm and $r_2 = d_2 / 2 = 1.875$ cm.

The cross-sectional areas are $A_1 = \pi r_1^2$ and $A_2 = \pi r_2^2$ .

From the law of continuity, the ratio of velocities is:

$\frac{V_1}{V_2} = \frac{A_2}{A_1} = \frac{\pi r_2^2}{\pi r_1^2} = \left(\frac{r_2}{r_1}\right)^2$

Substituting the values of the radii (or diameters, as the ratio is the same):

$\frac{V_1}{V_2} = \left(\frac{d_2}{d_1}\right)^2 = \left(\frac{3.75 \text{ cm}}{2.5 \text{ cm}}\right)^2$

To simplify the ratio $\frac{3.75}{2.5}$ , we can multiply the numerator and denominator by 100 to remove decimals: $\frac{375}{250}$ . Dividing both by 125 gives $\frac{3}{2}$ .

So, the ratio of velocities is:

$\frac{V_1}{V_2} = \left(\frac{3}{2}\right)^2 = \frac{9}{4}$

Thus, the ratio of the velocities in the two pipes is 9:4.

Common mistakes

Confusing constant velocity of a fluid particle with constant velocity at a point.
Incorrectly applying the law of continuity to non-ideal fluids.
Misinterpreting the relationship between velocity and cross-sectional area in fluid flow.
Assuming acceleration is constant in a viscous fluid, leading to incorrect velocity-time graphs.

Revision tips

Review the definitions of streamline flow and turbulent flow carefully.
Practice applying the law of continuity (<math>A_1 V_1 = A_2 V_2</math>) to different scenarios.
Understand the factors that contribute to terminal velocity and how it is reached.
Visualize the velocity-time graphs for objects falling through viscous fluids.

Practice MCQs

Q1. A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. Which plot correctly represents the velocity (v) of the pebble as a function of time (t)?

Q2. Which of the following diagrams does not represent a streamline flow?

Q3. Along a streamline, what is true about the fluid flow?

Q4. An ideal fluid flows through a pipe with two sections having diameters 2.5 cm and 3.75 cm. What is the ratio of the velocities in the two sections?

Frequently asked questions

What is the main concept covered in CBSE Class 11 Physics Chapter 9 NCERT Solutions?

Chapter 9 focuses on the Mechanical Properties of Fluids, including concepts like viscosity, streamline flow, turbulent flow, terminal velocity, and the law of continuity.

How do these NCERT Solutions help students prepare for exams?

These solutions provide detailed, step-by-step explanations for MCQs, helping students understand the underlying physics principles and problem-solving techniques for fluid mechanics topics, which is crucial for exam preparation.

What is streamline flow?

Streamline flow is a type of fluid motion where fluid particles move along smooth, well-defined paths called streamlines. At any point, the velocity of all particles passing through that point is constant.

What is terminal velocity?

Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration.

Why can't streamlines cross each other?

Streamlines cannot cross each other because if they did, a fluid particle at the point of intersection would have two different velocities simultaneously, which is physically impossible for a fluid in motion.

How does the law of continuity relate velocity and area in fluid flow?

The law of continuity states that for an ideal fluid in steady flow, the product of the cross-sectional area and the fluid velocity is constant (<math>A \times V = \text{constant}</math>). This means that if the area decreases, the velocity must increase, and vice versa.

Content reviewed by the NCERT Help team. Editorial Team and update policy

NCERT Solutions PDF PDF on NCERT Help. URL unchanged for search indexing.