### General

# Solutions for Text book exercises of CBSE Class XI Physics

- General
### General

# Solutions for Text book exercises of CBSE Class XI Physics

- Physical World and Measurement
### Physical World and Measurement

Topics covered are :

**1. Physical World**- Laws of Physics**2.****Units and Measurement**-Need for measurement: Units of measurement; fundamental and derived units. Length, mass and time measurements; accuracy and precision of measuring instruments; errors in measurement; significant figures.

Dimensions of physical quantities, dimensional analysis and its applications.### Units and Vectors: Tools for Physics

#### 1.1 The Important Stuff

##### 1.1.1 The SI System

Physics is based on measurement. Measurements are made by co mparisons to well-defined standards which define the units for our measurements

### Dimensions and Units

Every expression you write down that tries to describe something about the real world has to be dimensionally consistent. After all, what does the expression 5mi hr +3ft mean? Or an equation such as 6sec−2km = 4kg? Or the statement that the distance from here to downtown Miami is 8? Answer: Nothing! (Well, maybe in the last case there is a context, and you know that the speaker meant eight miles, but often you don't know this, and it means there's a mistake.)

You can figure out correct units for something just by solving a little algebra.

- Here is a quiz on Units and Dimensions. The objective of this quiz is to give you an idea about what kind of questions are asked in the examinations. There will be 10 questions in the quiz and it is not timed.
This is a multiple choice quiz on Measurement of Physical Quantities.

- Kinematics
### Kinematics

Topics covered are :

**1. Motion in a Straight Line**Frame of reference, Motion in a straight line: Position-time graph, speed and velocity.

Uniform and non-uniform motion, average speed and instantaneous velocity. Uniformly accelerated motion, velocity time and position-time graphs.

**2. Motion in a Plane**Scalar and vector quantities; Position and displacement vectors, Vectors and their notations; multiplication of vectors by a real number; addition and subtraction of vectors. Relative velocity. Unit vector; Resolution of a vector in a plane - rectangular components. Scalar and Vector product of vectors.

Motion in a plane, cases of uniform velocity and uniform acceleration-projectile motion. Uniform circular motion.

A study of motion will involve the introduction of a variety of quantities that are used to describe the physical world. Examples of such quantities include distance, displacement, speed, velocity, acceleration, force, mass, momentum, energy, work, power, etc. All these quantities can by divided into two categories - vectors and scalars. A vector quantity is a quantity that is fully described by both magnitude and direction. On the other hand, a scalar quantity is a quantity that is fully described by its magnitude. The emphasis of this unit is to understand some fundamentals about vectors and to apply the fundamentals in order to understand motion and forces that occur in two dimensions.

### 2-1 Position, Displacement, and Distance

In describing an object's motion, we should first talk about position - where is the object? A position is a vector because it has both a magnitude and a direction: it is some distance from a zero point (the point we call the origin) in a particular direction. With one-dimensional motion, we can define a straight line along which the object moves. Let's call this the x-axis, and represent different locations on the x-axis using variables such as and , as in Figure 2.1

- Laws of Motion
### Laws of Motion

**Laws of Motion**Concept of force. Inertia, Newton's first law of motion; momentum and Newton's second law of motion; impulse; Newton's third law of motion.

Law of conservation of linear momentum and its applications.

Equilibrium of concurrent forces. Static and kinetic friction, laws of friction, rolling friction, lubrication.

Dynamics of uniform circular motion: Centripetal force, examples of circular motion

### The First Law is concerned with changes in velocity caused by non-zero net forces.

#### Isaac Newton stated three laws of motion

The first law deals with forces and changes in velocity. For just a moment, let us imagine that you can apply only one force to an object. That is, you could choose push the object to the right or you could choose to push it to the left, but not to the left and right at the same time, and also not up and to the right at the same time, and so on.Explains the three laws of Motion with practical application examples.

Newton's 1st law can appear to be violated if you don't recognize the existence of contact forces.

Newton's 1st law: for an object to remain at rest, or move with constant speed & direction, the Net Force acting on it must be ZERO.

Describes Circular Motion and Centripetal Force with good examples.

DEFINITION OF UNIFORM CIRCULAR MOTIONUniform circular motion is the motion of an object traveling at a constant speed on a circular path.Explains the concepts of Impulse, Momentum, Collisions.

Linear Momentum/Conservation of Momentum/Collisions/Energy

Linear Momentum•

The definition of linear momentum is:

Since mass is an intrinsically positive quantity, p and v always point in the same direction (in the direction of motion). The S.I. unit of momentum is a kg Newton's second law may be expressed (and was originally expressed) in terms of the time rate change of momentum or:

- Work, Energy and Power
### Work, Energy and Power

**Work, Energy and Power**Work done by a constant force and a variable force; kinetic energy, work-energy theorem, power.

Potential energy of a spring, conservative forces: conservation of mechanical energy (kinetic and potential energies); non-conservative forces: motion in a vertical circle; elastic and inelastic collisions in one and two dimensions.

Brief Summary of Work, Power and Energy with Question and Answers.

In our daily life work have many different meanings. Ex: Consider a person holding a weight at a distance 'h' off the floor as shown in figure. In every day usage, we might say that the man is doing a work, but in our scientific definition, no work is done by force acting on a stationary object. We could eliminate the effort of holding the weight by merely tying the string to some object and the weight could be supported with no help from us.

In our daily life, the term work refers to any kind of mental and physical activity. For example, Vinod is working in a factory. The machine is in working order, a Professor giving lecture in class and a police man regulating traffic are said to be doing work. But in scientific language, work has a different and definite meaning.

Another link which explains the concepts and given practice problems with solutions.

- Motion of System of Particles and Rigid Body
### Motion of System of Particles and Rigid Body

**System of Particles and Rotational Motion**Centre of mass of a two-particle system, momentum conservation and centre of mass motion.

Centre of mass of a rigid body; centre of mass of a uniform rod.

Moment of a force, torque, angular momentum, laws of conservation of angular momentum and its applications.

Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparison of linear and rotational motions.

Moment of inertia, radius of gyration.Values of moments of inertia for simple geometrical objects. Statement of parallel and perpendicular axes theorems and their applications.

Explains Vector Product, Torque, Angular Momentum, Collisions.

The central topic of this chapter is angular momentum, a quantity that plays a key role in rotational dynamics. In analogy to the principle of conservation of linear momentum, we find that the angular momentum of a system is conserved if no external torques act on the system. Like the law of conservation of linear momentum, the law of conservation of angular momentum is a fundamental law of physics, equally valid for relativistic and quantum systems.

Explains centre of mass with respect to Newton's Laws

Explains equilibrium in two dimensions with illustrations.

If the resultant of all external forces acting on a rigid body is zero, then the body is said to be in equilibrium.

Therefore, in order for the rigid body to be in equilibrium, both the resultant force and the resultant couple must be zero.

Moment of Inertia

- Gravitation
### Gravitation

Topics covered are :

Keplar's laws of planetary motion.The universal law of gravitation.

Acceleration due to gravity and its variation with altitude and depth.

Gravitational potential energy and gravitational potential. Escape velocity. Orbital velocity of a satellite. Geo-stationary satellites.

Explains concepts and derivation of Gravitation, Kepler's Laws.

#### 5.1Newton's Law of Gravitation

We have already studied the effects of gravity through the consideration of the gravitational acceleration on earth g and the associated potential gravitational energy Ugrav.

We now broaden our study and consider gravitation in a more general manner through the Law of Gravitation enunciated by Newton in 1687 Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.

Lesson gives the derivation of Kepler's laws of Motion.

- Properties of Bulk Matter
### Properties of Bulk Matter

Topics covered are :

**1. Mechanical Properties of Solids :**Elastic behaviour, Stress-strain relationship, Hooke's law, Young's modulus, bulk modulus, shear modulus of rigidity, Poisson's ratio;**2. Mechanical Properties of Fluids :**Pascal's law and its applications (hydraulic lift and hydraulic

brakes). Effect of gravity on fluid pressure. Viscosity, streamline and turbulent flow, critical velocity. Bernoulli's theorem and its applications.

Surface energy and surface tension**3. Thermal Properties of Matter :**Heat, temperature, Thermal expansion; thermal expansion of solids, liquids and gases, anomalous expansion of water; specific heat capacity; Heat transfer-conduction, convection and radiation, thermal conductivity, Newton's law of cooling,Explains all the concepts of Elasticity, properties, Hooke's Modulus, Stress, Strain with illustrations and practice problems.

Elasticity

A PowerPoint Presentation by

Paul E. Tippens, Professor of Physics

Southern Polytechnic State University

- This Lesson gives detailed explanation for the concepts of elasticity.

ELASTIC PROPERTIES OF MATERIALS

GOALS

When you have mastered the contents of this chapter, you will be able to achieve the following goals:

Definitions Define each of the following terms, and use it in an operational definition: elastic body Young's modulus Stress bulk modulus strain, modulus of rigidity elastic limit Hooke's Law State Hooke's law.

Explains the concepts of Surface Tension, Capillarity, Bubble

Definition

In the fall a fisherman's boat is often surrounded by fallen leaves that are lying on the water. The boat floats, because it is partially immersed in the water and the resulting buoyant force balances its weight, as Section 11.6 discusses. The leaves, however, float for a different reason. They are not immersed in the water, so the weight of a leaf is not balanced by a buoyant force. Instead, the force balancing a leaf's weight arises because of the surface tension of the water. Surface tension is a property that allows the surface of a liquid to behave somewhat as a trampoline does. When a person stands on a trampoline, the trampoline stretches downward a bit and, in so doing, exerts an upward elastic force on the person. This upward force balances the person's weight. The surface of the water behaves in a similar way. In Figure 1, for instance, you can see the indentations in the water surface made by the feet of an insect known as a water strider, because it can stride or walk on the surface just as a person can walk on a trampoline.

For Concepts of Surface Energy.

Consider the atoms in the bulk and surface regions of a crystal:

Surface: atoms possess higher energy since they are less tightly bound.

Bulk: atoms possess lower energy since they are much tightly bound.

→ The sum of all the excess energies of the surface atoms is the surface energy.

→ Surface energy is of the essence of "energy”, and can be defines in term of Gibbs free energy:

Explains Pascal's Law, Fluid Pressure, Fluid Motion.

A French scientist named Blaise Pascal (1623 - 1662) discovered some important facts about pressure in fluids. Pascal invented the syringe, and the hydraulic lift. Hydraulic devices use liquids to exert pressure.

Pascal made many important contributions to both science and mathematics. One of these contributions was his observation about the transmission of pressure in fluids. It is known as Pascal's Law.

Thermal Expansion in Solids, Liquids and Gases.

- Thermodynamics
### Thermodynamics

Thermal equilibrium and definition of temperature. Heat, work and internal energy. First law of thermodynamics. Isothermal and adiabatic processes. Second law of thermodynamics: reversible and irreversible processes. Heat engine and refrigerator.

This Lesson explains Second Law of thermodynamics, Heat Engines, Refrigerators, Reversible and Irreversible processes.

The Second Law of Thermodynamics

The second law of thermodynamics asserts that processes occur in a certain direction and that the energy has quality as well as quantity. The first law places no restriction on the direction of a process, and satisfying the first law does not guarantee that the process will occur. Thus, we need another general principle (second law) to identify whether a process can occur or not.

Explains the first law of Thermodynamics and related terms

- Behaviour of Perfect gases and Kinetic theory of gases
### Behaviour of Perfect gases and Kinetic theory of gases

**1. Behaviour of Gases -**Equation of state of a perfect gas, work done in compressing a gas.**2. Kinetic theory of gases**- assumptions, concept of pressure. Kinetic interpretation of temperature; rms speed of gas molecules; degrees of freedom, law of equi-partition of energy (statement only) and application to specific heat capacities of gases; concept of mean free path, Avogadro's number.Explains Ideal gas law, kinetic theory of gases, Diffusion.

The Ideal Gas Law An ideal gas is an idealized model for real gases that have sufficiently low densities, interacting only by elastic collisions.

- Oscillations and Waves
### Oscillations and Waves

**1. Oscillations**Periodic motion - time period, frequency, displacement as a function of time. Periodic functions.

Simple harmonic motion (S.H.M) and its equation; phase; oscillations of a spring-restoring force and force constant; energy in S.H.M. Kinetic and potential energies; Time period of simple pendulum.

Free, forced and damped oscillations, resonance.

**2. Waves**Wave motion. Transverse and longitudinal waves, speed of wave motion. Displacement relation for a progressive wave. Principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect.

Explains Waves and wave motion, transverse and longitudinal waves etc.

Reviews the concepts of Simple Harmonic Motion.

Another pdf to cover Simple Harmonic Motion.