Practice Problem for Class-XI on Error || Unit – 02

Numericals on Error Calculation of the NCERT class XI

Q-1 :: The diameter of a wire measured in an experiment was 0.022 cm, 0.023 cm, 0.026 cm, 0.025 cm, 0.024 cm and 0.025 cm find
(i) the mean value of diameter
(ii) absolute error in a each measurement
(iii) Percentage error

Q-2:: Refractive index of a flint glass (μ) was measured in an experiment and was found to be 1.655, 1.667, 1.666 , 1.659, 1.669 and 1.654. Find
(i) the mean value of μ
(ii) mean absolute error
(iii) Relative error
(iv) Percentage error

Q-3:: While determining the time period of oscillation of a simple pendulum, the readings from various measurements are 1.73 s, 1.62 s, 1.52 s, 1.45 s and 1.83 s. Calculate the values of mean value of time period, absolute error, mean absolute error and relative error.

Q-4:: While determining the density of a sea water , the readings from various measurements are 1.03 g/cc, 1.12 g/cc, 0.92 g/cc, 1.05 g/cc and 1.13 g/cc. Calculate the values of mean density , absolute error, mean absolute error and relative error.

Q-5:: The resistance of a wire as measured in an experiment was found to be 10.3 Ω , 10.7Ω , 9.8 Ω , 10.4 Ω and 9.6Ω . Calculate
(i) mean value of resistance
(ii) absolute error in each measurement
(iii) mean absolute error
(iv) fractional error
(v) percentage error.

Q-6:: The diameter of a wire as measured by a screw gauge was found to be 1.328 mm, 1.330 mm, 1.325 mm, 1.334 mm and 1.336 mm. Calculate
(i) mean value of diameter
(ii) absolute error in each measurement
(iii) mean absolute error
(iv) fractional error
(v) percentage error.

Q-7:: Using a screw gauge, the diameter of a metal rod was measured. The observation are given as follows : 0.39 mm, 0.38 mm, 0.37 mm, 0.41 mm, 0.38 mm, 0.38 mm, 0.37 mm, 0.40 mm, 0.39 mm. Calculate
(i) the most accurate value of the diameter,
(ii) the relative error, and
(iii) the percentage error in the measurement of the diameter.

Q-8::A student performs an experiment and found following values of the refractive index of
1.29, 1.33, 1.34, 1.35, 1.32, 1.36, 1.30, 1.33
Find the mean value of refractive index, the mean absolute error. The relative error and percentage error.


NCERT XI Unit 1 :: Physical World

The word Science originates from the Latin verb Scientia meaning ‘to know’.
What is Science and what is the so-called Scientific Method?
Science is a systematic attempt to understand natural phenomena in as much detail and depth as possible, and use the knowledge so gained to predict, modify and control phenomena.
Science is exploring, experimenting and predicting from what we see around us.
The curiosity to learn about the world, unravelling the secrets of nature is the first step towards the discovery of science.
The scientific method involves several interconnected steps :
1. Systematic observations,
2. controlled experiments,
3. qualitative and quantitative reasoning,
4. mathematical modelling,
5. prediction and verification or falsification of theories.
6. Speculation and conjecture
A scientific theory, to be acceptable, must be verified by relevant observations or experiments.

Science is ever dynamic.
There is no ‘final’ theory in science and no unquestioned authority among scientists.
As observations improve or experiments give new results, theories must be changed according to modifications.
For example, when Johannes Kepler (1571-1630) examined the extensive data on planetary motion collected by Tycho Brahe
(1546-1601), the planetary circular orbits in heliocentric theory (sun at the centre of the solar system) imagined by Nicolas Copernicus
(1473–1543) had to be replaced by elliptical orbits to fit the data better.
Sometime , the existing theory is simply unable to explain new observations. In the beginning of the twentieth century, it was realised that Newtonian mechanics, till then a very successful theory. It could not explain some of the most basic features of atomic phenomena.
Similarly, the wave picture of light of Huygen of that time , failed to explain the photoelectric effect properly.
This led to the development of a new theory (Quantum Mechanics) to deal with atomic and molecular phenomena.
The result of experiment of scattering of alpha particles by gold foil, in 1911 by Ernest Rutherford (1871–1937) established the nuclear model of the atom, which then became the basis of the quantum theory of hydrogen atom but in 1913 better model of atom was given by Niels Bohr (1885–1962).
The concept of antiparticle was first introduced theoretically by
Paul Dirac (1902–1984) in 1930 and confirmed two years later by the experimental discovery of positron (anti-electron) by Carl Anderson.
Physics is a basic discipline in the category of Natural Sciences, which also includes other disciplines like Chemistry and Biology. The word Physics comes from a Greek word ˈfiziks , meaning nature.
We can broadly describe physics as a study of the basic laws of nature and their manifestation in different natural phenomena. The scope of physics is described briefly in the next section.
Here we remark on two principal thrusts in physics :
1. Unification and
2. reduction.

In Physics, we attempt to explain diverse physical phenomena in terms of a few concepts and laws.
The effort is to explain different physical phenomenon by a single law .
For example, the same law of gravitation (given by Newton)
describes the fall of an apple to the ground, the motion of the moon around the earth and the motion of planets around the sun.
Similarly, the basic laws of electromagnetism (Maxwell’s equations) govern all electric and magnetic phenomena.
The attempts to unify fundamental forces of nature reflect this same quest for unification.
A related effort is to derive the properties of a bigger, more complex, system from the properties and interactions of its constituent simpler parts.This approach is called reductionism
For example, the subject of thermodynamics, developed in the nineteenth century, deals with bulk systems in terms of
macroscopic quantities such as temperature, internal energy, entropy, etc. Subsequently, the subjects of kinetic theory and statistical mechanics interpreted these quantities in terms of the properties of the molecular constituents of the bulk system.
In particular, the temperature was seen to be related to the average kinetic energy of molecules of the system.
We can get some idea of the scope of physics by looking at its various sub-disciplines. Basically, there are two domains of interest : macroscopic and microscopic.
The macroscopic domain includes phenomena at the laboratory, terrestrial and astronomical scales. The microscopic domain
includes atomic, molecular and nuclear phenomena*.
Classical Physics deals mainly with macroscopic phenomena and includes subjects like
1. Mechanics,
2. Electrodynamics,
3. Optics
4. Thermodynamics.

Mechanics founded on Newton’s laws of motion and the law of gravitation is concerned with the motion (or equilibrium) of particles, rigid and deformable bodies, and general systems of particles. The
propulsion of a rocket by a jet of ejecting gases, propagation of water waves or sound waves in air, the equilibrium of a bent rod under a load, etc., are problems of mechanics.
Electrodynamics deals with electric and magnetic phenomena
associated with charged and magnetic bodies. Its basic laws were given by Coulomb, Oersted, Ampere and Faraday, and encapsulated by Maxwell in his famous set of equations. The motion of a current-carrying conductor in a magnetic field, the response of a circuit to an ac voltage (signal), the working of an antenna, the propagation of radio waves in the ionosphere, etc., are problems of electrodynamics.
Optics deals with the phenomena involving light. The working
of telescopes and microscopes, colours exhibited by thin films, etc., are topics in optics.
Thermodynamics deals with systems in macroscopic equilibrium and is concerned with changes in internal energy, temperature, entropy, etc., of the system through external work and transfer of heat. The efficiency of heat engines and refrigerators, the direction of a physical or chemical process, etc., are problems of interest in thermodynamics.
The microscopic domain of physics deals with the constitution and structure of matter at the minute scales of atoms and nuclei (and even
lower scales of length) and their interaction with different probes such as electrons, photons and other elementary particles.
Classical physics is inadequate to handle this domain and Quantum
Scope of physics
It covers a tremendous range of magnitude of physical quantities like length,mass , time, energy, etc.
At one end, it studies phenomena at the very small scale of length
(10-14m or even less) involving electrons, protons, etc.; at the other end, it deals with astronomical phenomena at the scale of galaxies or even the entire universe whose extent is of the order of 1026m.
The two length scales differ by a factor of 1040 or even more.
The range of time scales can be obtained by dividing the length scales by the speed of light : 10–22 s to 1018 s. The range of
masses goes from, say, 10–31 kg (mass of an electron) to 1055 kg (mass of known observable universe).

Physics is exciting in many ways.
To some people the excitement comes from a few basic concepts and laws , a number of natural phenomena can be explained.
To some others, the challenge in carrying out imaginative new experiments to unlock the secrets of nature, is thrilling.
Applied physics is equally demanding .
Application of physical laws to make useful devices is the most interesting and exciting part of applied physics .
The connection between physics, technology and society can be seen in many examples. The discipline of thermodynamics arose from the
need to improve the working of heat engines. The steam engine, is inseparable from the Industrial Revolution in England in the eighteenth century, which had great impact on the course of human civilisation.
Sometimes technology gives rise to new physics; at other times physics generates new technology. An example of the latter is the
wireless communication technology that followed the discovery of the basic laws of electricity and magnetism in the nineteenth century. As late as 1933, the great physicist Ernest Rutherford had dismissed the possibility of taking energy from atoms. But only a few years later, in 1938, Hahn and Meitner discovered the phenomenon of neutron-induced fission of uranium, which would serve as the basis of nuclear power reactors and nuclear weapons.
Another important example of physics giving rise to technology is the silicon ‘chip’ that triggered the computer revolution in the last three decades of the twentieth century.
A most significant area to which physics has and will contribute is the development of alternative energy resources. The fossil fuels of
the planet are drilling fast and there is an urgent need to discover new and affordable sources of energy. Considerable progress has
already been made in this direction ,for example, in conversion of solar energy, geothermal energy, etc., into electricity, but much more is still to be accomplished.

At the present stage of our understanding, we know of four fundamental forces in nature, which are described in brief here :
1 Gravitational Force
The gravitational force is the force of mutual attraction between any two objects by virtue of their masses.
It is a universal force.
For example, experience the force of gravity due to the earth. In particular, gravity governs the motion of the moon and artificial satellites around the earth, motion of the earth and planets around the sun, and, of course, the motion of bodies falling to the earth.
It plays a key role in the large-scale phenomena of the universe, such as formation and evolution of stars, galaxies and galactic clusters.
2 Electromagnetic Force
Electromagnetic force is the force between charged particles.
When charges are at rest, the force is given by Coulomb’s law : attractive for unlike charges and repulsive for like charges.
Charges in motion produce magnetic effects and a magnetic field
gives rise to a force on a moving charge.
Electric and magnetic effects are, in general, inseparable – hence the name electromagnetic force.
Like the gravitational force, electromagnetic force acts over large distances and does not need any intervening medium.
It is enormously strong compared to gravity.
The electric force between two protons, for example, is 1036 times the gravitational force between them, for any fixed distance.
The electromagnetic force that governs the structure of atoms and molecules, the dynamics of chemical reactions and the mechanical, thermal and other properties of materials.
The macroscopic forces like ‘tension’, ‘friction’, ‘normal force’, ‘springforce’, etc. are electromagnetic in nature .
Gravity is always attractive, while electromagnetic force can be attractive or repulsive. Another way of putting it is that mass
comes only in one variety (there is no negative mass), but charge comes in two varieties : positive and negative charge.
Electric force is in atmosphere also ,where the atoms are ionised and that leads to lightning.
If we reflect a little, the enormous strength of the electromagnetic force compared to gravity is evident in our daily life.
When we hold a book in our hand, we are balancing the gravitational force on the book due to the huge mass of the earth by the ‘normal force’ provided by our hand.
The normal force is nothing but the net electromagnetic force between the charged constituents of our hand and the book, at the surface in contact.
3 Strong Nuclear Force
The strong nuclear force binds protons and neutrons in a nucleus. It is evident that without some attractive force, a nucleus will be
unstable due to the electric repulsion between its protons. A new basic force must be involved , which is strong nuclear force .
It is the strongest of all fundamental forces, about 100 times the electromagnetic force in strength.
It is charge-independent and acts equally between a proton and a proton, a neutron and a neutron, and a proton and a neutron.
Its range is extremely small, of about nuclear dimensions (10–15 m).
It is responsible for the stability of nuclei. The electron, it must be noted, does not experience this force.

4 Weak Nuclear Force
The weak nuclear force appears only in certain nuclear processes such as the - decay of a nucleus. In - decay, the nucleus emits an
electron and an uncharged particle called neutrino. The weak nuclear force is not as weak as the gravitational force, but much weaker
than the strong nuclear and electromagnetic forces. The range of weak nuclear force is exceedingly small, of the order of 10-16m.

Towards Unification of Forces
We already discussed about the unification is a basic quest in physics.
Newton unified terrestrial and celestial domains under a common law of gravitation.
The experimental discoveries of Oersted and Faraday showed that electric and magnetic phenomena are in general inseparable. Maxwell unified electromagnetism and optics with the discovery that light is an electromagnetic wave.
Einstein attempted to unify gravity and electromagnetism but could
not succeed in this venture.
The electromagnetic and the weak nuclear force have now been unified and are seen as aspects of a single ‘electro-weak’ force.

In any physical phenomenon governed by different forces, several quantities may change with time. Some special physical quantities, however, remain constant in time. They are the conserved quantities of nature. Understanding these conservation principles is very important to describe the observed phenomena quantitatively.
1. Law of conservation of mechanical energy
2. Law of conservation of linear momentum
3. Law of conservation of angular momentum
4. Law of conservation of charge

For motion under an external conservative force, the total mechanical energy i.e. the sum of kinetic and potential energy of a body is a constant.
The familiar example is the free fall of an object under gravity. Both the kinetic energy of the object and its potential energy change continuously with time, but the sum remains fixed.
If the object is released from rest, the initial potential energy is completely converted into the kinetic energy of the object just before it hits the ground.
When all forms of energy e.g., heat, mechanical energy, electrical energy etc., are counted, it turns out that energy is conserved. The general law of conservation of energy is true for all forces and for any kind of transformation between different forms of energy.
Before the Einstein’s theory of relativity, the law of conservation of mass was regarded as another basic conservation law of nature.
In the analysis of chemical reactions , if the total binding energy
of the reacting molecules is less than the total binding energy of the product molecules, the difference appears as heat and the reaction is exothermic. The opposite is true for energy absorbing (endothermic) reactions.
According to Einstein’s theory, mass m is equivalent to energy E given by the relation E= mc2, where c is speed of light in vacuum.

In a nuclear process mass gets converted to energy (or vice-versa). This is the energy which is released in a nuclear power generation and nuclear explosions.

The total linear momentum and the total angular momentum of an isolated system are also conserved quantities .They are the basic conservation laws of nature in all domains. For example, during a collision of two objects; yet momentum conservation law enables us to bypass the complications and predict or rule out possible outcomes of the collision.

In nuclear and phenomena also, the conservation laws are important tools of analysis. Indeed, using the conservation laws of energy and momentum for – decay, Wolfgang Pauli (1900-1958) correctly predicted in 1931 the existence of a new particle , called neutrino, emitted in - decay along with the electron.
For example, the acceleration due to gravity at the moon is one-sixth that at the earth, but the law of gravitation is the same both on the moon and the earth. The laws of conservation of linear momentum and the law of conservation of angular momentum have no restriction of space. The conservation laws of charge is also plays an important role in electromagnetism .

Practice paper for AHSEC class 12 on Magnetic effect and Magnetic properties

Total marks 25    Total time-1hour

Set A (each question carries one mark)

01. What is 1 tesla?

02. Give the dimensional formula of permeability

03. What is the resonance condition of  cyclotron?

04. What is an ideal voltmeter?

05. State gauss law in magnetism.

Set B (its question carries 2 marks)

01. How a galvanometer can be converted into an ammeter? Explain with diagram

02. Define the magnetic elements of earth

03. Find expression for torque acting on a bar magnet placed in a uniform magnetic field

04. Give the difference between diamagnetic and paramagnetic substance

Set C(Each question carries 3 marks)

01. Using ampere’s circuital law find expression for magnetic field due to solenoid.

02. Find expression for magnetic field at the axial point of  a current loop

03. Find the expression for force acting between two parallel current carrying conductor in the same direction.

04. Find expression for magnetic moment due to an revolving electron what is Bohr magneton?

Practice paper for class 12 AHSEC : 2020

  1. Total marks-25  Total time-1hour

Set A(Each question carries 1 mark)

01. Write down the properties of electric charge

02. Draw the diagram of electric lines of force due to thin sheet of charge

03. What is an equipotential surface?

04. Give the resistance of a resistor with colour code of red black green silver

05. How mobility of charge carriers is related to temperature?

Set B(Each question carries 2 marks)

01. Give the difference between polar and nonpolar dielectrics.

02. find the expression for torque acting on an electric dipole placed in a uniform electric field.

03. Explain the two laws of kirchoff laws with diagram

04 . Find the expression for capacitance of parallel plate capacitor

Set C(each question carries 3 marks)

01. Express coulomb’s law in vector form

02. Using gauss theorem find an expression for electric field due to the hollow sphere at a point outside and  on its surface

03. Find expression for electric potential due to an electric dipole at any point

04. Using the concept of drift velocity establish ohm’s law





Practice paper for AHSEC class 12 of 2020

Total mark -36

Total time -90 minutes

Each question carries carries 3 marks

Q1- Obtain the relation between angle of minimum deviation for a prism and its refractive index .

Q2- Draw the ray diagram for reflecting type telescope . Write down advantages of reflecting type telescope over refracting type telescope .

Q3- define critical angle  . Write down the condition for total internal reflection .What is optical fibre .

Q4-Write down Huygens principles . Draw the diagram for wavefront  due to a point source.

Q5- Prove that for destructive interference path difference between the two light waves should be odd integral multiple of λ/ 2.

Q6- State Malus law . Prove that when light is incident at polarising angle on a reflecting surface angle between reflected and refracted light is 90 º

Q7- Draw a ray diagram for Davission and Germer  experiment . Write down few uses of de Broglie’s hypothesis.

Q8- State Bohr’s postulate  . Write down its failures .

Q9- Draw and explain binding energy curve.

Q10-  Explain the working of zener diode as voltage regulator

Q11- Give the Boolean expression and truth table of NAND gate . How OR gate can be obtained from NOR gate and NAND gate ?

Q12- Define the following terms :-  noise , attenuation and modulation .


Download Now