Section A

Select and write the correct answers to the following questions:

(i) A particle of mass

, tied to a long string is whirled to perform vertical circular motion, under gravity. Minimum speed of a particle is . Consider following statements.

(P) Maximum speed must be .

(Q) Difference between maximum and minimum tensions along the string is . Select correct option.

(a) Only the statement is correct

(b) Only the statement is correct

(c) Both the statements are correct

(d) Both the statements are incorrect

(ii) If pressure of an ideal gas is decreased by isothermally, then its volume will:

(a) decrease by

(b) increase by

(c) decrease by

(d) increase by

(iii) A standing wave is produced on a string fixed at one end with the other end free. The length of the string:

(a) must be an odd integral multiple of

(b) must be an odd integral multiple of

(c) must be an odd integral multiple of

(d) must be an even integral multiple of

(iv) A parallel plate capacitor is charged and then isolated. The effect of increasing the plate separation on charge, potential, capacitance respectively are:

(a) Constant, decreases, decreases

(b) Increases, decreases, decreases

(c) Constant, decreases, increases

(d) Constant, increases, decreases

(v) Kirchhoff’s first law, i.e, at a junction, deals with the conservation of.
(a) charge
(b) energy
(c) momentum
(d) mass

(vi) A conductor rod of length (l) is moving with velocity (v) in a direction normal to a uniform magnetic field (B). What will be the magnitude of induced emf produced between the ends of the moving conductor?
(a) BLv

(vii) In a series LCR circuit, the phase difference between the voltage and the current is 450 . Then the power factor will be:
(a) 0.607
(b) 0.707
(c) 0.808
(d) 1

(viii) What is the angular momentum of the electron in the third Bohr orbit in the hydrrogen atom?





(ix) A charged particle is in motion having initial velocity when it enters into a region of uniform magnetic field perpendicular to , Because of the magnetic force the kinetic energy of the particle will:
(a) remain unchanged
(b) get reduced
(c) increase
(d) be reduced to zero

(x) A conducting thick copper rod of length carries a current of and is located on the Earth’s equator. There the magnetic flux lines of the Earth’s magnetic field are horizontal, with the field of , south to north. The magnitude and direction of the force on the rod, when it is oriented so that current flows from west to east, are:

(a) , downward

(b) , downward

(c) , upward

(d) , upward

  1. Answer the following questions:

(i) Why are curved roads banked?

(ii) Define athermanous substances and diathermanous substances.

(iii) State and explain the principle of conservation of angular momentum.

(iv) Define linear simple harmonic motion.

(v) If the density of oxygen is at a pressure of , find the root mean square velocity of oxygen molecules.

(vi) Define magnetic length.
(vii) A ceiling fan having moment of inertia attains its maximum frequency of in seconds. Calculate its power rating. (viii) Write ideal gas equation for a mass of of nigrogen gas.

4. Section B

5. Attempt any Eight of the following questions:

  1. Why is the surface tension of paints and lubricating oils kept low?
  2. When heat is supplied to a system, the external work done is . Find the increase in integral energy of the system (in joule) ( ).
  3. Draw a neat labelled diagram of radiant power of a blackbody per unit range of wavelength as function of wavelength.
  4. What are primary and secondary sources of light?
  5. Why two or more mercury drops from a single drop when brought in contact with each other?
  6. What do you mean by electromagnetic induction? State Faraday’s law of induction.
  7. What is mean by dual nature of matter?
  8. A system releases of heat while of work is done on the system. Calculate the change in internal energy.
  9. A violin string vibrates with fundamental frequency of . What are the frequencies of first and second overtones?
  10. White light consists of wavelengths from to 700 . What will be the wavelength range seen when white light is passed through glass of refractive index 1.55?
  11. A galvanometer has a resistance of and its full scale deflection current is . What resistance should be added to it to have a range of ?
  12. Calculate the value of magnetic field at a distance of 2 from a very long straight wire carrying a current of 5 A. (Given: )

6. Section C

7. Attempt any Eight of the following questions:

  1. A spherical drop of oil falls at a constant speed of in steady air. Calculate the radius of the drop. the density of the oil is , density of air is and the coefficient of viscosity of air is poise. ).
  2. Obtain the differential equation of linear Simple Harmonic Motion.
  3. State the characteristics of stationary waves.
  4. A capacitor has some dielectric between its plates and the capacitor is connected to a DC source. The battery is now disconnected and then the dielectric is removed. State whether the capacitance, the energy stored in it. the electric field, charge stored and voltage will increase, decrease or remain constant.
  5. Define admittance. The total impedance of a circuit decreases when a capacitor is added in series with and Explain why?
  6. Is it always possible to see photoelectric effect with red light?
  7. Explain the construction and working of solar cell.
  8. Disintegration rate of a sample of per hour at 20 hrs from the start. It reduces to per hour after 30 hours. Calculate its half-life and the initial number of radioactive atoms in the sample.
  9. Calculate the wavelength associated with an electron, its momentum and speed. When it is accelerated through a potential of ?
  10. The distance between two consecutive bright fringes in a biprism experiment using light of wavelength is by how much will the distance change if light of wavelength is used?
  11. One mole of an ideal gas is initially kept in a cylinder with a movable frictionless and massless piston at pressure of and temperature . It is then expanded till its volume is doubled. How much work is done if the expansion is isobaric?
  12. The resistance of a potentiometer wire is and its length is . A resistance box and a battery are connected in series with it. What should be the resistance in the box, if it is desired to have a potential drop of ?

8. Section D

9. Attempt any Three of the following questions:

  1. (i) What are eddy currents? State applications of eddy currents.

(ii) Magnetic field at a distance from a long straight wire is . What must be current through the wire?
28. (i) State the postulates of Bohr’s atomic model.

(ii) A short bar magnet is placed in an external magnetic field of 700 gauss. When its axis makes an angle of with the external magnetic field, it experiences a torque of . Find the magnetic moment of the magnet and the work done in moving it from its most stable to most unstable position.

  1. (i) Compare the rate of emission of heat by a black body at with the rate of emission of heat of same body at

(ii) An aircraft of wing span of flies horizontally in earth’s magnetic field of at a speed of 400 . Calculate the emf generated between the tips of the wings of the aircraft.

  1. (i) Derive an expression for effective capacitance of three capacitors connected in parallel. (ii) A capacitor, a inductor and a resistor are connected in series with an source whose emf is given by (volt). What is the frequency, reactance, impedance, current and phase angle of the circuit?
  2. (i) Define magnetization and magnetic intensity.

(ii) In a common-base connection, the emitter current is and collector current is . Determine the common base DC current gain.

10. [.]) Answer Key

11. Section A

  1. (i) (c) Both the statements are correct

(ii) (d) Increase by

(iii) (a) Must be an odd integral multiple of

(iv) (a) Constant, decreases, decreases

(v) (a) Charge

(vi) (a) BLv

(vii) (b) 0.707

(viii) (a)

(ix) (a) Remain unchanged

(x) (d) , upward

  1. (i) To avoid the risk of skidding as well as to reduce the wear and tear of the car tyres, the road surface at a bend is titled inward i.e, the other side of the road is raised above its inner side. This is called banking of road.

(ii) Substance that don’t allow transmission of infrared radiation through them are called athermanous substance.

(iii) The angular momentum of a body is conserved if the resultant external torque on body is zero. This law is used by a figure skater to increase their speed of rotation for a spin by reducing the body’s moment of inertia.

(iv) The linear periodic motion of a body, in which the restoring force is always directed towards the mean position and its magnitude is directly proportional to the displacement from the mean position.


The root mean square velocity of oxygen molecules,

(vi) The distance between two poles (North and South poles) is called the magnetic length (2l).

(vii) Given:

watt watt.

(viii) Ideal gas equation


Therefore, the corresponding ideal gas equation is

12. Section B

  1. The surface tension of paints and lubricating oils kept low for better surface coverage.
  2. Given

Increases in internal energy (dv) =?

we have,


  1. The source that emit light on their own are called primary source. Some sources are not self-luminous, i.e, they do not emit light on their own but reflect or scatter the light incident on them. Such sources of light are called secondary sources.
  2. A spherical shape has the minimum surface area to volume ratio of all geometric forms. When two drops of a liquid are brought in contact, the cohesive forces between their molecules coalesce the drops into a single larger drop.
  3. The phenomenon of production of emf in circuit by a changing magnetic flux through the circuit is called electromagnetic induction.

Faraday’s first law: Whenever there is a change in magnetic flux associated with a circuit, an emf is induced in the circuit.

Faraday’s second law: The magnitude of the induced emf is directly proportional to the time rate of change of magnetic flux through the circuit.

  1. Dual nature of matter.

(i) Since radiation has dual nature ie, it possesses properties of both wave and particle.

(ii) Universe is composed of radiation and matter therefore de-Broglie concluded that the moving material poetical must also possess dual nature, since nature loves symmetry.

  1. Given:
  1. Given,
    The first overtone,

The second overtone,

  1. Let and be the wavelengths of light in water for and (wavelengths in vacuum) respectively.

Let be the wavelength of light in vacuum.

The wavelength range seen when white light is passed through the glass would be to .

  1. Given:

Maximum voltage to be measured is .

The galvanometer resistance .

The resistance to be added in series,

  1. Given:

The magnetic induction,

13. Section C

  1. Given,
  1. In a linear SHM (Simple Hormonic Motion), the force is directed toward the mean position of its magnitude is directly proportional to the displacement of the body from mean position.

where is force constant and is displacement from the mean position.

According to Newton’s Second law of motion

from – (1) and (2)


sub. – (4) in (3)

14. Characteristics of stationary waves:

(i) Stationary waves are produced by the interference of two identical progressive waves travelling in opposite directions, under certain condition

(ii) The overall appearance of standing wave is of alternate intensity maximum and minimum.

(iii) The distance between adjacent node .

(iv) The distance between successive node .

(v) The stationary wave does not propagate in any direction.

(vi) The stationary wave does not transport energy through the medium.

(vii) There is no progressive change of phase from particle to particle.

  1. Assume parallel-plate capacitor of plate area A and plate separation is filled with a dielectric of relative permittivity (dielectric constant) k. Its capacitance is

If it is charged to a voltage (potential) V, the charge on its plates is

Since the battery is disconnected after it is charged, the charge on its plates and consequently the product remain unchanged.

On removing the dielectric completely, its capacitance becomes from equation (1).

That is, its capacitance decreases by the factor . Since , its new voltage is

So that its voltage increases by the factor .

The stored potential energy, , so that remaining constant, increases by the factor The electric field, , so that also increases by factor

  1. Admittance: The reciprocal to impedance of an circuit is called admittance.

For an LC circuit, the impedance

reactance of the inductor when a capacitor of capacitance is added in secies and

Because in the case of an inductor the current lags behind the voltage by a phase angle of rad while in the case of a capacitor the current leads the voltage by a phase angle of . The decrease in net reactance decreases the total impedance.

  1. No, it is not possible but due to present technology it may be possible.

Explanation: The photons in red light to not have the necessary energy required to rip an electron out of its orbital (this needed energy is equal to the electron’s work function. Because light behaves like particles rather than a continuous stream, even very high-intensity red light will never be able to overcome an electron’s work function (in this situation), as every individual photon fails to do so. This shows the particle behaviour of light, because of light behaved like a wave, the red light would be able to overcome the electron’s work function with high intensity or a long time.

  1. Construction: A simple pn-junction solar cell consist of a p-type semiconductor substrate backed with a metal electrode. A thin layer of silicon is grown over the p-type of substrate by doping with suitable donor impurity. Metal finger electrode are prepared on top of -layer so that there is enough space between the fingers for sunlight to reach the -layer and underlying -junction.

I: Solar cell current; : Load resistance, ARC : Antireflective coating

Working: When exposed to sunlight, the absorption of incident radiation creates electron hole pairs in and near the depletion layer. The photogenerated electrons and holes moves towards the -side and -side, respectively. If no external load is connected, these photogenerated charges get collected at the two sides of the junction and give rise to forward photovoltage. If a closed circuit a current I passes through external load as long as the solar cell is exposed to sunlight.

A solar cell consist several solar cells which are connected in series for higher output.


The half life of the material,



antilog 0.4014

per hour


  1. Given: .

We assume that the electron is initially at rest.

This is the speed of the electron.

This the momentum of the electron. The wavelength associated with the electron,

  1. Given: .

Distance between consecutive bright fringes,

  1. Work done in isobaric process given by

can be found by using the ideal gas equation for initial state.

  1. Given:

where is the resistance in the box.

15. Section D

  1. (i) Whenever a conductor or part of it is moved in magnetic field cutting magnetic field lines, the free electrons in the bulk of metal starts circulating in closed path equivalent to current carrying loops. These current resemble to eddies in fluid stream and hence called as eddy current.

Application: (1) Electric brakes, (2) Galvanometer.

(ii) Given: ,

The current through the wire,

  1. (i) (a) The electron revolves with a constant speed in circular orbit around the nucleus.

(b) The radius of the orbit of an electron can only take certain fixed values such that the angular momentum of the electron in these orbits in an integral multiple of being the Planck’s constant.

(c) An electron can make a transition from one of its orbit to another orbit having lower energy. In doing so, it emits a photon of energy equal to the difference in its energies in the two orbits.

(ii) Given: gauss tesla, ,

The magnetic moment of the magnet is

The most stable state of the bar magnet is for . It is in the most unstable state when is

  1. (i)

Rate of emission is,

(ii) Given:

The magnitude of the induced emf,

  1. (i)

Consider 3 capacitances of capacitances and connected in parallel.

Let be the charges deposited on the capacitors as shown in the fig. Suppose a potential difference ‘ ‘ is applied across the combination.

Since different current flows through different branches so the charges are given by.

According to the principle of consewation of charges,

If these capacitors are replaced by a single capacitor of capacity Cp such that


This is the required expression

(ii) Given: , [volt]

Comparing with . we get

The frequency of the alternating emf as



Peak current,

Phase angle,

  1. (1) Magnetization: The ration of the net magnetic dipole moment to the volume of matecial is called magnetization.

Magnetic intensity: The magnetic intensity is defined as the magentic induction in an isotropic medium divided by the permeability of the medium.

(ii) Given:

Common-emitter current again,

Therefore, common-base current again,