Class 12 Physics

If the rotational kinetic energy of a body is E and moment of inertia is I then angular momentum will be:

       (A) \( EI \)        (B) \( \sqrt{2EI} \)       (C) \( \frac{E}{I} \)             (D) \( \sqrt{IE} \)

Which quantity in rotational motion is analogous to force in linear motion?

(A) Torque      (B) Moment of inertia     (C) Angular velocity        (D) Angular momentum

 a) Define angular momentum. Write its SI unit. 

b) The speed of a motor engine decreases from 900 rev/min. to 600rev/min. in 10 seconds.

Calculate: 3

i) The angular acceleration

ii) Number of revolutions made by the motor during this interval

iii) How many additional seconds are required for motor to come to rest in the same rate

             OR

a) For a simple pendulum, show that the acceleration is directly proportional to the displacement of bob from its mean position. 

b) A bob of mass 8kg performs SHM of amplitude 30cm. The restoring force is 60N. Calculate: 

i) Time period ii) The maximum acceleration iii) Kinetic energy when displacement is 12 cm.

What is factor affecting radius of gyration of a body?

A) Angular speed              B) Axis of rotation

C) Angular acceleration    D) Acceleration due to gravity

a) The angular velocity of the earth around the sun increases when it comes closure to the sun, why? 

b) A disc having moment of inertia \( 10\text{ kg m}^2 \) about its center rotates steadily with angular velocity of \( 20\text{ rad s}^{-1} \). Find: 

i) Rotational kinetic energy

ii) Number of revolution per second

The displacement versus time graph of particles in SHM is shown in figure. The maximum velocity of the particle is

     (A) \( 1 \text{ cm s}^{-1} \)      (B) \( 0.2 \text{ cm s}^{-1} \)   (C)\( 3.14 \text{ cm s}^{-1} \)      (D)\( 31.4 \text{ cm s}^{-1} \) 

Define the moment of inertia. 

b) A uniform rod of mass $m$ and length L is rotating about an axis AB passing through its one end and perpendicular to the length. Calculate the moment of inertia of the rod about the axis AB. 

c) A fly wheel of moment of inertia \( 0.32\text{ kgm}^2 \) is rotated steadily at 120 rad/sec by a 50 watt electric motor. Calculate: 

      i) the kinetic energy of the fly wheel.

      ii) the frictional couple opposing the rotation.

           OR

a) One end of a light spring having spring constant 18 N/m is attached to a rigid support. A mass of 0.15kg is suspended from other end of the spring. A student pulls down it such that extension of spring increases by 4cm. The student now releases it, as a result, the mass performs SHM.

i) Define simple harmonic motion.

ii) Calculate the maximum acceleration and time period of SHM. 

b) Write an expression for total energy of a particle executing SHM. Also draw a graph showing the variation of K.E. and P.E. of it.

2. A particle undergoes SHM having time period T. What is the time taken by it to move from mean position to half of amplitude?

 (A)\( \frac{T}{2} \)

(B) \( \frac{T}{3} \)

(C) \( \frac{T}{6} \)

(D) \( \frac{T}{12} \)

The frequency of tuning fork is 384Hz and velocity of sound in air is 352m/s. How far the sound has transversed while fork complete 36 vibrations?

(A) 33m      (B) 36m       (C) 352m          (D) 72m

2. The length of a pendulum is increased by 21%. By what percentage of the period of the motion increases?

A) 9.8%        B) 10%    C) 11%      D) 21%

Two capillary tubes P and Q of radii 4 mm and 2  mm are dipped in water. What is the ratio of heights through which liquid rises in the tubes P and Q?

 (A) 1:2         (B) 2:1      (C) 1:4      (D) 4:1

a) Derive a relation between surface tension and surface energy. 

b) N identical spherical drops of water falling with a terminal velocity\( v_1 \) were to coalesce to form a bigger drop and fall with a new terminal velocity \( v_1 \)\( v_2 \) through air. (Neglect air resistance)

i) Obtain a relation between \( v_1 \) and \( v_1 \)

ii) If N=2 and \( v_1 = 0.4 \text{ ms}^{-1} \) then calculate \( v_2 \)

Two capillary tubes A and B of radii 2mm and 4 mm are dipped in the same liquid. What is the ratio of heights through which liquid rises in the tubes A and B?

 (A) 1:2

(B) 2:1

(C) 1:4

 (D) 4:1

In an experiment, a spherical ball of radius 'r' and density '\( ' \rho ' \) falls freely through the glycerin of density '\( \sigma \), as shown in figure.

a) Write the components of forces acting on the body by drawing free body diagram.                       

b) Sketch a graph by showing the nature of variation of velocity of ball with time. 

 c) If this drop soon attains constant downward velocity then find its expression. 

  Figure : 

A cork rises from the bottom of the water and finally floats in water. Its graphical representation will be:

a) State Stoke's law and use it to derive an expression for the determination coefficient of viscosity of given liquid. 

b) Write equation of continuity. Also write its two applications.

OR 

a) Define simple harmonic motion. Write general equations for displacement and acceleration in simple harmonic motion. 

 b) Plot a graph of velocity of a particle in SHM. 

c) What will be the time period of simple pendulum at the centre of the earth? Justify. 

A system undergoes an isochoric process so that its temperature changes from\( 127^\circ\text{C} \)  to \( 227^\circ\text{C} \). What is the ratio of initial pressure to final pressure?

A) \( \frac{4}{5} \)         B) \( \frac{5}{4} \)        C)\( \frac{227}{127} \)      D) \( \frac{127}{227} \)

The temperature of inversion of a thermocouple is 600°C and the neutral temperature is 310°C. What must be the temperature of cold junction?

    (A) 0°C       (B) 10°C                     (C) 20°C                  (D) 30°C

The given figure represents the P-V diagram of a cyclic process.

a) Define indicator diagram. 

 b) Estimate the workdone during II process. 

 c) Identify the thermodynamic processes represented by I, II, III and IV.

 An ideal liquid is taken through series of changes represented in diagram. The workdone by the gas at the end of cycle is  is a

(A) \( P_1V_1 \)

 (B) \( 5P_1V_1 \)

(C) \( 10P_1V_1 \)

(D) Zero

 What is meant by entropy? Write the first law of thermodynamics in terms of entropy. 

 Can a room be cooled by leaving the door of an electric refrigerator open? Justify.  

c) A quantity of monoatomic gas at 30°C is compressed suddenly to \( (\frac{8}{27})^{th} \)parts of its initial volume. Find the change in temperature assuming \( \gamma (= \frac{C_p}{C_v}) \) to be \( \frac{5}{3} \) 

 In which of the following thermodynamic process of the gas, work done is minimum?*

A) Isothermal    B) Adiabatic    C) Isobaric    D) Isochoric

a) Apply first law of thermodynamics to obtain the relation \( C_p - C_v = R \), where symbols have their usual meanings. 

 b) A petrol engine consumes \( 10\text{kg} \) of petrol in one hour. The calorific value of petrol is \( 1.14 \times 10^4\text{ calg}^{-1} \). The power of the engine is \( 30\text{kW} \). Calculate the efficiency of the engine. 

Given figure represents the block diagram of a heat engine. What is the efficiency of this engine?

      A) 25%          B) 50%        

     C) 60%           D) 75%

.A Carnot engine is working between 300K and 600K has output 200J. What is the energy supplied to the engine?

 (A) 400J       (B) 800J      (C) 1200J        (D) 1600J

 If efficiency of petrol engine is \( \eta_1 \)and that of diesel engine is \( \eta_2 \) then, which of the following expression is correct?

A) \( \eta_1 = \eta_2 \)   B)\( \eta_1 > \eta_2 \)

C) \( \eta_1 < \eta_2 \)     D) \( \eta_1 \ge \eta_2 \)

What is the distance between two consecutive particles in a wave which are in the same phase?

A) \( \frac{\lambda}{4} \)     B)\( \frac{\lambda}{2} \)        C) \( \frac{3\lambda}{4} \)      D) \( \lambda \)

a) The diagram shows a standing wave in an open organ pipe.

 i) Redraw the diagram and show the position of nodes and antinodes.              

 ii) Derive an expression for frequency of this mode. 

 b) What will be the effect of velocity of transverse wave in a stretched string if the radius of the string is doubled? 

c) A car is sounding its horn has a frequency 400Hz and travelling towards a stationary traffic post. A traffic police at the post detects the change in frequency of 60Hz when the car crosses him. Find the velocity of car if velocity of sound in air is \( 340\text{ms}^{-1} \)

                         OR

 a) How can a plane wavefront be converted into a spherical wavefront? Justify. 

b) What is interference of light? Two coherent waves, each of intensity I, are producing an interference pattern. What will be the resultant intensity at a point of

i) constructive interference and ii) destructive interference? 

c) A monochromatic light of wavelength 5890 A^o is incident normally on a diffraction grating which has 6000 lines per centimeter.

i) At what angle will the second order image be seen?  ii) Is third order image possible with this grating? 

 What is the distance between node and antinode in a stationary wave in terms of wavelength?

A) \( \frac{\lambda}{2} \)    B) \( \frac{\lambda}{4} \)     C) \( \lambda \)     D) \( 2\lambda \)

a) What correction was made by Laplace over the Newton's formula for velocity of sound in a gas? Obtain the corrected formula.

b) Calculate the wavelength of wave in air at \( 25^\circ\text{C} \) if the frequency of sound wave is \( 256 \text{ Hz} \) and velocity of sound at \( 0^\circ\text{C} \)   is   \( 330\text{ms}^{-1} \) . 

a) Obtain Laplace's formula for velocity of sound in air starting from Newton's formula. 

 b) A car producing note of frequency \( 500\text{Hz} \) approaches and passes a stationary observer at the steady speed of \( 20\text{ms}^{-1} \). Calculate change of frequency heard by the observer (Velocity of sound = \( 340\text{ms}^{-1} \)). 

a) Define an organ pipe. 

b) What is the ratio of length of two pipes, an open organ pipe A and a closed organ pipe B both vibrating in third overtones are in resonance? Justify. 

 c) In the given figure below, figure (i) represents a situation that both source of sound (S) and Listener (L) are at rest position 'S' and 'L' respectively. Figure (ii) represents relative motion between moving source and stationary listener. 

i) Does the pitch of sound changes to the listener in second case? Justify 

ii) Develop an expression to support your answer in (i).

d) Write any two properties of medium which is necessary for the propagation of sound. 

A polarizer is used to 

(A) reduce intensity of light                                      (B) produce diffracted light
(C) increase intensity of light                                   (D) produce unpolarized light

 Time taken by light to cross a glass slab of thickness 5cm and refractive index of 1.5 will be:

A) 0.2 ns   B) 0.25 ns     C) 0.3 ns     D) 0.35 ns

a) Thin films such as soap bubbles show beautiful colors when illuminated by white light. Why? 
b) "The bright and dark fringes are equally spaced". Justify this statement from Young's double slits experiment. 
c) A diffraction grating has 400 lines per mm and is illuminated normally by monochromatic light of wavelength 600nm. Calculate
i) The grating spacing.
ii) The angle to the normal at which the first order maximum is seen.
iii) The numbers of diffraction maxima obtained. 

OR
a) Why is an end correction necessary for organ pipes? 

b) How is it possible to estimate that the vessel kept under an open tap of water is about to fill? Justify. 

c) In case of an organ pipe, notes of frequencies 200Hz, 600Hz and 1000Hz are heard. Is the pipe open or closed? 

d) Describe the various modes of vibration of the air column in a closed organ pipe. 

A ray of light strikes a glass plate at an angle of incidence\( 60^\circ \). If the reflected and refracted rays are perpendicular to each other in interface, what is the refractive index of glass?

 (A) \( \frac{1}{\sqrt{3}} \)

(B)\( \frac{\sqrt{3}}{2} \)

 (C) \( \frac{2}{\sqrt{3}} \)

(D) \( \sqrt{3} \)

The arrangement of potentiometer circuit for the determination of internal resistance of a cell (r) is shown in figure.

Derive an expression for internal resistance of the cell.

a) Using Kirchhoff's laws of electrical circuit; derive an expression for balanced condition of Wheatstone bridge. 

 b) Conclude with the reason, where the balance point will be shifted, towards A or B when, 

 i) Resistance R is increased, keeping all other parameters constant .

ii) Resistance S is decreased , Keeping R is Constant .

a) Two conductors X and Y carrying currents \( I_1 \) and \( I_2 \) are placed in air at a distance r apart as shown in figure.

i) Find the magnitude of force between them. 

 ii) What is the nature of force in this case? 

iii) Define one ampere current on the basis of the force between parallel current carrying conductors. 

b) Figure shows a rectangular metal frame ABCD placed in a uniform magnetic field of flux density\( 4.5 \times 10^{-3} \) T.

OR  

a) Define impedance of LCR circuit. 

b) A series LCR circuit is given in figure.

i) Calculate the impedance of the circuit if \( L=60\text{mH} \), \( C=0.50\mu\text{F} \) and \( R=300\Omega \) 

ii) How does resonance occur in above LCR circuit? Write the required expression

c) A device is connected across an ac source of voltage \( V=V_0 \sin \omega t \) and the current through X is given by\( I=I_0 \sin (\omega t + \frac{\pi}{2}) \)

i) Identify, which device is X? Also, write the expression for its reactance. 

ii) Draw graphs showing the variation of voltage and current with time over one cycle of an alternating current for X .

a) Analyze the given graph and name the type of material represented by graph A and graph B. 

b) Define potential gradient. A potentiometer wire is\( 10\text{m} \) long. It has a resistance of \( 20\Omega \). It is connected in series with a battery of \( 3\text{V} \) and a resistance of \( 10\Omega \). Calculate the potential gradient along the wire. 

Which of the following is the phenomenon of production of emf by maintaining a difference of temperature between two junctions of dissimilar metals?

 (A) Joule's effect      (B) Seebeck effect     (C) Peltier effect        (D) Thomson's effect

Which of the following represents the process of production of emf by maintaining a difference of temperature between the two junctions of a loop of two dissimilar metals?

A) Seebeck effect   B) Joule effect   C) Peltier effect      D) Thomson effect

Obtain an expression for the magnetic field intensity at any point due to a straight current carrying conductor using Ampere's circuital law. 

 A wire of length 0.5  m carrying a current of 2A is placed in a uniform magnetic field of strength 0.4T . Find the maximum and minimum force experienced by it. 

a) A circular coil of radius R is carrying a constant current I. Find an expression for magnetic field at point P, which is at a distance x on its axial line. 

b) Why is Hall voltage much more measurable in semiconductors than metals? Explain. 

c) Draw magnetic field lines around the two parallel current carrying conductors in which currents are in opposite direction. 

d) Two long parallel conductors are placed 0.1 m apart and carry currents of 3 A and 2 A, respectively in the same direction. Calculate the force per unit length experienced by each conductor due to the other. (\( \mu_0 = 4\pi \times 10^{-7}\text{Hm}^{-1} \)) 

What happens to the susceptibility of ferromagnetic substance if temperature is decreased?

(A) Increases     (B) Decreases      (C) Remains same    (D) May increase or decrease

Which portion of the given figure represents the coercivity?                                    

A) CD    B) AD    C) AG     D) AE

What is the induced emf in a coil if the flux associated with it changes at the rate of 1 Weber per minute?

 (a) 1 Volt       (b) \( \frac{1}{60} \)Volt     (c) 60 Volt        (d) Zero

a) Define self inductance of a coil.

b) A current from A to B is increasing in magnitude. What is the direction of induced current, if any, in the loop as shown in figure? Justify. 

c) Calculate the self inductance of a coil of 100 turns if a current of 2A gives rise to magnetic flux of \( 5 \times 10^{-3} \) Weber through the coil. 

a) State and explain Lenz's law. 

b) A bar magnet falls through a metal ring, will its acceleration be equal to g? Justify your answer. 

c) According to Faraday's law of electromagnetic induction, induced \( \text{emf} = -N\frac{d\phi}{dt} \) What does the negative sign indicate? 

OR 

a) Define rms value of current. 

b) The emf in an ac circuit is represented as \( E = E_0 \sin \omega t \). Show that voltage through an inductor leads current by \( \frac{\pi}{2} \). Also draw a phasor diagram. 

c) Why does a capacitor block d.c.? 

In our country Nepal, the supply ac voltage is 220V. The peak value of voltage is about

     (A) 110V               (B) 220V               (C) 310V       (D) 350V

 A coil has a resistance of\( 8\Omega \)and an inductive reactance \( 6\Omega \). What will be the impedance?

A) \( 6\Omega \)   B) \( 8\Omega \)  C) \( 10\Omega \)   D) \( 14\Omega \)

a) Explain quantization of charge. 

b) An ion of specific charge \( 4.40 \times 10^7 \text{ C/kg} \) is moving in a circular orbit in a magnetic field of flux density 0.4T with velocity of \( 3.52 \times 10^5 \text{ ms}^{-1} \). Calculate the radius of this orbit. 

c) Why are x-rays used in Millikan's oil drop experiment? 

                      OR

a) Define the terms half life and mean life of a radioactive substance. 

b) If 2 gm of a radioactive material having half life period of 50 years disintegrates, find out mean life of the given sample. 

c) Given figure represents decay graph of a radio active sample of half life 10 years. Estimate the value of T₃

a) A graph between stopping potential (\( V_o \)) with the frequency (f) of incident radiation is shown in figure below. Answer the following questions.

i) Write the Einstein photoelectric equation in terms of stopping potential. 

ii) How will you determine Planck's constant from the graph? 

iii) What happens to stopping potential if frequency of incident photon increases gradually? Justify. 

b) In an experiment, voltage across two parallel plates is 50V and distance between them is 3cm. The magnetic field applied to make the beam undeflected is\( 10^{-4} \) Tesla.

i) Why electron beam remains undeflected? 

ii) Calculate the velocity of electron passing through the fields? 

       OR

a) Define the term radioactivity. 

b) Two radioactive samples A and B have equal number of atoms initially. Their half lives are 3 hours and 9 hours respectively. Compare their rate of disintegration after 18 hours from start. 

c) Develop a relation between half life and decay constant of a radioactive sample. 

d) What percentage of atoms decayed after five half life periods? Justify your answer with calculation. 

    Graph : 

a) A moving coil is very sensitive device to measure very small current.

i) Define voltage sensitivity of moving coil galvanometer. On which factors does it depend? 

ii) Why is magnetic field made radial in a moving coil galvanometer? 

b) State Faraday's laws of electromagnetic induction. The magnetic flux passing perpendicular to the plane of a coil is given by \( \phi = 4t^2 + 5t + 2 \), where \( \phi \)is in weber and t is in seconds. Calculate the magnitude of instantaneous emf induced in the coil when t = 3s. 

c) Derive an expression for energy stored in an inductor. 

                  OR

a) Obtain an expression for magnetic field strength at the centre of current carrying circular coil using Biot-Savart's law.

 b) A slice of indium antimonide 2.5 mm thick carries a current of 150 A. A magnetic field of flux density 0.5T, correctly applied, produces a maximum Hall voltage of 8.75  mV between the edges of the slice. Calculate the number of free charge carriers per unit volume assuming they each have a charge of \( -1.6 \times 10^{-19}\text{C} \) 

c) Derive an expression for the force exerted per unit length between two parallel current carrying conductors if currents are flowing in the same direction. Hence, define one ampere current.

a) Explain photoelectric effect and write Einstein photoelectric equation. 

 b) Obtain an expression for the velocity of an electron in the first excited state. 

c) Calculate the de-Broglie wavelength of an electron which has been accelerated through a potential difference of 300V.

[Mass of electron = 9.1 *10 ^-31  kg . Planck's constant,  h = 6.6 * 10 ^-34 JS ]

a) State and explain Bohr's postulates of an atomic model. 

b) i) Calculate the de-Broglie wavelength of a neutron having kinetic energy 150eV. 

 ii) A proton and an electron have same K.E. which one has greater de-Broglie wavelength?

[Given : Mass of neutron \( = 1.675 \times 10^{-27} \) kg, Planck's constant \( = 6.62 \times 10^{-34} \)JS]

a) What are excitation potential and ionization potential? 

b) Given figure shows the different energy levels of a hydrogen atom. Estimate the energy values for n=4 and 5. How many different transitions are possible? 

c) What is rectifier? Describe the working of full wave rectifier using two P-N junction diodes.

a) What is photo electric effect? 

b) Describe Einstein's photoelectric equation 

c) State and explain Bragg's law of X-ray diffraction 

d) Calculate the value of Planck's constant and work function from the given figure. 

What is rectification? Explain full wave rectification using two P-N junction diodes.

  For the digital circuit given below write the truth table showing the outputs A', B' and Y for all possible inputs A and B. 

a) During forward biasing of p-n junction diode, the width of depletion layer decreases. Justify. 

 b) Write the truth table for the combination of gates given in the figure below. 

c) Identify, which gate is obtained from the above combination of gates? 

.A diode as a rectifier converts

A) varying dc into constant dc

B) dc into ac

C) high voltage into low voltage

D) ac into dc

a) In Youngs double slits experiment, what changes will you observe in fringe width for the following operations:

 i) When experiment is shifted from air to inside water 

ii) When slits width is increased? 

 b) i) What is diffraction of light? 

 ii) Calculate the width of central diffraction peak on a screen 4m behind a 0.01m slit illuminated by 600nm light source. 

     OR

a) How can a spherical wave front be changed into plane wavefront? Draw a diagram to justify your answer.  

b) Apply Huygen's principle to verify the law of reflection of light. 

a) Define half and mean life. 

 b) Calculate the value of half life and decay constant from fig (a). 

 c) Which one curve in fig (b) has more value of decay constant? Justify.

Which of the followings is the ferromagnetic material?
(A) Aluminium               (B) Gold                (C) Copper                   (D) Cobalt

If a P-Wave were to go from a solid to a liquid, what would happen to its velocity?
A) remains the same        B) increases
C) decreases                   D) decreases up to zero

Which of the earth quake waves is first recorded on the seismograph?

 (a) P-waves          (b) Rayleigh Waves      (c) S-Waves      (d) Love Waves

a) Draw free body diagram of oil drop falling through air in Millikan's oil drop experiment for both cases; when field is given and when field is absent. What is the conclusion of this experiment? 

b) How do P and S waves differ?