### Physics model question class 12

## Set- 1

**(All answers of numerical problems should be expressed in the S.I. system.)**

**Attempt ***ALL ***the Multiple-Choice questions. (1x11=11)**

Tick (√) the correct answer.

1. If there is a change of angular momentum from 2 $kgm^2s^{-1}$ to 4 $kgm^2s^{-1}$ in 4 sec. Then the torque is

- 0.5 J
- 0.25 J
- 2 J
- 1.5 J

2. In SHM, the particle velocity is minimum at

- mean position
- extreme position
- at a distance A/2
- at a distance A/4

3. How high does water rise in a capillary tube whose inner diameter is 4.4 × $10^{-2}$ cm. The surface tension of water is 73 dyne/cm.

- 6.7 cm
- 7.3 cm
- 5.6 cm
- 4.3 cm

4. When a gas undergoes an adiabatic expansion, its internal energy

- increases
- decreases
- remains constant
- highly increases

5. In a Carnot engine, the temperature of the sink is $270^oC$ and that of the source is $327^oC$. The efficiency of the engine is

- 25 %
- 50 %
- 75 %
- 95 %

6. The Young’s modulus of steel is 2x$10^{11}$ $Nm^{-2}$ and density is 78x$10^2$kg$m^{-3}$. The velocity of sound in the steel is

- 340 m/s
- 900 m/s
- 4050 m/s
- 5060 m/s

7. In single slit diffraction

- slit width must be smaller than the wavelength of light.
- slit width must be larger than the wavelength of light.
- slit width must be equal to the wavelength of light.
- none of the above.

8. An ammeter having a resistance of 10Ω allows a current of 0.002 A to flow through it. For it to allow a current of 2A, we should

- join a resistance of 0.02Ω in series
- join a resistance of 0.02Ω in parallel
- join a resistance of 0.01Ω in series
- join a resistance of 0.01Ω in parallel

9. Which of the following combinations would give maximum emf?

- Ni and Cr
- Fe and Bi
- Sb and Bi
- Cu and Fe

10. Area of hysteresis curve indicates

- Retentivity
- Loss of energy per cycle
- Coercivity
- Gain of energy per cycle

11. The potential barrier at p-n junction is due to

- the majority carriers on the p-side of the junction
- the minority carriers on the n-side of the junction
- both majority and minority carriers on either side of the junction
- immobile donor and acceptor ions on either side of the junction

**Group-B **

** Attempt All the questions. (8×5) = 40 **

1.

a. For an object falling freely through a fluid, draw a free body diagram for sinking object at each of the following points during its descent: [3]

- The instant it is released.
- As it is accelerating.
- When it is traveling at its terminal velocity.

b. Why are rain drops always spherical in shape? [2]

2.

- From the displacement time graph shown in the figure, determine the amplitude and frequency of the oscillation represented. [2]
- Obtain an expression for the total energy of a particle executing simple harmonic motion. [3]

3.

- Define angular momentum and write its SI unit. [2]
- A ballet dancer spins with 2.4 rev/s with her arms outstretched when the moment of inertia about the axis of rotation is I. With her arms folded, the moment of inertia about the same axis becomes 0.6I. Calculate the new rate of spin. [3]

4.

- Derive the relation $C_p$ – $C_v$ = R, where the symbols have their usual meanings. [3]
- Draw a P-V diagram for an isothermal process and an adiabatic process. [2]

5.

- Sound waves are called pressure waves. Why? [2]
- A car is moving away from a stationary listener with a velocity of 20m/s. If the horn is sounding a frequency 512 Hz. Calculate the change in pitch of the sound received by the listener. [ Velocity of sound in air = 330 m/s] [3]

6.

- Explain what is meant by the r.m.s value of an alternating voltage.
- An alternating voltage V is represented by the equation

V=220 sin(120пt) where V is measured in volts and t is in seconds.

For this alternating voltage, determine the peak voltage, the rms voltage and the frequency.

**OR, **

The coil is rotated at constant speed, causing an emf to be induced.

- Sketch a graph to show how the induced emf varies with angle ϴ during one complete rotation of the coil starting when ϴ = 0.
- State the value of the flux linkage for the coil at the positions where the emf has its greatest values.

7. The radioactive isotope of iodine $l^{131}$ has a half-life of 8.04 days. Calculate

- The decay constant $l^{131}$. [2]
- The time taken for the activity of the sample to fall from 5.4x$10^4$ dis/s to 5.0x$10^4$ dis/s. [3]

**OR, **

What is a P-N junction diode? Explain the characteristics of it in the forward and reversed biased condition. [1+2+2]

8. The Einstein’s equation of photoelectric effect if given by hf = Ф+ $EK_{(max)}$ where the symbols carry their usual meanings.

- Explain the meaning of each term in the above equation. [3]
- Sketch a graph of $EK_{(max)}$ against f. [1]
- State the value of the gradient of the graph sketched in part (ii). [1]

**Group - C **

** Attempt all the questions. (3x8=24) **

1.

- State Biot-Savart’s law. Use this law to find the magnetic field at a point due to a long straight current carrying conductor. [1+3]
- Sketch the magnetic field due to two long parallel conductors carrying currents of 12 A and 8 A respectively in the same direction. If the wires are 10 cm apart find where a third parallel wire also carrying current must be placed so that the force experienced by it shall be zero. [1+3]

**OR, **

- What is the principle of a potentiometer? How this is used to measure the internal resistance of a cell. [1+3]
- Calculate the current through each resistance. [4]

2.

- What is the specific charge of an electron? Describe J.J. Thomson's experiment to determine the specific charge of an electron. [1+3]
- An oil drop of density 960 kg/$m^3$ and radius $10^{-7}$ m is driven vertically upward through air by an electric field of 1.95x$10^4$ V/m with a constant velocity of 3.5x$10^{-4}$ m/s. If the viscosity of air is 1.8x$10^{-5}$ Ns/$m^2$, calculate the number of electric charges on the drop. [Neglect the upthrust due to air]

**OR, **

- State Bohr's postulates and hence derive expression for the energy of nth orbit of hydrogen atom. [1+3]
- An X-ray tube works at a dc potential of 50 KV and the current through the tube is 0.5 mA. Find (i0 the number of electrons hitting the target per second
- the energy falling on the target per second as the kinetic energy of electrons
- the cut-off wavelength of emitted X-rays. (The charge of an electron = 1.6x$10^{-19}$C, Planck’s constant =6.62x$10^{-34}$Js).

3.

- What is the end correction of a pipe? Describe the different modes of vibration of the air column in a closed pipe. [1+3]
- A narrow beam of monochromatic blue light is directed at a double slit arrangement with slits S and T as shown. Parallel blue and dark fringes are seen on the screen.

The blue light has a wavelength of 460 nm. The distance from S to X is 0.16 μm and from T to X is 0.85 μm.

- Determine whether point X is a blue fringe or a dark fringe. [2]
- Describe how the appearance of the fringes would differ if red light had been used instead of blue light. [2]

## SET- 2

**Attempt all questions **

** Group-A **

** (Multiple choice questions) **

** Tick the most appropriate answer**. **[1×11=11] **

1. The time period of a pendulum on Earth is 1.0 s. What would be the period of a pendulum of the same length on a planet with half the density but twice the radius of Earth?

- 0.5 s
- 1.0 s
- 1.4 s
- 2.0 s

2. If all the ice on the polar caps of the earth melts, due to global warming then the duration of the day will be

- 24 hours
- more than 24 hours
- less than 24 hours
- 12 hours

3. The tendency of a liquid surface to contract is due to the following property

- cohesion
- adhesion
- viscosity
- surface tension

4. The figure shows a P-V diagram of an ideal gas. The work done by the gas in the process ABCDA is:

- 0.5PV
- 2PV
- 1.5PV
- 4PV

5. Heat is transferred to a heat engine from a furnace at a rate of 80 MW. If the rate of waste heat rejection to a nearby river is 50 MW, determine the net power output for this heat engine.

- 30 MW
- 40 MW
- 50 MW
- 60 MW

6. The intensity of light emerging from the two slits in Young’s experiment is in the ratio 1: 4. The ratio of intensity of the minimum to that of the consecutive maximum will be:

- 1: 4
- 1 : 9
- 1 : 16
- 2 : 3

7. The speed of sound in air at N.T.P. is 300 m/s. if air pressure becomes four times, then the speed of sound will be

- 150 m/s
- 300 m/s
- 600 m/s
- 1200 m/s

8. The logic gate that will have HIGH or “1” at its output when any one of its inputs is HIGH is a/an …………… gate.

- OR Gate
- NOT Gate
- AND Gate
- NAND Gate

9. The relative permeability of a medium is 500. What is its magnetic susceptibility?

- 500
- 501
- 49.9
- 499

10. The neutral temperature of a thermocouple is $350^0$C when the cold junction is at $0^0$C. When the cold junction is immersed in a bath of $300^0$C the inversion temperature is

- 70$0^0$C
- 60$0^0$C
- 35$0^0$C
- 67$0^0$C

11. Figure shows a part of a closed electrical circuit. Then $V_A-V_B$ is

- 8V
- 3V
- 9V
- 6V

**Group-B**** **

**(Short answer questions)**** **

**Attempt all the questions. [8×5=40] **

1.

- A spherical object of radius ‘r’ having density ‘ρ’ is falling in a viscous medium of density ‘σ ‘with the terminal velocity ‘v’. Use Stokes’ law to Obtain an expression for the coefficient of viscosity of the medium. [3]
- When two identical raindrops are falling with a terminal velocity 3.5m/sec, if they coalesce to a big drop, then find the terminal velocity of the bigger drop. [1]
- Why are the wings of an airplane slightly convex outwards while flattened inwards? [1]

OR

- Show that for small oscillations the motion of a simple pendulum is simple harmonic. [2]
- Consider a simple harmonic oscillator with mass 0.5kg, spring constant 10N/m, and amplitude 3cm. (i) What is the total energy of the oscillator? (ii) What is the speed when x=2cm? [1+1]
- Why are soldiers ordered to break steps while crossing a bridge? [1]

2.

- Derive an expression for the radius of gyration of a body about an axis in terms of distances of various particles of the body from the axis of rotation. [2]
- State conservation of angular momentum. [1]
- Calculate the terminal velocity of a glass ball falling through a tall jar containing glycerin. The densities of the glass ball and glycerin are 2.6 g/cc and 1.32 g/cc respectively and the viscosity of the glycerin is 0.85 poise and the radius of the glass ball is 2mm. [2]

3.

- Write Clausius's statement on the second law of thermodynamics. [1]
- Draw a PV- diagram and briefly write the working of the four-stroke Otto engine. [1+2]
- A refrigerator has to transfer an average of 263J of heat per second from temperature -$10^0$C to $25^0C$. Calculate the average power consumed, assuming no energy losses in the process [1]

4.

- A narrow beam of monochromatic light is incident normally on a slit, then a diffraction pattern is obtained on a screen. The necessary diagram explains the formation of secondary minima and secondary maxima. [2+2]
- A plane transmission grating gives an angle of diffraction of a line at $30^0$ in the third order. Find the number of lines per cm on the grating if the wavelength of light used is $5555^0A$. [1]

**OR **

- Write a condition for destructive interference. [1]
- Find the distance between any two consecutive bright bands due to the superpositions of light waves produced by two coherent sources. [3]
- When two slits are placed 0.3mm apart and are placed 50cm from a screen. What is the distance between the second and third dark lines of the interference pattern, when the slits are illuminated with light of wavelength 6×$10^{-7}$ m? [1]

5.

- What is a shunt. Find its expression when a galvanometer is converted to an ammeter. [1+2]
- A galvanometer can bear a maximum current of 25mA and a resistance of 5Ω. Find suitable resistance to convert it into a voltmeter of range 0-2V. [2]

6.

- Draw the phase diagram for LCR series a.c. circuit when the inductive reactance is greater than the capacitive reactance of the circuit. [1]
- Find the condition for the electrical resonance of an LCR series circuit. [2]
- When a 25Ω resistor, 300mH inductor, and 10μF capacitor are connected in a series with 240V, and 50Hz a.c. source. Calculate the value of current in the circuit and potential difference across the capacitor. [1+1]

7.

- How is a barrier potential formed in a PN-junction? [1]
- Why cannot metal have a hole current? [1]
- An n-type semiconductor has a large number of free electrons at room temperature. Is it electrically neutral or not? [2 ]
- What is nanotechnology? [1]

8.

- What are X-rays? On what factors the wavelength and the intensity of the emitted X-rays in a Coolidge tube depend? [1+1+1]
- Calculate the frequency and wavelength of the highest energy X-rays emitted by an X-ray tube operating at 150 KV. [1+1]

**Group-C**** **

**(Long answer questions)**** **

** Attempt all the questions**. **[3×8=24] **

1.

- Write the relation between intensity and intensity level. [1]
- Show that the intensity of sound is directly proportional to the square of the amplitude. [3]
- A train is traveling at 30m/s in still air. The frequency of the note emitted by the train whistle is 262Hz. What frequency is heard by a passenger on the other train moving in the opposite direction to the first at 18m/s (i) when approaches the first and (ii) when receding from the first? [2+2]

2.

- Write Biot-Savart’s law in vector form. [1]
- Use Biot-Savart's law to show that the magnetic field at centre of a current-carrying circular coil is inversely proportional to its radius. [3]
- Find the value of the magnetic field at centre O of a coil bent in the form of a square of side 2m carrying current 2A as shown in figure 1 and predict the direction of the magnetic field. [1+1]
- What is Hall effect. Why Hall voltage for n-type semiconductors is greater than copper? [1+1]

OOR,

- Define eddy current. What is the effect of eddy current in a transformer? [1+1]
- Show that Lenz’s law is an example of conservation of energy. [2]
- Obtain the expression for energy stored in an inductor. [2]
- A magnetic field of a flux density 10 T along the axis normal to a coil of 50 turns having 100$cm^2$ area. Find e.m.f. induced in the coil if the coil is removed from the magnetic field in 0.1sec. [2]

3.3.

- Derive the expression for the radius of the nth orbit of a hydrogen atom. [2]
- Write the relation between the binding energy of an electron with the principal quantum number. [1]
- Calculate the wavelength of the first line of the Balmer series, if the wavelength of the second line of this series is 4.88×$10^{-7}$ m. [3]
- State Bragg’s law of diffraction. Find the angle for the first-order diffraction when the spacing between two planes is λ? [1+1]

OR

- Prove that the path of a horizontal beam of electrons entering mid-way between two oppositely charged plates is parabolic. [2]
- What is the photoelectric effect? Present the necessary theory to determine the value of Planck’s constant. [1+3]
- Ultraviolet light of wavelength 3.6× $10^{-7}$m is made to fall on a smooth surface of potassium having work function 2.3 eV. Determine maximum energy of emitted photoelectrons and stopping potential. [1+1]

**SET- 3**

**Group -A **

**(Multiple choice questions) **

**Tick the most appropriate answer**. **[1×11=11]**** **

1. A proton and alpha particle are moving into a magnetic field having same kinetic energy, then the ratio of their radius is

- 1:1
- 1:2
- √2: 1
- 1: √2

2. The wavelength of the wave following the equation of sound wave y= 0.0015 Sin (62.4 x + 316 t) is

- 0.2unit
- 0.1unit
- 0.3unit
- cannot be determined

3. The instrument for the accurate measurement of emf of a cell is

- a voltmeter
- an ammeter
- a potentiometer
- a slide wire bridge

4. A resistance of 5 Ω is connected in the left gap of a meter bridge and 15 Ω in the other gap. the position of balancing point from left side is

- 25 cm
- 50 cm
- 75 cm
- 100 cm

5. For minima, the path difference between two waves must be

- n⅄
- (2n-1) ⅄
- (2n-1) ⅄/2
- (2n+1) ⅄

6. The specific heat capacity of an ideal gas under isothermal condition is

- 0
- 1
- infinity
- 8.31

7. A bar magnet is close to a coil. No other magnetic fields are present. An ammeter is connected to the coil as shown in figure.

The magnet and the coil are moved in the following ways.

- The magnet and the coil both move to the right with the same speed.
- The magnet is stationary and the coil moves to the left.
- The coil is stationary and the magnet moves to the right.

In which of the following will the ammeter indicate a current?

- I and II only
- I and III only
- II and III only
- I only

8. A ballet dancer dancing on the floor outstretches her arms to ………her spinning rate.

- increase
- decrease
- remain same
- increase first and then to decrease

9. The pendulum stops due to

- gravity
- lack of energy
- air friction
- its mass

10. The angle of contact does not depend upon

- nature of solid
- nature of liquid
- medium above the liquid surface
- inclination of solid

11. The efficiency of the Carnot engine working between steam point and ice point is …. %.

- 16.8
- 26.8
- 36.8
- 46.8

**Group 'B' (5x8= 40)**** **

1.

- Describe with necessary theory, Millikan’s oil drop experiment to determine the value of the charge associated with an electron. [3]
- Calculate the De-Broglie wavelength of electron having kinetic energy of 400 eV. [2]

2.

- What is cross field? [1]
- How can the velocity of a particle in a cross field be determined? [1]
- The specific charge of a particle is 4.4 x $10^7$ C.$kg^{-1}$. It is moving in a circular orbit with a velocity 3.52 x $10^5ms^{-1}$ in a magnetic field of flux density 0.4T. Find the radius of its orbit. [3]

3.

- Derive the expression for work done during adiabatic process. (2)
- Explain why $C_p$ is greater than $C_v$? (1)
- Draw the PV- diagram of isothermal, isobaric, isochoric and adiabatic processes. (2)

4.

- What are the main distinguishing assumptions made between Newton and Laplace formula of Velocity of sound? Explain in brief. (2)
- Show that pressure of gas is an independent factor for velocity of sound in the gas. (1)
- On a stormy day, a boy observes a lightning flash which is followed by a thunder 3 seconds later. How would you estimate the distance of the lightning strike from the boy? (Given: velocity of light = 3 x$10^8$ m/s, velocity of sound on that day = 332 m/s) (2)

**OR**** **

- What is the threshold of hearing? (1)
- The intensity level from a loudspeaker is 100 dB at a distance of 10 m. What is the intensity level at a distance of 200 m? (2)
- What will be the change in frequency when a moving source of sound passes through a stationary observer? Show in mathematical steps. (2)

5.

- Describing the construction and working of a generator, show how sinusoidal emf is generated by it. (3)
- The magnetic field of flux density is 20 mT, so that the flux is perpendicular to the plane of the coil having an area of 1 $cm^2$. Calculate the flux through the coil. The coil is now pulled from the magnetic field in a time of 0.10 s. Calculate the average e.m.f. induced in it. [2]

6.

- What is meant by self-inductance? Derive an expression for energy stored in an inductor. [1+2]
- On what factor does the power factor of a circuit depend upon? [1]
- Can a transformer be used with dc? Why? [1]

7.

- What is angular momentum? How is it related to the moment of inertia of a rigid body? [1+2]
- A constant torque of 200 Nm turns a wheel about its center. Find the kinetic energy gained after 20 revolutions made by it if its moment of inertia about its center is 100 kg $m^2$. [2]

8.

- Show that the motion of helical mass spring system is always simple harmonic. [3]
- A particle of mass 0.3 kg vibrates with a period of 2 seconds. If its amplitude is 2 seconds, what and where is its maximum kinetic energy? [2]

**OR **

- How is the coefficient of viscosity of liquid determined by falling a spherical ball through it? Explain with necessary mathematics. [3]
- A boat having length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. What will be the mass of the man? [2]

**Group C [3x8=24]**** **

1. Wheatstone bridge circuit design is the best application of Kirchhoff’s laws.

- What are the two basic Kirchhoff’s laws? [2]
- Apply Kirchhoff’s laws to derive the expression for an unknown resistance in Wheatstone bridge. [3]

When K is closed, no current flows through A. Calculate the value of R. [3]

c. In the given figure, when the switch K is open, what current flows through an ammeter (A)?

OR,

When a charge particle moves in a uniform magnetic field, it experiences a force called Lorentz force

- What is the vector representation of force? [1]
- Represent graphically the direction of force, magnetic field and velocity of the particle.[1]
- How is Ampere’s circuital law used for determining the magnetic field produced due to current flowing on the solenoid? [3]
- A 2 MeV proton moves vertically downwards through a uniform magnetic field of 2.5 Tesla. Calculate the force acting on it.

(Mass of proton= 1.67x $10^{-27}$Kg, charge of proton = 1.6x$10^{-19}$ C ) [3]

2.

- Discuss photoelectric effect and derive Einstein's photoelectric equation. [1+2]
- What are X-rays? Describe the modern Coolidge tube method to produced X-rays. [1+3]
- Why is the production of X-rays called the inverse of the photoelectric effect? [1]

OR

- Show that electron motion in a magnetic field is circular. Prove that frequency and time period are independent with the velocity of electron. [1+2+1]
- Starting from Einstein’s photoelectric equation, how the value of Planck’s constant is determined. [2]
- Light of frequency 5.0×$10^{14}$Hz liberates electrons with energy 2.31×$10^{-18}$ J from a certain metallic surface. What is the wavelength of ultraviolet light which liberates electrons of energy 8.93 ×$10^{-19}$J from the same surface?

(c = 3×$10^8$ ms-1, h = 6.62×$10^{-34}$ JS) [2]

3.

- Light added to light may produce darkness. Explain. [1]
- Find the expression for fringe width in Young’s Double slit experiment. [3]
- What is the highest order spectrum, which may be seen with monochromatic light of wavelength 600nm by mean of a diffraction grating with spacing 5000 lines/cm. [3]
- How will the resolving power of a diffraction grating be increased? [1]

**SET - 4**

** Attempt ALL the Multiple-Choice questions. (1x11=11) **

**Tick (√) the correct ans**wer.

1. The product of moment of inertia and angular acceleration gives

- force
- torque
- linear momentum
- angular momentum

2. When light travels from air to glass, which of the following properties does not change?

- Frequency
- Velocity
- Amplitude
- Wavelength

3. The first law of thermodynamics is a restatement of the

- law of conservation of momentum
- Newton’s law of cooling
- law of conservation of mass
- law of conservation of energy

4. The maximum acceleration of a body executing SHM is ao and the maximum velocity is vo. The amplitude of this motion is given by

- $\frac{v^2_o}{a_o}$
- $\frac{v_o}{a_o}$
- $\frac{a^2_o}{v_o} $
- $\frac{1}{v_oa_o}$

5. The area of the hysteresis curve indicates

- Retentivity
- Loss of energy per cycle
- Coercivity
- all of the above

6. The efficiency of the Carnot engine working between 27°C and 127°C is

- 25%
- 50%
- 75%
- 100%

7. Diffraction isn't seen in the case

- if the screen is far
- the wavelength of light is smaller than slit
- the wavelength of light is greater than slit
- wavelength is very large

8. With the increase in temperature of liquid and gasses, their viscosity will

- decrease
- increase
- increase and then decrease
- decrease and then increase

9. A horizontal beam of electrons is passed between two horizontal parallel plates, 2.0 cm apart, as shown.

The upper plate has an electrical potential of +4.0 V, and the lower plate has an electrical potential of – 4.0 V. What is the force on each electron when between the plates?

- 3.2 × $10^{-17}$ N downwards
- 3.2 × $10^{-19}$N upwards
- 6.4 × $10^{-19} N downwards
- 6.4 × $10^{-17}$ N upwards

10. Two parallel wires carry currents of 20A and 40A in opposite directions. Another wire carrying a current antiparallel to 20A is placed midway between the two wires. The magnetic force on it will be

- towards 20A
- towards 40A
- zero
- perpendicular to the plane of the currents.

11. The heat developed in a system is proportional to the current through it.

- It cannot be Thomson heat.
- It cannot be Peltier heat.
- It cannot be Joule heat.
- It can be any of the three heats mentioned above.

**Group – 'B' **

** Attempt ***ALL ***questions. (5x8 = 40) **** **

1.

- Define surface tension and angle of contact. Prove that the surface energy and surface tension are numerically the same. [2+2]
- What is capillarity? [1]

2.

- State Bernoulli’s principle. [1]
- Fig.2 below shows a liquid of density 1200 kg$m^{-3}$ flowing steadily in a tube of varying cross-sections. The cross-section at point A is 1.0 c$m^2$ and that at B is 20 m$m^2$, points A and B are in the same horizontal plane. The speed of the liquid at A is 10 cm/s. Calculate

- the speed at B. [2]
- the difference in pressure at A and B. [2

OR,

- The moment of inertia of a body is 100 kg $m^2$. What can be understood from this value? [1]
- A constant torque of 500 Nm turns a wheel, which has a moment of inertia of 20 kg $m^2$ about its center. Find the angular velocity and kinetic energy gained in 2s. [2+2]

3.

- What is the working principle of a heat engine? [1]
- Draw a PV diagram of a petrol engine and explain its working.

4. A student is trying to make an accurate measurement of the wavelength of green light from a mercury lamp (λ = 546 nm). Using a double slit of separation of 0.50 mm, he finds he can see ten clear fringes on a screen at a distance of 0.80 m from the slits. He then tries an alternative experiment using a diffraction grating that has 3000 lines per centimeter.

- What will be the width of the ten fringes that he can measure in the first experiment? [2]
- What will be the angle of the second-order maximum in the second experiment? [2]
- (Suggest which experiment you think will give the more accurate measurement of wavelength (λ). [1]

5.

- Describe the construction and explain the working of a transformer. Define the efficiency of a transformer. [2+1]
- Mention two types of loss in a transformer. [2]

6.

- State Faraday’s law of electromagnetic induction. [1]
- Define magnetic flux for a coil placed at right angles to a magnetic field.[1]
- Determine for which of the two coils X and Y, each placed at right-angles to the magnetic field, is the magnetic flux linkage is the greatest. [3]

7. The graph shows the maximum kinetic energy of the emitted photoelectrons as the frequency of the incident radiation on a sodium plate is varied.

- From the graph determine the maximum frequency of incident radiation that can cause a photoelectric effect? [1]
- Calculate the work function for sodium. [2]
- Use the graph to calculate the value of the Planck constant in Js. [2]

OR,

- The figure aside shows the experimental setup of Millikan’s oil drop experiment. Draw a free body diagram to represent the motion of an oil drop when it is constantly moving in a downward direction in absence of an electric field as well as in presence of an electric field along with the forces acting on it.[1]
- Find the expression for a charge on oil drop of radius
*r*moving with constant velocity*v*in a downward direction. [2] - Determine the magnitude of charge produced on oil drop of radius 1.5x$10^{-6}$ mm when its terminal velocity changes from 0.25 mm/s to 0.1mm/s while moving through an electric field of 105 V/m. The coefficient of viscosity of oil drop is 1.8x$10^{-5}$ Ns $m^{-2}$. [2]

8. A NOR gate ‘opens’ and gives an output only if both its inputs are ‘low’, but an OR gate ‘closes’. An AND gate ‘opens’ only if both inputs are ‘high’, but a NAND gate ‘closes’.

- Copy and complete the truth table in Fig. 8 for each gate. ‘High’ is represented by 1 and ‘low’ by 0. [2]
Input 1 Input 2 OR output NOR output AND output NAND output 0 0 1 0 0 1 1 1 - Write a truth table for the circuit in Fig 8(b), including the states at E, F and G.

**Group – 'C' **

** Attempt All questions. (8x3 = 24) **

9.

- Differentiate between a progressive wave and a stationary wave. [2]
- The diagram shows an experiment to measure the speed of a sound in a string. The frequency of the vibrator is adjusted until the standing wave shown in the diagram is formed.

- The frequency of the vibrator is 120Hz. Calculate the speed at which a progressive wave would travel along the string. [3]
- The experiment is now repeated with the load on the string halved. In order to get a similar standing wave, the frequency has to be decreased to 30 Hz. Explain, in terms of the speed of the wave in the string, why the frequency must be adjusted. [2]

10.

- State the laws of radioactive disintegration. [2]
- A sample of phosphorus-32 contains 8.6x$10^{12}$ nuclei at time t =0. The decay constant of phosphorus 32 is 4.8x$10^{-2}$ $day^{-1}$. Calculate the number of decayed phosphorus-32 nuclei in the sample after 10 days. [3]
- Equal masses of two samples of charcoal A and B are burnt separately and the resulting carbon dioxide is collected in two vessels. The radioactivity of $C^{14}$ is measured for both the gas samples. The gas from charcoal A gives 2100 counts per week and the gas from charcoal B gives 1400 counts per week. Find the age difference between the two samples. Half-life of $C^{14}$ = 5700 yrs. [3]

OR

- What is the significance of the negative energy of the electron in an orbit? [2]
- The energy levels of an atom are shown in Fig.10. Which one of these transitions will result in the emission of a photon of wavelength 275 nm? [2]
- X-rays are incident on the zinc sulphide crystal of crystal spacing 3.08x$10^{-8}$ cm such that first order reflection takes place at glancing angle $12^o$. Calculate the wavelength of X-rays and glancing angle for second order maximum. [4]

11.

a. The sensitivity of a potentiometer indicates the smallest potential difference that can be measured with it.

- How can we increase the sensitivity of a potentiometer wire? [2]
- What will be the effect on the position of null deflection in a potentiometer if the length of the potentiometer wire is increased? [1]
- What will be the effect on the position of null deflection in a potentiometer if the current flowing through the potentiometer wire is increased? [1]

b. Two cells of e.m.f 2 V and 1v and internal resistance 1Ω and 2Ω respectively have their positive terminals connected by a wire of 10Ω resistance, and their negative terminals by a wire of 4Ω resistance. A resistance of 10Ω joins the mid-points of these two wires. Calculate the current through each cell and the potential difference between the ends of the wire. [4]

**OR **

- At an airport, a person is made to walk through the doorway of a metal detector for security reasons. If the person is carrying anything made of metal, the metal detector emits a sound. On what principle does this metal detector work? [2]
- Draw the phasor diagram of LCR circuit and write down the expression for phase angles when

- The circuit is inductor dominant. [1]
- The circuit is capacitor dominant. [1]

c. The current amplitude I versus driving angular frequency ωd for a driven LCR circuit is given in the figure. Where the vertical axis is set by IS = 4.00 A. The inductance is 200 μH and the emf amplitude is 8.0 V. Find out the values of (a) impedance Z at IS = 4.00 A, (b) R, and (c) C? [4]

**SET- 5**

**Attempt all the questions. **

**Group -B**

**Short Answer Questions 8×5 = 40 **

1.

- Define ‘surface tension’. [1]
- Establish a relation between surface tension and surface energy of a liquid.
- Two spherical rain drops of equal size are falling vertically through air with a certain terminal velocity. If these two drops were to coalesce to form a single drop and fall with a new terminal velocity, explain how the terminal velocity of the new drop compares to the original terminal velocity. [2]

2. Angular speed of a rotating body is inversely proportional to its moment of inertia.

- Define moment of inertia. [1]
- Explain why angular velocity of the Earth increases when it comes closer to the sun in its orbit. [2]
- If the Earth were to shrink suddenly, What would happen to the length of the day? Give a reason.

OR,

- State Bernooulli principle. [1]
- Derive Bernoulli equation. [2]
- You can squirt water from a garden hose a considerably greater distance by partially covering the opening with your thumb. Explain how this works. [2]

3.

- Define ‘harmonics’ in music [1]
- Calculate the frequency of a monotonous sound produced by a 30cm long flute open at both ends and being played in the first harmonic. [velocity of sound in air = 330 $ms^{-1}$] [2]
- The flute mentioned in question (ii) was being played by a passenger on a stationary bus. The bus then moves uniformly. Explain what change in the pitch of the flute sound, if any, a person sitting on a bench at the bus park will feel when the bus starts moving.

4.

- State the second law of thermodynamics. [1]
- A refrigerator transfers heat from a cold body to a hot body. Does this not violate the second law of thermodynamics? Give a reason. [2]
- In the given figure, a heat engine absorbs $Q_1$ amount of heat from a source at temperature $T_1$ and rejects $Q_2$ amount of heat to a sink at temperature $T_1$ doing some external work W.

- Obtain an expression for the efficiency of this heat engine.
- Under what condition does the efficiency of such an engine become zero percentage if at all? [1]

5. A student wants to measure the magnetic flux density between the poles of two weak bar magnets mounted on a steel yoke as shown in the figure, the magnitude of the flux density is between 0.02T and 0.04T.

- Define Magnetic flux density. [1]
- One way of measuring the magnetic flux density could be the use of a hall probe. Suggest one reason why a hall probe is not a suitable instrument to measure the magnetic flux density for the arrangement shown in the above figure. [1]
- Another method of measuring the magnetic flux density for the arrangement shown in the above figure is to insert a current-carrying wire between the poles of the magnet. Explain how the magnetic flux density can be determined using this method. You are allowed to use any additional apparatus. [3]

6.

- Law of electromagnetic induction can be expressed mathematically as $\varepsilon$ = $-N\frac{d\phi}{dt}.$

- State what the symbols and $\frac{d\phi}{dt}$ represent in the equation.[2]
- Explain the significance of the negative sign. [1]
- Two identical copper balls are dropped from the same height as shown in the figure. Ball P passes through a region of uniform horizontal magnetic field of flux density B.

Explain why ball P takes longer than ball Q to reach the ground. [2]

7. Ultraviolet radiation of frequency 1.5×$10^{15}$ Hz is incident on the surface of an aluminum plate whose work function is 6.6×$10^{-19}$J.

- Show that the maximum speed of the electrons emitted from the surface of the aluminum is 8.6×$10^{5}ms^{-1}$. [3]
- State and explain what change, if any occurs to the maximum speed of the emitted electrons when the intensity of the ultraviolet radiation is increased. [2]

8.

- State Bohr’s postulates of atomic model [3]
- The figure shows lyman series of energy transmission in hydrogen atom. Calculate the frequency of a photon emitted by an electron jumping from the second excited state to the ground level. [2]

OR,

- Sketch the symbol of a p-n junction diode and indicate the polarity of its ends. [1]
- Copy the outline of a diode bridge rectifier and complete it by adding diode in the gaps. [2]
- Explain what will happen if one of the four diodes is damaged so that it stops conducting totally in any direction. Sketch a graph to show how the pd across the Load RL would vary with time in this situation. [2]

**Group- C: **

**Long Answer Questions. (3×8 = 24) **

9. Earthquakes set rocks and buildings in motion. When a rock is subjected to compression a restoring force develops inside it. This restoring force is given by an equation F = -Ax where x is displacement and A is a constant.

- Prove that this force will make the rock vibrate with simple harmonic motion. [2]
- Show that the speed of an object undergoing simple harmonic motion is given by the expression v = $\pm \omega \sqrt{(A^2-x^2)}$ where the symbols carry standard meanings. [2]
- Calculate the maximum speed of a building shaken by s-waves of 21 Hz and amplitude 0.05m. [2]
- Explain why tall buildings are more susceptible to damage by s-waves which generally have low frequency. [2]

10. The figure below shows the variation of emf and current with typical LRC circuit.

- Explain whether the phase constant is positive or negative.
- Sketch a phasor diagram for the given case. [2]
- Is the circuit more inductive or capacitive? Explain. [2]
- To increase the rate at which energy is transferred to the load, Should the inductance be increased or decreased ? Justify your answer. [2]

OR,

A student sets up a circuit as shown in the figure given below to measure the emf of a test cell.

- Explain why he is unable to find a balance point and state the change he must make in order to achieve the balance.
- State how he would recognize the balance point.
- He obtained the balance point for distance 37.5 cm using standard cell of emf 1.50V. And for the test cell, the balance distance AB was 25.0 cm. Calculate the emf of the test cell. [2]
- He could have used an ordinary voltmeter to measure the emf of the test cell directly. The student, however, argues that the above instrument is more precise than an ordinary voltameter. Justify his logic. [2]

11.

- Explain what is meant by quantization of charge. [2]
- In Millikan's oil drop experiment, an oil drop of weight 1.5×$10^{-14}$ N is held stationary between plates 10 mm apart by applying a p.d. Of 470V between the plates..

- State the condition necessary for the drop to remain stationary. Also, sketch the forces acting on the oil drop. [2]
- Calculate the charge on the oil-drop.
- Explain what would happen if the above oil drop is suddenly struck by a stray alpha particle. [2]

OR,

- Drive an expression N = $N_oE^{-\lambda x}$ for a radioactive process where the symbols carry their standard meanings. [3]
- A student measured the activity of a sample of radioactive rock. Her results are presented in the graph.

- Explain why the data are scattered. [1]
- Determine the half-life of this sample. [2]
- How will the shape of this curve change if she repeats the experiment with a sample with a larger decay constant. Give reason to your answer. [2]

Source: Kathmandu world school, Gundu, Bhaktapur