qbank

2006 Board Questions:-

1. What is electric flux? Write its S.I. units. Using Gauss’s theorem, deduce an expression for the electric field at a point due to a uniformly charged infinite plane sheet.


1. Write the relation for the forece acting on a charge carrier q moving with a velocity through a magnetic field in vector notation. Using this relation, deduce the conditions under which this force will be (i) maximum (ii) minimum.

2. The electric field E due to a point charge at any point near it is defined as where q is the test charge and F is the force acting on it. What is the physical significance of in this expression? Draw the electric field lines of a point charge Q when Q > 0 and Q < 0. 2

3. Define electric flux. Write its S.I. units. A spherical rubber balloon carries a charge that is uniformly distributed over its surface. As the balloon is blown up and increases in size, how does the total electric flux coming out of the surface change? Give reason.

2008 Board Questions:-` 1. (a) Using Gauss’ law, derive an expression for the electric field intensity at any point outside a uniformly charge thin spherical shell of radius R and charge density 2 / C m s Draw the field lines when the charge density of the sphere is (i) positive, (ii) negative. (b) A uniformly charged conducting sphere of 2.5m in diameter has a surface charge density of 100 2 / C m m calculate the (i) Charge on the sphere (ii) Total eclectic flux passing through the sphere

2. (a) Derive an expression for the torque experienced by an electric dipole kept in a uniform electric field. (b) Calculate the work done to dissociate the system of three charges placed on the vertices of a triangle as shown.

ELECTRIC CHARGES AND FIELDS

Here q = 1.6´ 10-10C


1. Define the term ‘dielectric constant’ of a medium in terms of capacitance of a capacitor.

2. The electric field and electric potential at any point due to a point charge kept in air is 20 NC-1 and 10 JC-1 respectively. Compute the magnitude of this charge.

3. The given graph shows the variation of charge q versus potential difference V for two capacitors . The two capacitors C1 and C2 have same plate separation but the plate area of C2 is double than that of C1. Which of the lines in the graph correspond to C1 and C2 and why?


1. Deduce an expression for the electric potential due to an electric dipole at any point on its axis. Mention one contrasting feature of electric potential of a dipole at a point as compared to that due to a single charge.

2. A parallel plate capacitor, each with plate area A and separation d, is charged to a potential difference V. The battery used to charge it is then disconnected. A dielectric slab of thickness d and dielectric constant K is now placed between the plates. What change, if any, will take place in Charge on the plates Electric field intensity between the plates Capacitance of the capacitor. Justify your answer in each case.

ELECTROSTATIC POTENTIALS AND CAPACITANCE

10cm10cm

10cm

q

+2q–4q

q AB

V


1. Derive the expression for the electric potential at any point along the axial line of an electric dipole?

2. Prove that an ideal capacitor, in an a.c. circuit does not dissipate power.


1. Sketch a graph showing variation of resistivity of carbon with temperature.

2. Write the mathematical relation between mobility and drift velocity of charge carriers in a conductor. Name the mobile charge carriers responsible for conduction of electric current in i. An electrolyte ii. An ionized gas.

3. Derive a mathematical expression for the force per unit length experienced by each of the two long current carrying conductors placed parallel to each other in air. Hence define one ampere of current.

4. Explain why two parallel straight conductors carrying current in the opposite direction kept near each other in air repel?

5. The given circuit diagram shows a series LCR circuit connected to a variable frequency 230 V source:

a. Determine the source frequency which drives the circuit in resonance. b. Obtain the impedance of the circuit and the amplitude of current at the resonating frequency. c. Determine the rms potential drops across the three elements of the circuit. d. How do you explain the observation that the algebraic sum of the voltages across the three elements obtained in (c) is greater than the supplied voltage?

CURRENT ELECTRICITY

~230 V

5.0 H 40 Ω80 uF

6. A 10 m long wire of uniform cross-section and 20Ω resistance is used in a potentiometer. The wire is connected in series with a battery of 5 V along with an external resistance of 480Ω. If an unknown emf E is balanced at 6.0 m length of the wire, calculate:

7. Two cells E1 and E2 in the given circuit diagram have an emf of 5 V and 9 V and internal resistance of 0.3Ω and 1.2Ω respectively.

Calculate the value of current flowing through the resistance of 3Ω.

8. Define the terms threshold frequency and stopping potential in relation to the phenomenon of photoelectric effect. How is the photoelectric current affected on increasing the (i) frequency (ii) intensity of the incident radiations and why?


1. A cylindrical metallic wire is stretched to increase its length by 5%. Calculate the percentage change in its resistance.

2. State Kirchhoff's rules of current distribution in an electrical network. Using these rules determine the value of the current in the electric circuit given below.

3. Write the mathematical relation for the resistivity of a material in terms of relaxation time, number density and mass and charge of charge carriers in it. Explain, using this relation, why the resistivity of a metal increases and that of a semi-conductor decreases with rise in temperature. 4. Given below are two electric circuits A and B Calculate the ratio of power factor of the circuit B to the power factor of circuit A.

E1 E1

6Ω

3Ω

4.5Ω


1. The plot of the variation of potential difference across a combination of three identical cells in series, versus current is as shown below. What is the emf of each, cell?

2. Derive an expression for the impedance of a.c. circuit consisting of an inductor and a resistor.

3. A potentiometer wire of length lm is connected to a drive cell of emf 3 V as shown in the figure. When a cell of 1.5 V emf is used in the secondary circuit, the balance point is found to be 60cm. On replacing this cell and using a cell of unknown emf, the balance point shifts to 80cm

(i) Calculate unknown emf of the cell. (ii) Explain with reason, whether the circuit works, if the drive cell is replaced with a cell emf 1V. (iii)Does the high resistance R, used in the secondary circuit affect the balance point? Justify your answer.

V

6V

0 1V i

3V

BA

1.5VR


1. The vertical component of Earth’s magnetic field at a place is times the horizontal component. What is the value of angle of dip at this place?

2. State the principle of working of a cyclotron. Write two uses of this machine.

3. With the help of a neat and labelled diagram, explain the underlying principle and working of a moving coil galvanometer. What is the function of: i. Uniform radial field ii. Soft iron core in such a device?

4. Draw a schematic diagram of a cyclotron. Explain its underlying principle and working, stating clearly the function of the electric and magnetic fields applied on a charged particle. Deduce an expression for the period of revolution and show that it does not depend on the speed of the charged particle.


1. Why should the material used for making permanent magnets have high coercivity?


1. A metallic rod of length l is rotated at a constant angular speed, normal to a uniform magnetic field B. Derive an expression for the current induced in the rod, if the resistance of the rod is R.

MOVING CHARGES AND MAGNETISM

MAGNETISM AND MATTER

x

x

o

Ro2

i

1

1

R


1. How is the mutual inductance of a pair of coils affected when: 3 i. Separation between the coils is increased? ii. The number of turns of each coil is increased? iii. A thin iron sheet is placed between the two coils, other factors remaining the same? Explain your answer in each case.


1. The primary coil of an ideal step-up transformer has 100 turns and the transformation ratio is also 100. The input voltage the power is 220 V and 1100 W respectively. Calculate: a. number of turns in the secondary b. the current in the primary c. voltage across the secondary d. the current in the secondary e. power in the secondary


1. Distinguish between the terms 'average value' and 'rms value' of an alternating current. The instantaneous current from an a.c. source is I = 5 sin (314 t) ampere. What are the average and rms values of the current?

2. Explain with the help of a labelled diagram the underlying principle and working of a step-up transformer. Why cannot such a device be used to step-up d.c. voltage?

3. Draw a labelled diagram of an a.c. generator. Explain briefly its principle and working.

4. Explain, with the help of a schematic diagram, the principle and working of a Light Emitting Diode. What criterion is kept in mind while choosing the semi conductor material for such a device? Write any two advantages of Light Emitting Diode over conventional incandescent lamps.

ELECTROMAGNETIC INDUCTION

HUMAN EYE AND COLOURFUL WORLD


1. The oscillating magnetic field in a plane electromagnetic wave is given by By = (8 x 10–6) sin [2 x 1011t + 300πx] T (i) Calculate the wavelength of the electromagnetic wave. (ii) Write down the expression for the oscillating electric field.


1. Draw a labelled diagram of Hertz’s experimental set-up to produce electromagnetic waves. Explain the generation of- electromagnetic waves using this set-up.

2. Define the term ‘critical frequency’ in relation to sky wave propagation of electromagnetic waves. On a particular day, the maximum frequency reflected from the ionosphere is 10 MHz. On another day, it was found to decrease to 8 MHz. Calculate the ratio of the maximum electron densities of the ionosphere on the two days.


1. Write any four characteristics of electromagnetic waves. Give two uses each of 1. Radio-waves 2. Micro-waves.

2. What is meant by the term “magnetic field lines”? List two properties of magnetic field lines.


1. Name the part of the electromagnetic spectrum of wavelength 10-2 m and mention its one application.


1. Draw a labelled ray diagram of a reflecting type telescope. Write its any one advantage over refracting type telescope.

2. What is diffraction of light? Draw a graph showing the variation of intensity with angle in a single slit diffraction experiment. Write one feature which distinguishes the observed pattern from the double slit interference pattern.

ELECTROMAGNETIC WAVES

RAY OPTICS AND OPTICAL INSTRUMENTS

3. How would the diffraction pattern of a single slit be affected when: i. The width of the slit is decreased? ii. The monochromatic source of light is replaced by a source of white light?

4. What is interference of light? Write two essential conditions for sustained interference pattern to be produced on the screen.

5. A convex lens made up of glass of refractive index 1.5 is dipped, in turn, in: i. Medium A of refractive index 1.65 ii. Medium B of refractive index 1.33 Explain, giving reasons, whether it will behave as a converging lens or a diverging lens in each of these two media.


1. A convex lens of refractive index 1.5 has a focal length of 18 cm in air. Calculate the change in its focal length when it is immersed in water of refractive index.

2. Define the term 'resolving power' of an astronomical telescope. How does it get affected on 1. Increasing the aperture of the objective lens? 2. Increasing the wavelength of the light used? Justify your answer in each case.

3. Explain, with the help of a schematic diagram, the principle and working of a Light Emitting Diode. What criterion is kept in mind while choosing the semiconductor material for such a device? Write any two advantages of Light Emitting Diode over conventional incandescent lamps.


1. A glass lens of refractive index 1.5 is placed in a trough of liquid. What must be the refractive index of the liquid in order to make the lens disappear?

2. Draw a ray diagram of a reflecting telescope. State two advantages of this telescope over a refracting telescope.

3. (a) For a ray of light traveling from a denser medium of refractive index n1 to

a rarer medium of refractive index n2, prove that where ic is

the critical angle of incidence for the media.

(b) Explain with the help of a diagram, how the above the principle is used for

transmission of video signals using optical fibers.

= sin ien2

n2


1. Draw a graph showing the variation of intensity versus the position on the screen in Young’s experiment when (a) both the slits are opened and (b) one of the slits is closed.

2. What is the effect on the interference pattern in Young’s double slit experiment when: i. Screen is moved closer to the plane of slits? ii. Separation between two slits is increased. Explain your answer in each case.


1. What are coherent sources? Why are coherent sources required to produce interference of light? Give an example of interference of light in everyday life. In Young's double slit experiment, the two slits are 0.03 cm apart and the screen is placed at a distance of 1.5 m away from the slits. The distance between the central bright fringe and fourth bright fringe is 1 cm. Calculate the wavelength of light used.

2. State the condition under which the phenomenon of diffraction of light takes place. Derive an expression for the width of the central maximum due to diffraction of light at a single slit. A slit of width 'a' is illuminated by a mono chromatic light of wavelength 700 nm at normal incidence. Calculate the value of 'a' for position of 1. First minimum at an angle of diffraction of 30°. 2. First maximum at an angle of diffraction of 30°.


1. State the reason, why heavy water I generally used as a moderator in a nuclear reactor.

2. How does the fringe width of interference fringes change, when the whole apparatus of Young’s experiment is kept in a liquid of refractive index 1.3?

3. How is a wavefront defined? Using Huygen’s construction draw a figure showing the propagation of a plane wave refraction at a plane surface separating two media. Hence verify Snell’s law of refraction.

WAVE OPTICS


1. With that purpose was famous Davisson-Germer experiment with electrons performed?


1. In a plot of photoelectric current versus anode potential, how does a) The saturation current vary with anode potential for incident radiations of different frequencies but same intensity? b) The stopping potential vary for incident radiations of different intensities but same frequency?

2. Photoelectric current vary for different intensities but same frequency of incident radiations? Justify your answer in each case.


1. A ray of light passing through an equilateral triangular glass prism from air undergoes minimum deviation when angle of incidence is 3/4th of the angle of prism. Calculate the speed of light in the prism.

2. The energy level diagram of an element is given below. Identify, by doing necessary calculations, which transition corresponds to emission of a spectral line of wavelength 102.7nm.

(a) What is plane polarised light? Two polaroids are placed at 90o to each other and the transmitted intensity is zero. What happens when one more Polaroid is placed between these two, bisecting the angle between them? How will the intensity of transmitted light vary on further rotating the third Polaroid?

(b) If a light beam shows no intensity variation when transmitted through a polaroid which is rotated, does it mean that the light is unpolarised? Explain briefly.

DUAL NATURE OF RADIATION AND MATTER

A

CB

D

-0.85eV

-1.5eV

-3.4eV

-13.6eV


1. Why is the mass of a nucleus always less than the sum of the masses of its constituents, neutrons and protons.

2. If the total number of neutrons and protons in a nuclear reaction is conserved, how then is the energy absorbed or evolved in the reaction? Explain.


1. An electron, an alpha-particle and a proton have the same kinetic energy. Which one of these particles has the largest de-Broglie wavelength?

2. The radioactive isotope D decays according to the sequence.

3. If the mass number and atomic number of D2 are 176 and 71 respectively, what is (i) the mass number (ii) atomic number of D?


1. An electron and alpha particle have the same de-Broglie wavelength associated with them. How are their kinetic energies related to each other?

2. An electromagnetic wave of wavelength is incident on a photosensitive surface of negligible work function. If the photo-electrons emitted from this surface have the de-Broglie wavelength


1. Draw a graph showing the variation of binding energy per nucleon with mass number for different nuclei. Explain, with the help of this graph, the release of energy by the process of nuclear fusion.

ATOMS

NUCLEI

λ1, prove that λ = λ12

2mch


1. Calculate the amount of energy released during the a-decay of Given : a) Atomic mass of b) Atomic mass ofIs this decay spontaneous? Give reason.


1. A nucleus Ne undergoes decay and becomes Na Calculate the maximum

kinetic energy of electrons emitted assuming that the daughter nucleus and anti-neutrino carry negligible kinetic energy.


1. Draw a circuit diagram for use of NPN transistor as an amplifier in common emitter configuration. The input resistance of a transistor is 100Ω. On changing its base current by 10μA, the collector current increases by 2 m A. If a load resistance of 5kΩ is used in the circuit, calculate: 1 + 2 i. The current gain ii. Voltage gain of the amplifier

2. What is an intrinsic semiconductor? How can this material be converted into (i) P-type (ii) N-type extrinsic semiconductor? Explain with the help of energy band diagrams.

SEMI CONDUCTOR ELECTRONICS, MATERIALS, DEVICES AND SIMPLE CIRCUITS

2310

2311

2310

Mass of Ne = 22.994455 u

2311

Mass of Ne = 22.989770 u

1u = 931.5 Me V/c2

3. Draw and explain the output waveform across the load resistor R, if the input waveform is as shown in the given figure.

Explain how the width of depletion layer in a p-n junction diode changes when the junction is (i) forward biased (ii) reverse biased.

4. Explain, with the help of a nuclear reaction in each of the following cases, how the neutron to proton ratio changes during (i) alpha-decay (ii) beta-decay?


1. The output of an OR gate is connected to both the inputs of a NAND gate. Draw the logic circuit of this combination of getes and write its truth table.

2. State the principle of working of p-n diode as a rectifier. Explain, with the help of a circuit diagram, the use of p-n diode as a full wave rectifier. Draw a sketch of the input and output waveforms.

3. Draw the symbolic representation of a (i) p-n-p, (ii) n-p-n transistor. Why is the base region of transistor thin and lightly doped? With proper circuit diagram, show the biasing of a p-n-p transistor in co mmon base configuration. Explain the movement of charge carriers through different parts of the transistor in such a configuration and show that.


1. Distinguish between an intrinsic semiconductor and P-type semiconductor Give reason, why, a P-type semiconductor crystal is electrically neutral, although nh>>ne?

2. The give inputs A, B are fed to a 2-input NAND gate. Draw the output wave form of the gate.

+5V

-5V

A

A(input)

B(input)

t1 t4t2t3 t5

t6

3. The figure below shows the V-1 characteristic of a semiconductor diode.

(i) Identify the semiconductor diode used. (ii) Draw the circuit diagram to obtain the given characteristic of this device. (iii)Briefly explain how this diode can be used as a voltage regulator.


1. Name the type of communication in which the signal is a discrete and binary coded version of the message or information.

2. Define the term modulation. Name three different types of modulation used for a message signal using a sinusoidal continuous carrier wave. Explain the meaning of any one of these.


1. Why is frequency modulation preferred over amplitude modulation for transmission of music?

2. What is a digital signal? Explain the function of modem in data communication. Write two advantages of digital communication.


1. A transmitting antenna at the top of a tower has a height of 36m and the height of the receiving antenna is 49m. What is the maximum distance between them, fro satisfactory communication in the LOS mode? (Radius of earth = 6400km)

2. Draw a plot of the variation of amplitude versus w for an amplitude modulated wave. Define modulation index. State its importance for effective amplitude modulation.

COMMUNICATION SYSTEMS

I(mA)

I(μA)

100

100

80

80

60

60

40

4020

20

2030

10Vbr0.2 0.4 0.6 0.8 1.0

V(V)

SECTION – I

Straight Objective Type

This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out

of which ONLY ONE is correct.

24. A spherically symmetric gravitational system of particles has a mass density

>≤

ρ =0

ρ

rof r Rrof r R0

where ρ0 is a constant. A test mass can undergo circular motion under the influence of the gravitational

field of particles. Its speed V as a function of distance r (0 < r < ∞) from the centre of the system is

represented by

(A) (B)

V

rR rR

V

)D( )C(

rR

V

rR

V

[Ans.C ]

IIT-JEEPhysics

Question Papers2008

Sol.

v

0 r R In Out

For r < R 3RGMmr =

rmv2

∴ v2 ∝ r2

∴ v ∝ r

For r > R 2rGMm =

rmv2

∴ v ∝ r

1

25. An ideal gas is expanding such that PT2 = constant. The coefficient of volume expansion of the gas is

(A) T1 (B)

T2 (C)

T3 (D)

T4

[Ans.C ]

Sol. Given PT2 = C, As PV = nRT

∴ V

nRT3 = C ∴ V =

CnRT3

dTdV =

CnRT3 2

= TV3 [Put T3 =

nRCV ]

VdTdV

=

T3

26. Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is

60º). In the position of minimum deviation, the angle of refraction will be

(A) 30º for both the colours (B) greater for the violet colour

(C) greater for the red colour (D) equal but not 30º for both the colours

[Ans. A]

Sol.

r1 r2

For minimum deviation

r1 = r2 = 2A = 30º

Option A is correct

27. Which one of following statements is Wrong in the context of X-rays generated from a X- ray tube ?

(A) Wavelength of characteristic X-rays decreases when the atomic number of the target increases

(B) Cut-off wavelength of the continuous X-rays depends on the atomic number of the target

(C) Intensity of the characteristic X-rays depends on the electrical power given to the X-ray tube

(D) Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube

[Ans.B ]

Sol. (λc) cuttoff wavelength is given as

λc = .E.K

hc = eVhc

Hence λc does not depend on atomic number of target but depends on potential difference between

cathode and anode (target

28. Figure shows three resistor configurations R1, R2 and R3 connected to 3 V battery. If the power dissipated

by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then

Figure :

1Ω

1Ω

1Ω

1Ω1Ω

3V

R1 1Ω1Ω

1Ω 1Ω

R2

3V1Ω

1Ω

1Ω

1Ω1Ω

1Ω 1Ω

3V

R3 (A) P1 > P2 > P3 (B) P1 > P3 > P2

(C) P2 > P1 > P3 (D) P3 > P2 > P1

[Ans.C ]

Sol. Resistance of R1 using wheat stone bridge equivalent circuit

Req. of R1 = 1 Ω

3V

1 Ω

1 Ω 1Ω

1 Ω

Equivalent resistance R2

3V

1 Ω

1 Ω

1 Ω

1 Ω

1 Ω

2Ω

2Ω ⇒

1Ω

3V

⇒

Req of R2 = ½ R

1/2 Ω

3V

Similary Req of R3 = 2Ω

Power = R

V2

V is same for all

∴ power ∝ R1

Q R2 < R1 < R3

∴ P2 > P1 > P3

29. Students I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a

simple pendulum. They use different lengths of the pendulum and/or record time for different number of

oscillations. The observations are shown in the table.

Least count for length = 0.1 cm

Least count for time = 0.1 s

Student Length of the

pendulum (cm)

Number of

oscillations (n)

Total time for

(n) oscillations(s)

Time period(s)

I 64.0 8 128.0 16.0

II 64.0 4 64.0 16.0

III 20.0 4 36.0 9.0

If EI, EII and EIII are the percentage errors in g, i.e.

×

∆ 100gg for students, I, II, and III respectively,

(A) EI = 0 (B) EI is minimum

(C) EI = EII (D) EII is maximum

[Ans.B ]

Sol. Student % error in l (% l) % error in T (% T) % error in g = %l + 2×%T

I 10064

1.0× =0.156 100

1281.0

81

×× =0.00976 0.1755

II 10064

1.0× =0.156 100

641.0

41

×× =0.03906 0.2341

III 10020

1.0× =0.5 100

361.0

41

×× =0.0694 0.6388

SECTION – II

Multiple Correct Answers Type

This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices (A), (B),

(C) and (D), out of which ONE OR MORE is/are correct.

30. Two balls, having linear momenta ipp1 =r

and ipp2 −=r

, undergo a collision in free space. There is no

external force acting on the balls. Let 1'pr

and 2'pr

be their final momenta. The following option(s) is (are)

NOT ALLOWED for any non-zero value of p, a1, a2, b1, b2, c1 and c2.

(A) kcjbia'p 1111 ++=r

; jbia'p 222 +=r

(B) kc'p 11 =r

; kc'p 22 =r

(C) kcjbia'p 1111 ++=r

; kcjbia'p 1222 −+=r

(D) jbia'p 111 +=r

; jbia'p 122 +=r

[Ans.A,D]

Sol. 1Pr

= iP

2Pr

= – iP

Net linear momentum just before collision

21i PPPrrr

+= = iP – iP = 0

There is no external force acting on the balls, hence net linear momentum will be conserved.

P'f = ′+′ 21 PPrr

= 0

In option (A), ′+′ 21 PPrr

= kcj)bb(i)aa( 12121 ++++ ≠ 0

Q c1 is non zero

In option D also

21 'P'Prr

+ = jb2i)aa( 121 ++ ≠ 0

Q b1 is non zero

31. A particle of mass m and charge q, moving with velocity V enters Region II normal to the boundary as

shown in the figure. Region II has a uniform magnetic field B perpendicular to the plane of the paper. The

length of the Region II is l. Choose the correct choice(s).

Figure :

Region I Region II Region III

V

l

(A) The particle enters Region III only if its velocity mBqV l

>

(B) The particle enters Region III only if its velocity mBqV l

<

(C) Path length of the particle in Region II is maximum when velocity V = mBql

(D) Time spent in Region II is same for any velocity V as long as the particle returns to Region I

[Ans.A,C,D]

Sol.

B C

l

Region I Region II Region III

If radius of circle is more than l then particle will be in region III

R = qBmv

qBmv > l

V > m

Bql

Option A is correct option B is wrong

B

When v is m

qBl then particle will take maximum path as shown. Option C is correct.

Time period = 21

qBm2

π

R

C

Region II

So this spent time in region II is independent of velocity.

∴ option (D) is correct.

32. In a Young’s double slit experiment, the separation between the two slits is d and the wavelength of the

light is λ. The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose

the correct choice(s).

(A) If d = λ, the screen will contain only one maximum

(B) If λ < d < 2λ, at least one more maximum (besides the central maximum) will be observed on the

screen

(C) If the intensity of light falling on slit 1 is reduced so that it becomes equal to that of slit 2, the

intensities of the observed dark and bright fringes will increase

(D) If the intensity of light falling on slit 2 is increased so that it becomes equal to that of slit 1, the

intensities of the observed dark and bright fringes will increase

[Ans.A,B ]

Sol.

∞

–∞

∆x=d

∆x=–d

∆x=0 d

Now when d = λ

∆x = λ at ∞ on above side and ∆x = –λ at ∞ on below side. So there are three maxima. One at centre and

two are at infinite however screen can't be of infinite size so option A is correct.

∞ ∆x=d=1.9λ

∆x = 0

λ

–λ

∆x = –d=–1.9λ

⇒ λ < d < 2λ ∴ say d = 1.9 λ See above figure

Three maxima are possible as shown the path difference for these maxima are zero, λ and –λ.

So option B is correct.

Previous intensity of dark fringe = ( )2II4 − = I

When intensity of both slit become equal then intensity of dark fringe = 0

∴ intensity of dark fringe decreases

∴ option C and D are wrong.

33. Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the

figure. Use this plot to choose the correct choice(s) given below.

Figure : B/A

0

2

4

6 6

8

100 200A

(A) Fusion of two nuclei with mass numbers lying in the range of 1 < A < 50 will release energy

(B) Fusion of two nuclei with mass numbers lying in the range of 51 < A < 100 will release energy

(C) Fission of a nucleus lying in the mass range of 100 < A < 200 will release energy when broken into

two equal fragments

(D) Fission of a nucleus lying in the mass range of 200 < A < 260 will release energy when broken into

two equal fragments

[Ans. B,D]

Sol. Energy is released when binding energy per nucleon increases in fusion of two nuclei of mass number

from 51 to 100, final nuclei has mass number 102 to 200 where B.E./A is greater similarly in fission of

200 to 260 final mass no becomes 100 to 130.

SECTION – III Reasoning Type

This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of

which ONLY ONE is correct.

34. STATEMENT – 1

An astronaut in an orbiting space station above the Earth experiences weightlessness.

and

STATEMENT – 2

An object moving around the Earth under the influence of Earth’s gravitational force is in a state of

‘free-fall’.

(A) STATEMENT – 1 is True, STATEMENT- 2 is True; STATEMENT -2 is a correct explanation for

STATEMENT -1

(B) STATEMENT – 1 is True, STATEMENT- 2 is True; STATEMENT -2 is NOT a correct explanation

for STATEMENT -1

(C) STATEMENT-1 is True, STATEMENT-2 is False

(D) STATEMENT-1 is False, STATEMENT-2 is True

[Ans.A ]

Sol.

35. STATEMENT -1

In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown

resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at

the same point as before by decreasing the value of the standard resistance.

and

STATEMENT-2

Resistance of a metal increases with increase in temperature.


STATEMENT -1


for STATEMENT -1



[Ans.D ]

Sol.

R

l1 l2

G

Standard resistance Unknown resistance

X

X = R 2

1

l

l

As Temperature increase x will increase to get same Null point i.e. same value of 2

1

l

l, value of standard

Resistance R should increase.

∴ Assertion is false, However Reason statement is true

36. STATEMENT – 1

Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical

dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same

height. The hollow cylinder will reach the bottom of the inclined plane first.

and

STATEMENT – 2

By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical

when they reach the bottom of the incline.


STATEMENT -1


for STATEMENT -1



[Ans.D ]

Sol. From energy conservation 1/2 mvc2 + 1/2 Icω2 = mgh

ω = vc/R

(Ic)solid < (Ic)hollow

Hence (vc)solid > (vc)hollow

Hence solid cylinder will reach the bottom first.

37. STATEMENT – 1

The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when

held vertically up, but tends to narrow down when held vertically down.

and

STATEMENT – 2

In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.


STATEMENT -1


for STATEMENT -1



[Ans.A ]

Sol. Volume rate of flow Q = Av

When velocity increases cross-sectional area decreases and vice-versa.

SECTION – IV

Linked Comprehension Type

This section contains 3 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be

answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Question Nos. 38 to 40

A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The

angle of the incline suddenly changes from 60º to 30º at point B. The block is initially at rest at A. Assume

that collisions between the block and the incline are totally inelastic (g = 10 m/s2).

Figure :

60º

30º

3 33m mC

B

AM

v

38. The speed of the block at point B immediately after it strikes the second incline is -

(A) 60 m/s (B) 45 m/s (C) 30 m/s (D) 15 m/s

[Ans.B ]

Sol.

A M

60° 30° VB||

VB⊥r

30° E

D B

VB

3 m 3 3 m C

From ∆ABD

tan 60° = BDAD

⇒ AD = BD tan 60° = 3 × 3 m = 3m

speed of block at B just before collision with incline BC is VB

21 MVB

2 = Mg (AD) (Applying conservation of mechanical energy) ⇒ VB = 60 m/s.

Collision between block and incline is totally inelastic. Just after collision with incline BC

component of velocity of block perpendicular to incline BC is zero (because collision is perfectly

inelastic)

Component of velocity of block

parallel to incline BC is V′B|| = VB cos 30° = 45 m/s.

(Component of velocity parallel to surface of contact does not change).

Speed of block just after collision with incline BC is 45 m/s.

39. The speed of the block at point C, immediately before it leaves the second incline is

(A) 120 m/s (B) 105 m/s (C) 90 m/s (D) 75 m/s

[Ans.B ]

Sol. BD = 33 tan30º = 3 m

From conservation of mechanical energy

Total mechanical energy at point B = total mechanical energy at point C

( ) )3(Mg45M21 2

+ = 2CMV

21

VC = 105 m/s

40. If collision between the block and the incline is completely elastic, then the vertical (upward) component

of the velocity of the block at point B, immediately after it strikes the second incline is

(A) 30 m/s (B) 15 m/s (C) 0 (D) – 15 m/s

[Ans.C ]

Sol. Collision is elastic.

A M

60° θ V′′B

VB⊥r

30° E

D B

VB

3 m 3 3 m C

VB|| 30°

F

G

Just after collision with incline BC,

Component of velocity of block along BC is V''B11 = VBcos30º = 45 m/s

Component of velocity perpendicular to BC is V''B⊥r = VBsin30º = 15 m/s along BF

V"B = velocity of block just after collision

tanθ = 11B

rB''V''V ⊥ =

4515 =

31

θ = 30º

B"Vr

is in horizontal direction

Hence vertical component of B"Vr

is zero.


A small spherical monoatomic ideal gas bubble (γ = 5/3) is trapped inside a liquid of density ρl (see

figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles

of gas. The temperature of the gas when the bubble is at the bottom is T0, the height of the liquid is H and

the atmospheric pressure is P0 (Neglect surface tension)

Figure :

H

P0

y

Liquid

41. As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

(A) Only the force of gravity

(B) The force due to gravity and the force due to the pressure of the liquid

(C) The force due to gravity, the force due to the pressure of the liquid and the force due to viscosity of

the liquid

(D) The force due to gravity and the force due to viscosity of the liquid

[Ans.D ]

Sol. Free Body Diagram of gas bubble

mg

FB

FV

FB → Buoyancy forceFV → Viscous forcemg → Gravity force

Buoyancy force is due to pressure difference.

42. When the gas bubble is at a height y from the bottom, its temperature is

(A) 5/2

0

00 gyP

gHPT

ρ+ρ+

l

l (B) 5/2

0

00 gHP

)yH(gPT

ρ+

−ρ+

l

l

(C) 5/3

0

00 gyP

gHPT

ρ+ρ+

l

l (D) 5/3

0

00 gHP

)yH(gPT

ρ+

−ρ+

l

l

[Ans.B ]

Sol. As the number of moles remains conserved

ni = nf

i

iiTVP =

f

ffTVP

H y

Bubble

Liquid

Tfii

ffVPVP . Ti ... (i)

Since bubble does not exchange heat hence process is adiabatic in nature

PiViγ = PfVf

γ

Vf/Vi = (Pi/Pf)1/γ ... (2)

Putting (2) in (1)

Tf =

i

fPP

γ

/1

f

i

PP .Ti

Tf =

i

fPP 1 – 1/γ . Ti

Pi = P0 + L

ρ g H

Pf = P0 + L

ρ g (H – y)

Tf = 5/2

L0

L0HgP

)yH(gP

ρ+

−ρ+T0.

43. The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)

(A) ρlnRgT0 5/70

5/20

)gyP()gHP(

l

l

ρ+

ρ+ (B) 5/3

05/2

0

0

)]yH(gP[)gHP(nRgT

−ρ+ρ+

ρ

ll

l

(C) ρlnRgT0 5/80

5/30

)gyP()gHP(

l

l

ρ+

ρ+ (D) 5/2

05/3

0

0

)]yH(gP[)gHP(nRgT

−ρ+ρ+

ρ

ll

l

[Ans.B ]

Sol. Buoyant force

FB = ρLVfg

FB = gP

nRT

f

fL

ρ

= i

/1

f

i

i

f

f

L TPP

PP

PnR

γ

ρ

= i/1f

/11i

L T.P

1.P

nRγγ−

ρ

FB = i5/3f

5/2i

L T.PP

nRρ

FB = 5/3L0

05/2

L0

L

)]yH(gP[T

)gHP(nR

−ρ+ρ+

ρ


In a mixture of H – He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their

respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by

collisions). Assume that the Bohr model of atom is exactly valid.

44. The quantum number n of the state finally populated in He+ ions is

(A) 2 (B) 3 (C) 4 (D) 5

[Ans.C ]

Sol. Energy level diagram

•

–0.85 eV–1.51 eV–3.4 eV

10.2 eV

–13.6 eV n = 1

n = 2 n = 3 n = 4

H-atom

(First excited state)

When hydrogen atom transfers its total excitation energy to He+ ion then He+ ion are excited to n = 4

quantum state as seen from energy level diagram

•

–3.4 eV–6.04 eV

10.2 eV

–13.6 eV

n = 1

n = 2

n = 3

–54.4 eV

n = 4

He+ ion

First excited state

Hence quantum number of state finally populated in He+ ions is 4.

45. The wavelength of light emitted in the visible region by He+ ions after collisions with H atoms is

(A) 6.5 × 10–7 m (B) 5.6 × 10–7 m

(C) 4.8 × 10–7 m (D) 4.0 × 10–7 m

[Ans.C ]

Sol. The wavelength of light emitted in the visible region by He+ ions in final excited state is

λ = 34E

hc

→∆ ∆E4→ 3 = (6.04 –3.4) eV

= 2.64 eV λ = eV64.2

hc

λ = 64.2104.12 7−× l = 4.8 × 10–7 m

46. The ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion is

(A) 41 (B)

21 (C) 1 (D) 2

[Ans.A]

Sol. K.E. ∝ Z2/n2

+He

HE.KE.K = 2

He

2H

ZZ

+

= 2)2()1( =

P h y s i c s ( C o d e 0 )

2007SECTION - I

This section contains 9 multiple choice questions numbered 1 to 9. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

1. A resistance of 2 Ω is connected across one gap of a metre–bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2 Ω, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is

(A) 3 Ω (B) 4 Ω (C) 5 Ω (D) 6 Ω.

2. In an experiment to determine the focal length (f) of a concave mirror by the u–v method, a student places the object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then,

(A) x < f (B) f < x < 2f (C) x = 2f (D) x > 2f.

3. Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance ‘a’ from the center P (as shown in the figure). Now, the mid–point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes 2x, is

F

m P

a

m

a

2 2

F a2m a x−

(B) 2 2

F x2m a x−

(C) F x2m a

(D) 2 2F a x

2m x− .

4. A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.

(A) A potential difference appears between the two cylinders when a charge density is given to the inner cylinder.

(B) A potential difference appears between the two cylinders when a charge density is given to the outer cylinder.

(C) No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders.

(D) No potential difference appears between the two cylinders when same charge density is given to both the cylinders.

5. Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,

(A) Negative and distributed uniformly over the surface of the sphere. (B) Negative and appears only at the point on the sphere closest to the point charge. (C) Negative and distributed non–uniformly over the entire surface of the sphere. (D) Zero.

6. A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge the flows from Y to X is

(A) 0 (B) 54 µC (C) 27 µC (D) 81 µC.

3 Fµ

3 ΩS

9 V

3 Ω

6 FµX

Y

7. A ray of light traveling in water is incident on its surface open to air. The angle of incidence is θ, which is less than the critical angle. Then there will be

(A) Only a reflected ray and no refracted ray. (B) Only a refracted ray and no reflected ray. (C) A reflected ray and a refracted ray and the angle between them would be less than

180º – 2θ. (D) A reflected ray and a refracted ray and the angle between them would be greater than

180º – 2θ.

8. In the options given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is

(A) ( ) ( ) ( )236 137 9792 53 39E U E I E Y 2E(n)> + +

(B) ( ) ( ) ( )236 137 9792 53 39E U E I E Y 2E(n)< + +

(C) ( ) ( ) ( )236 140 9492 56 36E U E Ba E Kr 2E(n)< + +

(D) ( ) ( ) ( )236 140 9492 56 36E U E Ba E Kr 2E(n)= + + .

9. The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

(A) 802 nm (B) 823 nm (C) 1882 nm (D) 1648 nm.

SECTION – II

Assertion – Reason Type

This section contains 4 questions numbered 10 to 13. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

10. STATEMENT – 1 A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops

due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle 30º with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.

because STATEMENT – 2 The coefficient of friction between the block and the surface decreases with the increase

in the angle of inclination. (A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation

for Statement – 1. (B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a correct

explanation for Statement – 1. (C) Statement – 1 is True, Statement – 2 is False. (D) Statement – 1 is False, Statement – 2 is True. 11. STATEMENT – 1 In an elastic collision between two bodies, the relative speed of the bodies after collision

is equal to the relative speed before the collision. because STATEMENT – 2 In an elastic collision, the linear momentum of the system is conserved. (A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation


explanation for Statement – 1. (C) Statement – 1 is True, Statement – 2 is False. (D) Statement – 1 is False, Statement – 2 is True. 12. STATEMENT – 1 The formula connected u, v and f for a spherical mirror is valid only for mirrors whose

sizes are very small compared to their radii of curvature.

because STATEMENT – 2 Law of reflection are strictly valid for plane surfaces, but not for large spherical surfaces. (A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation


explanation for Statement – 1. (C) Statement – 1 is True, Statement – 2 is False. (D) Statement – 1 is False, Statement – 2 is True. 13. STATEMENT – 1 If the accelerating potential in an X–ray tube is increased, the wavelengths of the

characteristic X–ray do not change. because STATEMENT – 2 When an electron beam strikes the target in an X–ray tube, part of the kinetic energy is

converted into X–ray energy. (A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation


explanation for Statement – 1. (C) Statement – 1 is True, Statement – 2 is False. (D) Statement – 1 is False, Statement – 2 is True.

SECTION – III Linked Comprehension Type

This section contains 2 paragraphs C14-16 and C17-19. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

P14–16: Paragraph for Question Nos. 14 to 16 Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of

inertia I and 2I respectively about the common axis. Disc A is imparted an initial angular velocity 2ω using the entire potential energy of a spring compressed by a distance x1. Disc B is imparted an angular velocity ω by a spring having the same spring constant and compressed by a distance x2. Both the discs rotate in the clockwise direction.

14. The radio x1/x2 is

(A) 2 (B) 12

(C) 2 (D) 12

.

15. When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is

(A) 2I3tω (B) 9I

2tω

9I4tω (D) 3I

2tω .

16. The loss of kinetic energy during the above process is

(A) 2I

2ω (B)

2I3ω

(C) 2I

4ω (D)

2I6ω .

P17–19: Paragraph for Question Nos. 17 to 19 A fixed thermally conducting cylinder has a radius R and

height L0. The cylinder is open at its bottom and has a small hole at its top. A piston of mass M is held at a distance L from the top surface, as shown in the figure. The atmospheric pressure is P0.

2R

L

L0

Piston

17. The piston is now pulled out slowly and held at distance 2L from the top. The pressure in the cylinder between its top and the piston will then be

(A) P0 (B) 0P2

(C) 02

P Mg2 R+π

(D) 02

P Mg2 R−π

.

18. While the piston is at a distance 2L from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is

(A) 2

02

0

2P R (2L)R P Mg

π π +

(B) 2

02

0

P R Mg (2L)R P

π − π

(C) 2

02

0

P R Mg (2L)R P

π + π

(D) 2

02

0

P R (2L)R P Mg

π π −

.

19. The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is ρ. In equilibrium, the height H of the water column in the cylinder satisfies

(A) ρg(L0 – H)2 + P0 (L0 – H) + L0 P0 = 0

L0

H

(B) ρg(L0 – H)2 – P0 (L0 – H) – L0 P0 = 0 (C) ρg(L0 – H)2 + P0 (L0 – H) – L0 P0 = 0 (D) ρg(L0 – H)2 – P0 (L0 – H) + L0 P0 = 0.

SECTION – IV

Matrix-Match Type This section contains 3 questions. Each questions contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (p, q, r, s) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example.

If the correct matches are A-p, A-s, B-q, B-r, C-p, C-q and D-s, then the correctly bubbled 4 × 4 matrix should be as follows:

p q r s

p q r s

p q r s

p q r s

A

B

C

D

p q r s

20. Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriated bubbles in the 4 × 4 matrix given in the ORS.

Column I Column II (A) GMeMs

G – universal gravitational constant, Me – mass of the earth, Ms – mass of the sun.

(p) (volt) (coulomb) (metre)

(B) 3RTM

R – universal gas constant, T – absolute temperature, M – molar mass

(q) (kilogram) (metre)3 (second)–2

(C) 2

2 2

Fq B

F – force, q – charge, B – magnetic field.

(r) (metre)2 (second)–2

(D) e

e

GMR

G – universal gravitational constant, Me – mass of the earth, Re – radius of earth.

(s) (farad) (volt)2 (kg)–1

21. Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column I with the

statements in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the ORS.

Column I Column II (A) A charged capacitor is connected to

the ends of the wire. (p) A constant current flows through

the wire. (B) The wire is moved perpendicular to its

length with a constant velocity in a uniform magnetic field perpendicular to the plane of motion.

(q) Thermal energy is generated in the wire.

(C) The wire is placed in a constant electric field that has a direction along the length of the wire.

(r) A constant potential difference develops between the ends of the wire.

(D) A battery of constant emf is connected to the ends of the wire.

(s) Charges of constant magnitude appear at the ends of the wire.

22. Some laws / processes are given in Column I. Match these with the physical phenomena given in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the ORS.

Column I Column II (A) Transition between two atomic energy

levels. (p) Characteristic X–ray.

(B) Electron emission from a material. (q) Photoelectric effect. (C) Mosley’s law. (r) Hydrogen spectrum. (D) Change of photon energy into kinetic

energy of electrons. (s) β – decay.

2006 Time: 2 hours Note: The marking Scheme is (+3, −1) for question numbers 1 to 12 , (+5, −1) for question numbers 13 to 20,

(+5, −2) for question numbers 21 to 32 and (+6, 0) for question numbers 33 to 40. 1 Given, R1 = 1Ω C1 = 2µF R2 = 2Ω C2 = 4µF

C1 C2

R1

R2

V

(I)

C2

C1

R1

R2

V

C2

C1

R2 R1

V

(II) (III)

The time constants (in µS) for the circuits I, II, III are respectively (A) 18, 8/9, 4 (B) 18, 4, 8/9 (C) 4, 8/9, 18 (D) 8/9, 18, 4 Sol. (D) τ1 = 8/9 µS τ2 = 18 µS τ3 = 4 µS 2. Two blocks A and B of masses 2m and m, respectively, are connected by

a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitudes of acceleration of A and B, immediately after the string is cut, are respectively

(A) g, g/2 (B) g/2, g (C) g , g (D) g/2, g/2

A 2m

B m Sol. (B) aA = g/2 aB = g

3 mg

2 mg

A B

mg

3. A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal

length 15 cm, if the plane surface is silvered. The image will form at BA fo tfel mc 03 )B( BA fo tfel mc 06 )A(

BA fo thgir mc 06 )D( BA fo tfel mc 21 )C( Sol. (C)

−1 2 1 15FF f 2= + ⇒ = −

∞

15 cm

20 cm

L O

A

B

2 1 115 v 20

− = −

⇒ v = −12 cm i.e.12 cm left of AB

4. A biconvex lens of focal length f forms a circular image of sun of radius r in focal plane. Then (A) πr2 ∝ f (B) πr2 ∝ f2 (C) if lower half part is covered by black sheet, then area of the image is equal to πr2/2 (D) if f is doubled, intensity will increase Sol. (B) r = f tan α Hence, πr2 ∝ f2

θ α

r

+

5. Given a sample of Radium-226 having half-life of 4 days. Find the probability, a nucleus disintegrates after

2 half lives. (A) 1 (B) 1/2 (C) 1.5 (D) 3/4 Sol. (B) Disintegration of each nuclei is independent of any factor. Hence, each nuclei has same chance of

disintegration. 6. Graph of position of image vs position of point object

from a convex lens is shown. Then, focal length of the lens is

(A) 0.50 ± 0.05 cm (B) 0.50 ± 0.10 cm (C) 5.00 ± 0.05 cm (D) 5.00 ± 0.10 cm

10

−30

v cm

u cm −20 0 −10 (−9, +9) −31

30

31

Sol. (D)

1 1 1f v u= − ⇒ f = 5 cm

f = uvu v+

u vf u v

f u v u v∆ + ∆∆ ∆ ∆

= + ++

∆f = 0.15 (for f = 5 cm) The most appropriate answer is 5.00 ± 0.10 cm 7. A massless rod is suspended by two identical strings AB and CD of equal

length. A block of mass m is suspended from point O such that BO is equal to ‘x’. Further, it is observed that the frequency of 1st harmonic (fundamental frequency) in AB is equal to 2nd harmonic frequency in CD. Then, length of BO is

(A) L/5 (B) 4L/5 (C) 3L/4 (D) L/4

x m

O L

B

A C

D

Sol. (A)

1 21 T 1 T2

=µ µ

T2 = T1/4 For rotational equilibrium, T1x = T2(L −x) ⇒x = L/5

m

O B

A C

D

T2 T1

8. A system of binary stars of masses mA and mB are moving in circular orbits of radii rA and rB respectively. If

TA and TB are the time periods of masses mA and mB respectively, then

(A) A

B

TT

= 3 / 2

A

B

rr

(B) TA > TB (if rA > rB)

(C) TA > TB (if mA > mB) (D) TA = TB [+3, -1] Sol. (D)

2 2

A B A A B B2 2 2

A B A B

Gm m m r 4 m r 4(r r ) T T

π π= =

+

⇒ mArA = mBrB ∴ TA = TB

rA mA mB

C

rB

9. A solid sphere of mass M, radius R and having moment of inertia about an axis passing through the centre of

mass as I, is recast into a disc of thickness t, whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains I. Then, radius of the disc will be

(A) 2R15

(B) 2R15

(C) 4R15

(D) R4

[+3, −1]

Sol. (A)

2 22 3MR Mr5 2

=

r = 2R15

10. A student performs an experiment for determination of 2

24gT

π=

, ≈ 1m, and he commits an error of ∆ .

For T he takes the time of n oscillations with the stop watch of least count ∆T and he commits a human error of 0.1sec. For which of the following data, the measurement of g will be most accurate?

∆ ∆T n Amplitude of oscillation

(A) 5 mm 0.2 sec 10 5 mm (B) 5 mm 0.2 sec 20 5 mm (C) 5 mm 0.1 sec 20 1 mm (D) 1 mm 0.1 sec 50 1 mm Sol. (D) 11. The circular divisions of shown screw gauge are 50. It moves 0.5 mm on

main scale in one rotation. The diameter of the ball is (A) 2.25 mm (B) 2.20 mm (C) 1.20 mm (D) 1.25 mm

0 5

0 10

Sol. (C)

Zero error = 0.55 0.05 mm50

× =

Actual measurement

0.52 0.5 mm 25 0.05 mm50

= × + × −

20 25 30 0

= 1 mm + 0.25 mm − 0.05 mm = 1.20 mm 12 Consider a cylindrical element as shown in the figure. Current flowing

the through element is I and resistivity of material of the cylinder is ρ. Choose the correct option out the following.

(A) Power loss in first half is four times the power loss in second half. (B) Voltage drop in first half is twice of voltage drop in second half. (C) Current density in both halves are equal. (D) Electric field in both halves is equal.

./2 ./2

I

A B C

2r4r

Sol. (B)

1 1

2 2

R A 4R A 1

= =

2

1 12

2 2

P I R 4P 1I R

= =

1 1

2 2

V IR 4V IR 1

= =

1

2

J 1J 4

=

More than One Choice may be correct .(+5, −1) 13. In the given diagram, a line of force of a particular force field is shown. Out of the

following options, it can never represent (A) an electrostatic field (B) a magnetostatic field (C) a gravitational field of a mass at rest (D) an induced electric field Sol. (A), (C)

14. The electrostatic potential (φr) of a spherical symmetric system, kept at

origin, is shown in the adjacent figure, and given as

( )r 00

q r R4 r

φ = ≥π∈

( )r 00 0

q r R4 R

φ = ≤π∈

Which of the following option(s) is/are correct?

φr

R0 r

(A) For spherical region r ≤ R0, total electrostatic energy stored is zero. (B) Within r = 2R0, total charge is q. (C) There will be no charge anywhere except at r = R0.

(D) Electric field is discontinuous at r = R0. Sol. (A), (B), (C), (D) The potential shown is for charged spherical conductor.

15. A solid cylinder of mass m and radius r is rolling on a rough inclined plane of inclination θ. The coefficient of friction between the cylinder and incline is µ. Then

(A) frictional force is always µmg cos θ (B) friction is a dissipative force (C) by decreasing θ, frictional force decreases (D) friction opposes translation and supports

rotation. Sol. (C), (D) 16. Function x = A sin2 ωt + B cos2 ωt + C sin ωt cos ωt represents SHM (A) for any value of A, B and C (except C = 0) (B) if A = −B; C = 2B, amplitude = B 2

(C) if A = B; C = 0 (D) if A = B; C = 2B, amplitude = B

Sol. (A), (B), (D)

A B Cx (1 cos 2 t) (1 cos 2 t) sin 2 t2 2 2

= − ω + + ω + ω

For A = 0, B = 0

Cx sin 2 t2

= ω

For A = −B and C = 2B x = B cos 2ωt + B sin 2ωt Amplitude = B 2

For A = B; C = 0 x = A, Hence this is not correct option For A = B, C = 2B x = B + B sin 2ωt It is also represents SHM. 17. In a dark room with ambient temperature T0, a black body is kept at a temperature T. Keeping the

temperature of the black body constant (at T), sunrays are allowed to fall on the black body through a hole in the roof of the dark room. Assuming that there is no change in the ambient temperature of the room, which of the following statement(s) is/are correct?

(A) The quantity of radiation absorbed by the black body in unit time will increase. (B) Since emissivity = absorptivity, hence the quantity of radiation emitted by black body in unit time will

increase. (C) Black body radiates more energy in unit time in the visible spectrum. (D) The reflected energy in unit time by the black body remains same. Sol. (A), (B), (C), (D) 18. The graph between 1/λ and stopping potential (V) of three metals having

work functions φ1, φ2 and φ3 in an experiment of photo-electric effect is plotted as shown in the figure. Which of the following statement(s) is/are correct? [Here λ is the wavelength of the incident ray].

(A) Ratio of work functions φ1 : φ2 : φ3 = 1 : 2 : 4 (B) Ratio of work functions φ1 : φ2 : φ3 = 4 : 2 : 1

θ 0.001 0.002

metal 1

1/λ

V

0.004 nm−1

metal 2 metal 3

(C) tan θ is directly proportional to hc/e, where h is Planck’s constant and c is the speed of light. (D) The violet colour light can eject photoelectrons from metals 2 and 3.

Sol. (A), (C)

hc

eV− φ =λ

hcVe c

φ= −

λ

For plate 1: plate 2 plate 3

1 0.001hcφ

= 2 0.002hcφ

= 3 0.004hcφ

=

φ1 : φ2 : φ3 = 1 : 2 : 4 For plate 2, threshold wavelength

2

hc hc 1000 5000.002hc 2

λ = = = =φ

nm

For plate 3, threshold wavelength

3

hc hc 1000 250nm0.004hc 4

λ = = = =φ

Since violet colour light λ is 400 nm, so λviolet< λthreshold for plate 2 So, violet colour light will eject photo-electrons from plate 2 and not from plate 3. 19. An infinite current carrying wire passes through point O and in

perpendicular to the plane containing a current carrying loop ABCD as shown in the figure. Choose the correct option (s).

(A) Net force on the loop is zero. (B) Net torque on the loop is zero. (C) As seen from O, the loop rotates clockwise. (D) As seen from O, the loop rotates anticlockwise

A

B C

D

O′O

Sol. (A), (C) Magnetic force on wire BC would be perpendicular to the plane of the loop along the outward direction and

on wire DA the magnetic force would be along the inward normal, so net force on the wire loop is zero and torque on the loop would be along the clockwise sense as seen from O.

20. A ball moves over a fixed track as shown in the figure. From

A to B the ball rolls without slipping. Surface BC is frictionless. KA, KB and KC are kinetic energies of the ball at A, B and C, respectively. Then

(A) hA > hC ; KB > KC (B) hA > hC ; KC > KA

hc

A C

B

hA

(C) hA = hC ; KB = KC (D) hA < hC ; KB > KC Sol. (A), (B), (D) EA = mghA + KA EB = KB Ec = mghC + KC Using conservation of energy EA = EB = EC

KB > KC

KB > KA Mg(hA – hC) + (KA – KC) = 0

⇒ hA – hC = C AK KMg−

*Comprehension –I

The capacitor of capacitance C can be charged (with the help of a resistance R) by a

voltage source V, by closing switch S1 while keeping switch S2 open. The capacitor can

be connected in series with an inductor ‘L’ by closing switch S2 and opening S1.

21. Initially, the capacitor was uncharged. Now, switch S1 is closed and S2 is kept

open. If time constant of this circuit is τ, then

(A) after time interval τ, charge on the capacitor is CV/2

(B) after time interval 2τ, charge on the capacitor is CV(1−e−2)

(C) the work done by the voltage source will be half of the heat dissipated

when the capacitor is fully charged.

(D) after time interval 2τ, charge on the capacitor is CV(1−e−1)

L

V

R

S2

S1

C

Sol. (B)

Q = Q0(1 − e−t/τ)

Q = CV(1 − e−t/τ) after time interval 2τ.

22. After the capacitor gets fully charged, S1 is opened and S2 is closed so that the inductor is connected in series

with the capacitor. Then,

(A) at t = 0, energy stored in the circuit is purely in the form of magnetic energy

(B) at any time t > 0, current in the circuit is in the same direction

(C) at t > 0, there is no exchange of energy between the inductor and capacitor

(D) at any time t > 0, instantaneous current in the circuit may CVL

Sol. (D)

q = Q0 cos ωt

i = − dqdt

= Q0ω sin ωt

⇒ ikax = CωV = CVL

23. If the total charge stored in the LC circuit is Q0, then for t ≥ 0

(A) the charge on the capacitor is 0tQ Q cos

2 LC π

= +

(B) the charge on the capacitor is 0tQ Q cos

2 LC π

= −

(C) the charge on the capacitor is 2

2d QQ LCdt

= −

(D) the charge on the capacitor is 2

21 d QQLC dt

= −

Sol. (C)

Comprehension-II A wooden cylinder of diameter 4r, height h and density ρ/3 is kept on a hole of diameter 2r of a tank, filled with water of density ρ as shown in the figure. The height of the base of cylinder from the base of tank is H. 24. If level of liquid starts decreasing slowly when the level of liquid is at a

height h1 above the cylinder, the block just starts moving up. Then, value of h1 is

(A) 2h/3 (B) 5h/4 (C) 5h/3 (D) 5h/2

4r

H

ρ/3

ρ

h

2r

h1

h2

Sol. (C)

[P0 + ρgh1]π(4r2) + 24r hg3ρπ = [P0 + ρg(h1 +h2)]π(3r2) + P0πr2

h1 = 5h/3

g(ρ/3)π(3r2)h P0π (r)2 [P0 + ρg(h+h1)]π(3r2

(P0 + ρg h1)π(2r)2

25. Let the cylinder is prevented from moving up, by applying a force and water level is further decreased. Then,

height of water level (h2 in figure) for which the cylinder remains in original position without application of force is

(A) h/3 (B) 4h/9 (C) 2h/3 (D) h Sol. (B)

P0π(4r2) + 24r hg3ρπ = (P0 + ρgh2)π(3r2) + P0πr2

h1 = 4h/9

(ρ/3)ghπ(4r2) P0π (r)2 (P0 + ρgh1)π(3r2)

P0 g (2r2)π

26. If height h2 of water level is further decreased, then (A) cylinder will not move up and remains at its original position. (B) for h2 = h/3, cylinder again starts moving up (C) for h2 = h/4, cylinder again starts moving up (D) for h2 = h/5 cylinder again starts moving up Sol. (A) For h2 < 4h/9 cylinder does not moves up 27. Two waves y1 = A cos( 0.5 πx − 100 πt) and y2 = A cos( 0.46 πx − 92 πt) are travelling in a pipe placed along x-axis. Find the number of times

intensity is maximum in time interval of 1 sec. (A) 4 (B) 6 (C) 8 (D) 10

Sol. (A) |f1 − f2| = 4 s−1

28. Find wave velocity of louder sound (A) 100 m/s (B) 192 m/s (C) 200 m/s (D) 96 m/s Sol. (C)

v1 = v2 = 200 m/s 29. Find the number of times y1+ y2 = 0 at x = 0 in 1 sec (A) 100 (B) 46 (C) 192 (D) 96 Sol. (D) y1 + y2 = A cos 100πt + A cos 92π t = 0 cos 100πt = −cos 92πt 100πt = (2n + 1)π − 92πt

(2n 1)t192+

=

∆t = tn+1 − tn = 2192

Questions 30-32 could not be retrieved due to large length of comprehension. 33. There is a rectangular plate of mass M kg of dimensions (a × b). The plate

is held in horizontal position by striking n small balls each of mass m per unit area per unit time. These are striking in the shaded half region of the plate. The balls are colliding elastically with velocity v. What is v?

It is given n = 100, M = 3 kg, m = 0.01 kg; b = 2 m; a = 1m; g = 10 m/s2.

b

a

Sol. Torque about hinge side

b 3b ba n(2 mv) Mg2 4 2

× × =

2 Mg 2 M 10v 103 abnm 3 2 100 0.01

×= = × =

× ×m/s

34. In an insulated vessel, 0.05 kg steam at 373 K and 0.45 kg of ice at 253 K are mixed. Then, find the final

temperature of the mixture. Given, Lfusion = 80 cal/g = 336 J/g, Lvaporization = 540 cal/g = 2268 J/g, Sice = 2100 J/kg K = 0.5 cal/gK and Swater = 4200 J/kg K = 1 cal /gK Sol. ∑∆Q = 0 Heat lost by steam to convert into 0°C water HL = 0.05 × 540 + 0.05 × 10 ×1 = 27 + 5 = 32 kcal Heat required by ice to change into 0°C water

Hg = 10.45 20 0.45 802

× × + × = 4.5 + 36.00 = 40.5 kcal

Thus, final temperature of mixture is 0°C.

35. In hydrogen-like atom (z = 11), nth line of Lyman series has wavelength λ equal to the de-Broglie’s wavelength of electron in the level from which it originated. What is the value of n?

Sol. 22 21 2

1 1 1Rzn n

= − λ

22

1 1 1R(11)1 n

= − λ

h hmv

λ = =ρ

hr rh2 2 rmvr nh n

π πλ = = = .

10 22 r (0.529 10 )n

n (n)(11)

−π π ×λ = =

∴ 101 11

2 (0.529 10 )n−=λ π ×

7 210 2

11 11.1 10 (11) 1(2 )(0.529 10 )n n−

= = × − π ×

10 21 1n

n(2 )(0.529 10 )(1.1 10 )(11)−= = −π × ×

1n 25n

− =

n2 − 1 = 25 n n2 − 25 n − 1 = 0 n = 25 Hence answer = 24 36. A circular disc with a groove along its diameter is placed horizontally. A

block of mass 1 kg is placed as shown. The co-efficient of friction between the block and all surfaces of groove in contact is µ = 2/5. The disc has an acceleration of 25 m/s2. Find the acceleration of the block with respect to disc.

`

θ

cos θ = 4/5sin θ = 3/5

a = 25 m/s2

Sol. N1 = mg N2 = m a sin 37°

abd = 22 1ma cos37 N N 10m / sm

° − µ − µ= .

mg N2

N1

ma ma sin 37°

ma cos 37°

µ1

37. Heat given to process is positive, match the following option

of column I with the corresponding option of column II Column I Column II (A) JK (P) ∆W > 0 (B) KL (Q) ∆Q < 0 (C) LM (R) ∆W < 0 (D) MJ (S) ∆Q > 0

L

M

J

P(atm)

30

20

10K

20 10 V(m3)

Sol. (A)→ (Q), (B)→(P), (S), (C)→(S), (D)→ (Q), (R)

38. Match the following Columns Column I Column II

(A) Nuclear fusion (P) Converts some matter into energy (B) Nuclear fission (Q) Generally possible for nuclei with low atomic number (C) β-decay (R) Generally possible for nuclei with higher atomic number (D) Exothermic nuclear reaction (S) Essentially proceeds by weak nuclear forces

Sol. (A)→(P), (Q), (B)→(P), (R), (C)→(S), (P), (D)→(P), (Q), (R) 39 Match the following Columns

Column I Column II (A) Dielectric ring uniformly charged (P) Time independent electrostatic field out of system (B) Dielectric ring uniformly charged rotating

with angular velocity ω (Q) Magnetic field

(C) Constant current in ring i0 (R) Induced electric field (D) i = i0 cos ωt (S) Magnetic moment

Sol. (A)→(P), (B)→(Q), (S), (C)→(Q), (S), (D)→(Q), (R), (S) 40. A simple telescope used to view distant objects has eyepiece and objective lens of focal lengths fe and f0,

respectively. Then Column I Column II

(A) Intensity of light received by lens (P) Radius of aperture (R) (B) Angular magnification (Q) Dispersion of lens (C) Length of telescope (R) focal length f0, fe (D) Sharpness of image (S) spherical aberration

Sol. (A)→(P), (B)→(R), (C)→(R), (D)→ (P), (Q), (S)

qbank

Documents

Transcript of qbank