This document contains an unsolved physics paper from 2006 containing 7 sections with multiple choice and numerical questions on topics like circuits, mechanics, optics, nuclear physics, and thermodynamics. The document also provides passages of information and context for some of the quantitative questions. Some key details include: - Section I contains 10 multiple choice questions on circuits, mechanics, nuclear physics, and optics. - Section II contains 3 multiple answer questions on mechanics, harmonic motion, and photoelectric effect. - Sections III-VI contain additional quantitative and qualitative questions requiring calculations and reasoning. - Section VII contains 4 subjective problems requiring multi-step solutions related to hydrogen spectra, thermodynamics, rotational motion, and particle collisions

1. IIT JEE –Past papersPHYSICS- UNSOLVED PAPER - 2006

2. SECTION – ISingle Correct Answer Type

3. 01ProblemIn the following circuits ,C1 = 2 F and C = 4 F. The time constants for the circuits ( i ),( ii ),and ( iii ) ,respectively ,areA. s,18 s, (8/9) s18 s (8/9) s , 4 s(8/9) s , 4 s ,18 s4 s, (8/9) s , 18 s

4. Problem02Two blocks of masses 3m and 2m are connected as shown in the figure. The string between the two blocks is suddenly broken. The accelerations of the blocks A and B respectively at that instant are2g , 3gg , gg , (2/3)g(2/3)g, g

5. Problem03The half-life of Ra is 4 days. The probability of a Ra nucleus in a sample disintegrating in three half lives is 1/23/47/81/8

6. Problem04A uniform solid sphere of radius R having moment of inertia I about its diameter is melted to form a uniform disc of thickness t and radius r. The moment of inertia of the disc about an axis passing through its edge and perpendicular to its plane to its also equal to I. The radius r of the disc is a.b. c.d.

7. Problem05PQ and QS are two straight wires each of length l/2, cross-sectional radius of PQ is 2 r while that of QS is r. The current through the composite wire is I. Respectively of the material of both wires is r. Which of the following statements is correct?Potential difference across QS is two times the potential difference across PQ.Power dissipated across QS is for times the power dissipated across PQ.Electric field is same in both wires Current density is same in both wires

8. Problem06A mass less rod AB of length L is hung from two identical wires of equal length. A block of mass m is attached at a point on the rod as shown in the figure. The value of AO so that a tuning fork excites the wire on the left in its first harmonic and the wire on the right in its second harmonic is L/5L/4L/3L/2

9. Problem07A simple –pendulum experiment is performed to find the value of acceleration due to gravity by using expression L/T2 where L = 1 m. If L is the error in the measurement of length L, T is the least count of stop watch, then for which of the following values of amplitude (A), L and T, the error in the value of g is minimum?A = 0.4 m, L = 0.5 m, T = 0.1 sA = 0.4 m, L = 0.1 m, T = 0.05 sA = 0.05 m, L = 0.5 m, T = 0.1 sA = 0.05 m, L = 0.1 m, T = 0.05 s

10. Problem08A thin plano-convex lens of focal length 15 cm has its plane side silvered. An object is placed on the principal axis of the lens at a distance 20 cm from it as shown in the figure. The final position of the image is 60 cm to the right of the lens60 cm to the left of the lens30 cm to the left of the lens12 cm to the left of the lens

11. Problem09The variation of object distance (u) and image distance (v) for a lens is shown in the figure. The focal length of the lens will be(0.05 0.05) cm(0.05 0.10) cm(5.0 0.05) cm(5.0 0.10) cm

12. Problem10Image of sun is formed by a biconvex lens. (Focal length: f) on its focal plane in the form of a circle of radius r. Which of the following statements is correct?Area of images is and is proportional to fArea of images is and is proportional to f2Intensity of images increases with increase in the value of fArea of image becomes half if the lower half of the lens is covered with a black paper

13. Problem11In a binary star, system of masses m1 and m2 are rotating on a circle of radius R1 and R2, respectively under mutual gravitational force of attraction. Time period of mass m1 is T1 and that of m2 is T2. Then T1 = T2T1 > T2 if m1 > m2(T1/T2)2 = (R1/R2)2(T1/T2)2 = (R2/R1)2

14. 12ProblemThe main scale of a screw gauge moves by 0.5 mm in one complete rotation of circular scale having 50 divisions. The zero position of the screw gauge shows + 2 divisions on the circular scale. The diameter of a wire if the main scale reads 2 divisions and circular scale shows 20 divisions coinciding with zero of the main scale is 0.125 cm 0.120 cm0.225 cm0.118 cm

15. SECTION – IIMultiple Answer Type

16. 01ProblemA solid cylinder rolls without slipping down the rough inclined surface as shown in the figure. Which of the following statement (s) is/are correct?The force of friction is equal to Frictional force is dissipativeFrictional force favors rotational motion but opposes translational motionThe speed of the cylinder at the bottom of inclined plane i

17. Problem02Motion of a particle along a straight line is given as The motion will be simple harmonic for All values of A, B and C with A B and C oA = B and C = 2BA = - B and C = 28A = B and C = 0

18. Problem03The graph between cut off voltage (Vs) and reciprocal of wavelength of incident radiation in photoelectric effect for three metallic surface are shown in the figure, If the work function respectively are and 3, thena. 1: 2: 3 :: 1:: 2:: 3b.c. If violet light is used for metals 2 and 3, it liberates photoelectrons from the surface of metals. d. The minimum energy required to emit photoelectron follows the expression metal 3< metal 2 < metal 1

19. Problem04The potential at a distance r from the centre of a uniformly charged conducting sphere of radius R is given by expression which of the following facts is/are correct?No charge resides at any point within the spherical region (r < R) The electric field is discontinuous at r = RThe variation of electric field is as shown in the figureElectrostatic energy inside the sphere is zero

20. Problem05A small spherical ball is released from point A and it reaches point C on a hemispherical surface as shown in the figure. The portion AB of the hemisphere is rough and friction is sufficient to cause only rolling without slipping. The portion BC is smooth. Which of the following statements is/are correct (Where K stands for kinetic energy)? a.b. c. d.

21. Problem06Field lines shown in the figure is not possible forElectrostatic field Magneto static fieldInduced magnetic fieldGravitational field of rest mass

22. Problem07Initially a black body at temperature Tb is kept inside a closed chamber at temperature Tc. Now the chamber is slightly opened to sun rays, such that temperatures of black body and chamber remain constant, then which of the following statement is/are correct?Amount of energy emitted remains same Rate of absorption increasesBecause emissivity is equal to absorptive so that the sun rays absorbed will be emitted so the temperature of body will decrease Amount of rays radiated in the visible spectrum will increase

23. Problem08At the centre and perpendicular to the plane of paper of an annular arc, a long wire is place as shown in the figure. Which of the following statements is correct?Net force on the annular arc is zero Net torque on the annular arc is zeroThe arc will rotate clockwise as viewed from OThe arc will rotate anticlockwise as viewed from O

24. SECTION – IIIQuantitative AbilityRead the passage and answer the following questions

25. Passage-1A tank has a cylindrical hole of diameter 2r at its bottom in the figure. A cylindrical block having a diameter 4r and height h is placed on the hole to prevent flow of water into the hole. The block is made of material of density and density of water is . Water is filled completely in the tank upto a height h1 above the upper surface of cylindrical block

26. 01ProblemIf water is taken out of rank gradually, height h1 above the cylindrical block for which it starts rising is 2h/35h/45h/35h/2

27. Problem02Pressure is applied on the block and water level is h2 above the lower surface of block as shown in the figure. The maximum value of h2 for which cylinder does not move on releasing the pressure ish/32h/3h/44h/9

28. Problem03If water level is further reduced from h2 thenThe block will never riseThe block first rises then fallsThe block keeps on rising None of these

29. SECTION – IVQuantitative AbilityRead the passage and answer the following questions

30. Passage - 2In an LRC circuit shown in the figure, both switches are open initially. Now switch S1 is closed and S2 is kept open. After that S1 is opened and S2 is closed. Based on these, answer the following questions.

31. Problem01When S1 is closed and S2 open at t = 0 which of the following statements is not correct? The time constant of the circuit is equal to RC.The charge on the capacitor is given as The current through the circuit is given as The time constant is equal to the time in which the capacitor acquires 37 percent of maximum charge on the capacitor.

32. Problem02When switch S2 is closed with S1 open at t = 0, which of the following statements is not correct? At t = 0, the current in the inductor has a maximum value.At any instant, the expression Q/C = - L dI/dt holds good The maximum current in the circuit is equal to The charge on the capacitor oscillates sinusoid ally with frequency equal to

33. Problem03When S2 is closed and S1 open at t = 0, then energy stored in the electrical field of the capacitor and in the magnetic field of the inductor at any instant respectively are given as a.b.c.d.

34. SECTION – VQualitative Ability Read the passage and Answer the following questions

35. Passage - 3The equations of two plane progressive sound waves are given as and Answer the following equations based on the above equations.

36. Problem01How many time the value becomes zero at and in 1s? 4246100184

37. Problem02Wave speed of the faster moving wave is100 m/s184 m/s192m/s200 m/s

38. Problem03When the given waves superpose the number or times the intensity of sound becomes maximum in 1 s is 2468

39. SECTION – VIQualitative Ability Read the passage and Answer the following questions

40. Passage - 4In a conventional vehicle, power is dissipated due to friction. To reduce the loss of power due to friction MAGLEV train using a EDS (electro-dynamic suspension) technology was developed. It works on the principle of Lens's law. In this system, a train moves without contact with the track due to which there is no loss of power duet to friction. In EDS technology, electromagnets are attached to the train and conducting coils on the track. Which the train moves there is a change of flux in the conducting coil and due to induction, the train is lifted slightly above the track. There is a stability factor also. It the train comes downward, the repulsive force increases to restore its position and if it induced circulating currents, an opposing force acts on the train. A significant power is required to propel the train against this force at low speeds.

41. Problem01The advantage of EDS is that No power is required to propel the train No energy is lost due to conservative forcesNo power is dissipated against frictional forceNo force id required to overcome gravity

42. Problem02Which of the following statements about MAGLEV train is correct?It moves due to electrostatic attractionIt is lifted due to magnetic repulsionIt moves due to magnetic attractionIt is lifted due to electrostatic repulsion

43. Problem03The disadvantage of EDS is that It cannot overcome the force of gravity Repulsive force is conservative so it lifts the vehicle and brings down Magnetic force tends to bring down the trainLot of energy is lost to start the motion as there is more opposition to the motion at lower speeds.

44. SECTION – VIISubjective Problems

45. 01ProblemAn electron in a hydrogen – like species (atomic number = 11) undergoes a transition from nth orbit and emits radiation corresponding to Lyman series. If the wavelength of emitted radiation is equal to de Broglie wavelength of the electron in the nth orbit, determine the value of n.

46. Problem0260 g steam at 373 K is mixed with 450 g of ice at 253 K. Find the final sate of the system. Given:Latent of vaporization for steam = 540 cal g-1Latent of fusion of ice = 80 cal g-1Specific heat capacity of ice = 0.5cal g-1 0C-1Specific heat capacity of water = 1 cal g-10C-1

47. Problem03A small block of mass m is placed in a groove carved inside a disc. The disc is place on smooth horizontal surface and pulled with an acceleration of magnitude 25 m/s2 as shown in the figure. Fined the acceleration of block with respect to disc? Given: sin = 3/5, cos = 4/5 , g = 10 m/s2 and coefficient of fricition between the groove and the block is

48. Problem04 A uniform plate of length a = 0.6 m and width b = 0.4 m having mass M = 3 kg is free to rotate about an edge. Initially the plate is kept placed horizontally and small particles of each of mass m = 0.01 kg collide elastically and perpendicular to the plate on the second half of the plate at the rate n = 100 particles per unit time per unit area as shown in the figure. What will be the velocity of striking particles so that plate does not rotate?

49. SECTION – VIIMatching problems

50. 01ProblemPressure versus volume graph of a thermodynamic cyclic process of an ideal gas as shown in the figure. When the gas does work, W > 0 and when heat is absorbed by the gas, Q > 0. In process J – K Q > 0In process K – L Q < 0In process L – M W > 0In process M – J W < 0

51. Problem02The quantities of column –I depends on the entries of column – II. Match them with reference to a telescope. Column – I Column – II Light entering per unit area of telescope radius of aperture of objective lensLength of telescope dispersion of lensesMagnification focal length of objective lens (f0) and. Eye lens (Fe)Sharpness of image spherical aberration

52. Problem03The quantities of column –I depends on the entries of column – II. Match them with reference to nuclear reactions. Column – I Column – II Nuclear fission matter converted into energyNuclear fusion for atoms having higher atomic numberDecay for atom having lower atomic numberExothermic reaction weak nuclear forces

53. Problem04The entries of Column – I results into the physical quantities mentioned in Column – II. Match them Column – I Column – II Stationary dielectric ring having uniform electric fieldCharge Dielectric ring having uniform charge is Magneto static field Rotating with costar angular speed A constant current I0 in the loop. Time dependent induced electric field Outside the loopTime varying sinusoidal current in the loop magnetic moment in the loop

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