IIT JEE Physics 2006

IIT JEE –Past papers PHYSICS- UNSOLVED PAPER - 2006

SECTION – I Single Correct Answer Type

01 Problem In the following circuits ,C1 = 2 F and C = 4 F. The time constants for the circuits ( i ),( ii ),and ( iii ) ,respectively ,are A. s,18 s, (8/9) s 18 s (8/9) s , 4 s (8/9) s , 4 s ,18 s 4 s, (8/9) s , 18 s

Problem 02 Two 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 are 2g , 3g g , g g , (2/3)g (2/3)g, g

Problem 03 The half-life of Ra is 4 days. The probability of a Ra nucleus in a sample disintegrating in three half lives is 1/2 3/4 7/8 1/8

Problem 04 A 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.

Problem 05 PQ 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

Problem 06 A 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/5 L/4 L/3 L/2

Problem 07 A 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 s A = 0.4 m, L = 0.1 m, T = 0.05 s A = 0.05 m, L = 0.5 m, T = 0.1 s A = 0.05 m, L = 0.1 m, T = 0.05 s

Problem 08 A 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 lens 60 cm to the left of the lens 30 cm to the left of the lens 12 cm to the left of the lens

Problem 09 The 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

Problem 10 Image 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 f Area of images is and is proportional to f2 Intensity of images increases with increase in the value of f Area of image becomes half if the lower half of the lens is covered with a black paper

Problem 11 In 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 = T2 T1 > T2 if m1 > m2 (T1/T2)2 = (R1/R2)2 (T1/T2)2 = (R2/R1)2

12 Problem The 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 cm 0.225 cm 0.118 cm

SECTION – II Multiple Answer Type

01 Problem A 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 dissipative Frictional force favors rotational motion but opposes translational motion The speed of the cylinder at the bottom of inclined plane i

Problem 02 Motion 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 o A = B and C = 2B A = - B and C = 28 A = B and C = 0

Problem 03 The 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, then a. 1: 2: 3 :: 1:: 2:: 3 b. 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

Problem 04 The 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 = R The variation of electric field is as shown in the figure Electrostatic energy inside the sphere is zero

Problem 05 A 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.

Problem 06 Field lines shown in the figure is not possible for Electrostatic field Magneto static field Induced magnetic field Gravitational field of rest mass

Problem 07 Initially 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 increases Because 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

Problem 08 At 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 zero The arc will rotate clockwise as viewed from O The arc will rotate anticlockwise as viewed from O

SECTION – III Quantitative Ability Read the passage and answer the following questions

Passage-1 A 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

01 Problem If water is taken out of rank gradually, height h1 above the cylindrical block for which it starts rising is 2h/3 5h/4 5h/3 5h/2

Problem 02 Pressure 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 is h/3 2h/3 h/4 4h/9

Problem 03 If water level is further reduced from h2 then The block will never rise The block first rises then falls The block keeps on rising None of these

SECTION – IV Quantitative Ability Read the passage and answer the following questions

Passage - 2 In 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.

Problem 01 When 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.

Problem 02 When 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

Problem 03 When 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.

SECTION – V Qualitative Ability Read the passage and Answer the following questions

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

Problem 01 How many time the value becomes zero at and in 1s? 42 46 100 184

Problem 02 Wave speed of the faster moving wave is 100 m/s 184 m/s 192m/s 200 m/s

Problem 03 When the given waves superpose the number or times the intensity of sound becomes maximum in 1 s is 2 4 6 8

SECTION – VI Qualitative Ability Read the passage and Answer the following questions

Passage - 4 In 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.

Problem 01 The advantage of EDS is that No power is required to propel the train No energy is lost due to conservative forces No power is dissipated against frictional force No force id required to overcome gravity

Problem 02 Which of the following statements about MAGLEV train is correct? It moves due to electrostatic attraction It is lifted due to magnetic repulsion It moves due to magnetic attraction It is lifted due to electrostatic repulsion

Problem 03 The 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 train Lot of energy is lost to start the motion as there is more opposition to the motion at lower speeds.

SECTION – VII Subjective Problems

01 Problem An 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.

Problem 02 60 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-1 Latent of fusion of ice = 80 cal g-1 Specific heat capacity of ice = 0.5cal g-1 0C-1 Specific heat capacity of water = 1 cal g-10C-1

Problem 03 A 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

Problem 04 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?

SECTION – VII Matching problems

01 Problem Pressure 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 > 0 In process K – L Q < 0 In process L – M W > 0 In process M – J W < 0

Problem 02 The 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 lens Length of telescope dispersion of lenses Magnification focal length of objective lens (f0) and. Eye lens (Fe) Sharpness of image spherical aberration

Problem 03 The 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 energy Nuclear fusion for atoms having higher atomic number Decay for atom having lower atomic number Exothermic reaction weak nuclear forces

Problem 04 The 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 field Charge 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 loop Time varying sinusoidal current in the loop magnetic moment in the loop

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IIT JEE Physics 2006

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IIT JEE Physics 2006