fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Entrance Examination, February-2012 M.Sc.

Size: px

Start display at page:

Download "fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Entrance Examination, February-2012 M.Sc."

Janice Burke
6 years ago
Views:

1 Entrance Eaination, February- M.Sc. (PHYSICS) Marks: 75 Tie:. hrs Note:. Section A consists of 5 objective type questions of one ark each. There is negative arking of. arks for every wrong answer.. Section B consists of 5 objective type questions of one ark each. There is no negative arking in this section. SECTION A Q. If two sides of a triangle are represented by a iˆ ˆj kˆ and b ˆj kˆ, then the third side is represented by iˆ ˆj kˆ iˆ ˆj kˆ iˆ ˆj kˆ iˆ ˆj kˆ Q rˆ Q. If the electric field due to a point charge Q is epressed as E, then the 4 r divergence of this field is Q Q Q 4 r 4 r 4 r Q. Which one of the following stateents is true for the atri given below? A is syetric A is anti-syetric A i Q4. Coplete solution of the differential equation d y dy 7 6y e is given by (where c and c are arbitrary constants) d d A is Heritian A is skew-heritian c e ce e c e 4 6 ce e c 6 e ce c e c e e e 4 fiziks, H.No., G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-6 Phone: / B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-6 Eail: fiziks.physics@gail.co

2 Q5. A function f varies, as shown in the figure. Which of the following represents f? f log e log Q6. If rigid body with N particles is constrained to be fied at a single point, then the nuber of degrees of freedo is 6 N Q7. If a particle of ass oves under the influence of a force obeying dv r v dt, r then the rate of change of kinetic energy is positive zero negative can be positive or negative Q8. The trajectory of a particle oving under the influence of an attractive, inverse square law force, could be Elliptic Hyperbolic Parabolic Any of the above Q9. An astronaut oves in a spaceship travelling at a speed of.8c ( c is the speed of light). If the astronaut observes a photon approaching the ship fro space, then the speed of this photon with respect to the observer is.8c c.c.9c Q. A certain weight of liquid has a volue of cc at o C. If the volue epansion coefficient of the liquid is./ o C, then its volue at 5 o C is approiately 6 cc 6 cc 94 cc cc fiziks, H.No., G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-6 Phone: / B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-6 Eail: fiziks.physics@gail.co

3 Q. A string under tension T vibrates at a natural frequency, f. If the tension of the string is increased to T, then the natural frequency at which the string now vibrates is T f T f T T T f T Q. According to the kinetic theory of gases, the root-ean-square speed of gas olecules in a onoatoic ideal gas at a teperature T is f T T v k BT v k BT v k BT v k BT Q. If g of ice at o C is elted and converted into water at the sae teperature, then the change in entropy is, (assuing heat of fusion = 79.7 cal/g).9 cal/k cal/k cal/k -.9 cal/k Q4. If a syste is in equilibriu with entropy S at constant T and N, then the variation of S entropy with volue V T, N is given by S P T, N P T V, N V T P, N T P Q5. Which one of the following equations does not represent a travelling wave? y f vt S, N y f v t y ya sin k vt y ya ep i vt fiziks, H.No., G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-6 Phone: / B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-6 Eail: fiziks.physics@gail.co

4 Q6. The light L and sound S arising fro an eplosion on the sea surface were recorded by an observer in a subarine located at k below the sea surface at tie periods and t S sub respectively. The sae event was also recorded by an observer in a helicopter, at k above the sea surface, at ties t L hel, and L t sub S t hel respectively. Assuing that both the observers are at rest with respect to the event, which one of the following is true? t L t L ; t S t S t t ; t t sub hel sub hel L L S S sub hel sub hel t L t L ; t S t S t t ; t t sub hel sub hel L L S S sub hel sub hel Q7. When the current flowing in a priary coil of a transforer increases fro zero to 5A in a tie of. sec, the induced ef in the secondary coil was found to be 5 V. Then the utual induction between the two coils is. H H H H Q8. If a charge q is oving initially with a velocity of v vzˆ, parallel to a unifor agnetic field, B Bzˆ, the charge will then accelerate along ẑ oscillate back and forth around ẑ continue along ẑ with the sae speed v ove in a plane perpendicular to ẑ along the circular path. Q9. A filaent, assued to be a black body, is eitting radiation at a teperaturet. If the power to the filaent is doubled then the teperature will 4 increase by increase by increase by increase by 4 Q. If a particle of ass M at rest eplodes into two parts of asses and, then the ratio of their de Broglie wavelength is M fiziks, H.No., G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-6 Phone: / B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-6 Eail: fiziks.physics@gail.co 4

5 Q. If an electron and a proton are oving with the sae kinetic energy along the sae direction, when they pass through a unifor agnetic field perpendicular to the direction of their otion, which one of the following stateents regarding the radii of the trajectories of these two particles in the region of the agnetic field is true? they are the sae. radius is greater for the electron since it has a higher velocity. radius is greater for the proton since it has a higher ass. radius is lower for the proton since it has the higher ass. Q. The part of the output characteristics of an n p n transistor, which is used while operating it as an aplifier is the saturation region. cut-off region. active region. break down region. Q. Diodes D and D shown in the circuit are silicon diodes. The voltage drop across the diode D and the power dissipated by the diode D are respectively.7 V and W 5. V and W.7 V and.7 W 5. V and 5 W Q4. A source produces sound of constant frequency at khz. If a person oves away fro this source at twice the speed of sound, then the frequency of sound sensed by the person is larger than khz. frequency of sound sensed by the person is saller than khz. frequency of sound sensed by the person is equal to khz. person does not hear any sound. D D 5V 4. k fiziks, H.No., G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-6 Phone: / B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-6 Eail: fiziks.physics@gail.co 5

6 Q5. If a ray of light is travelling fro a denser ediu (glass) to air, and the refractive inde n of the denser ediu is.5, then the Brewster angle is SECTION - B Q6. A unit vector noral to the surface z y at the point (,, 5) is given by iˆ ˆj kˆ 6 iˆ 4 ˆj kˆ iˆ ˆj kˆ iˆ 4 ˆj kˆ 4 Q7. Which of the following cannot possibly be the eigenvalues of a real atri?,,, i, i,,, i, i Q8. Two independent solutions of the differential equation ay be chosen to be d y dy y d d e e, e e e e, e e e e, e e e, e Q9. The area of the shaded region between the straight line and parabola as shown in the figure is given by y, dy d d dy d dy dy d fiziks, H.No., G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-6 Phone: / B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-6 Eail: fiziks.physics@gail.co 6

7 i Q. Given a ib, the values of a andb are i a, b a, b a, b a, b Q. If one person speaks the truth in 7% of the cases and another in 8% of the cases, then the probability that they will contradict each other in describing a single event is Q. The straight line y k touches the parabola y k k k k any integer Q. The power series n n n converges for, if k is chosen as Q4. li is given by sin Q5. The inverse of the function y log log is log log 4 Q6. A satellite of ass M, launched into a circular orbit of radius R, has a tie periodt. If a 4 second satellite of ass.75m is launched into an orbit of radius R, the tie period of the second satellite will be given by T.65T.75T.54T fiziks, H.No., G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-6 Phone: / B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-6 Eail: fiziks.physics@gail.co 7

8 Q7. A block of ass rests on a frictionless horizontal table and is connected to two fied posts by springs having spring constants k and k. If the block is displaced fro its equilibriu position, the angular frequency of vibrations is given by k k Q8. A particle of ass oves in a circle of radius a under the action of a central force whose potential isv r kr k ka k. The energy of the particle given by k ka ka ka Q9. The utual potential energy V of two particles depends on their utual distance r, as V a r b r r ; a, b If the particles are in static equilibriu, then the separation is given by a b b a b a a b Q4. If a body of unifor cross-sectional area A and ass density floats in a liquid of density and at equilibriu displaces a volue V of the liquid, then the tie period of sall oscillations about the equilibriu position is T V g T g V A ga T T V Q4. A particle of ass, carrying a charge q hangs at rest fro a spring of stiffness k. If a charge q is brought and held directly below q at a distance of d, then the change in length of the spring, V ga z, in its new equilibriu state is proportional to d q d k q kd kq d fiziks, H.No., G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-6 Phone: / B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-6 Eail: fiziks.physics@gail.co 8

9 Q4. For which of the following force fields the potential energy is not defined? F yz 6yz, F z 6yz, F y yz y z 6 F y z y yz z, Fy z y yz z, Fz y y yz z F yz, Fy y z, Fz yz F / y z, F y / y z, F z / y z y Q4. A unifor hollow cylinder of ass M and radius R, rolls fro rest down an inclined plane through a distance L. If the plane akes an angle of with horizontal, then the rotational kinetic energy of the cylinder when it reaches the botto of the inclined plane is gl gl gl gl 4 8 Q44. If S, S and S denote the surface tensions of a liquid drop, its supporting liquid and the interface between the, respectively, then the liquid drop will spread over the surface of the supporting liquid when S S S S S S S S S S S S Q45. A solid block which is in side and having a thickness of.5 is copressed across z its thickness. If its Young s odulus is 6 N / then the force required to copress the solid by. in length across its thickness is N 8 N N.5 N Q46. Consider a long thin wire of cross sectional area A, with Young s odulus Y, tension T, ass per unit length M and density. In such a syste, which of the following stateents regarding the speeds of transverse and longitudinal waves will be true? The speeds are equal if the fractional increase in its length is. The speeds are equal if the fractional increase in its length is /. The speeds are equal if the fractional increase in its length is. The speeds can never be equal. fiziks, H.No., G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-6 Phone: / B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-6 Eail: fiziks.physics@gail.co 9

10 Q47. The surface tension, of a liquid of density, which rises to a height h in a capillary of a diaeter D is D hg 4 g Dh 4 g D h g Dh Q48. If the equilibriu state of the vapour near and above the critical point is described by the Van der Waal equation of state p v b RT a v, where v V / n is the olar volue, which one of the following stateents about the critical values of (olar) volue, pressure and teperature at the critical point is true? p v T T C p p ; v v T T T C T C p p ; v v T T T C T C p p ; v v T T T C T C Q49. If W is the work done on a syste in a reversible process and F is the change in its free energy, then W F W F W F W F Q5. In an infinitesial adiabatic process, the work done is a perfect differential is not a perfect differential is zero depends on the teperature Q5. The outer surface of a brass sheet at C is kept in contact with the outer surface of a steel sheet at C. If the thickness and cross-sectional areas of both the sheets are equal and the ratio of their theral conductivities is :, then the teperature of the interface at equilibriu is 66.7 C 5 C C C fiziks, H.No., G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-6 Phone: / B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-6 Eail: fiziks.physics@gail.co

11 Q5. A refrigerator is operated between two reservoirs aintained at 5 K and K respectively. If its coefficient of perforance is one-third that of a Carnot engine and it absorbs 5 J fro the low teperature reservoir, then the heat lost to the high teperature reservoir is 8 J 5 J 6 J 55 J Q5. If a etal rod is heated at one end and iersed in ice (at C) at the other end, then the ass of ice that elts in a given tie, t, is directly proportional to the length of the rod and inversely proportional to the area of cross-section. directly proportional to the area of cross-section and inversely proportional to theral conductivity of the rod. directly proportional to both the length and theral conductivity of the rod. directly proportional to the theral conductivity of the rod and inversely proportional to its length. Q54. Two waves are described by y asin4 tand y acos4 t. The phase difference between these two waves is / Q55. The fraction of kinetic energy in the total energy of a siple haronic oscillator, when its displaceent is half of its aplitude, is given by.5.75 Q56. Which one of the following stateents about sound waves is true? sound waves cannot be polarized. sound waves can only be circularly polarized. sound waves can only be plane polarized. sound waves can be plane polarized or circularly polarized. Q57. If surface waves in a lake have a phase velocity given by v a /, where a is constant, then their group velocity is v v v a v fiziks, H.No., G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-6 Phone: / B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-6 Eail: fiziks.physics@gail.co

12 Q58. If a dipole p situated at the region,, is pointing in the z -direction, then the force on a point charge q at a,, is pq F zˆ 4 a pq F 4 a zˆ pq F zˆ 4 a zero Q59. Wires of equal resistance are joined together in the for of two pyraids with a coon base, as shown in the figure. If current enters through A and leaves through B, then the resistance between the two points A and B is A B 5 4 Q6. The resonance frequency of an LCR circuit was found to be Hz. If another capacitor of equal value is connected in parallel to the eisting one in the circuit, then the new resonance frequency is 4 Hz 697 Hz 849 Hz 6 Hz 4 Q6. If a MeV alpha particle He incident on ipact paraeter is e / 4.44MeV f 7 47 Ag nucleus is scattered at 9, then the Q6. The electron in a Hydrogen ato in its ground state gets elevated to the highest perissible ecited state, by absorbing energy equal to. ev. The change in the angular oentu of the electron is h h h h fiziks, H.No., G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-6 Phone: / B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-6 Eail: fiziks.physics@gail.co

13 Q6. Photons with energies p and q are incident one after another on a etal having work function, where p and q are integers. The ratio of respective aiu velocities is p q q p p q q p Q64. Separate Copton effect eperients are carried out using visible light and X -rays. If the scattered radiation is observed at the sae scattering angle, then the X -rays have greater shift in wavelength and greater change in photon energy. the two radiations have the sae shift in wavelength and X -rays have a greater change in photon energy. the two radiations have the sae shift in wavelength and visible light has greater change in photon energy the two radiations have the sae shift in wavelength and the sae change in photon energy. Q65. Which of the following represents the first ecited state wave function of a assive particle confined to ove in a one-diensional bo of length L (the -ais represents the space co-ordinate and the y -ais represents the shape of the wave-function, in each figure). fiziks, H.No., G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-6 Phone: / B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-6 Eail: fiziks.physics@gail.co

14 Q66. When a bea of ev electrons is incident on a crystal at an angle, a first order Bragg reflection occurs, then the lattice spacing is Q67. If a particle of ass.67 7 kg is confined to ove in a bo of length infinite depth, the iniu kinetic energy of the particle would be. MeV. MeV Q68. The current I L flowing in the circuit is. MeV. MeV 4 and A.5 A.5 A A V k I L k k 5V Q69. If the binary nuber is converted into the headecial syste, then it is written as 6AH 6H 6H EH Q7. The iniu current required to achieve Zener action in the diode shown in the circuit is.5a and the aiu power it can withstand is W. The input voltage range over which this diode can regulate the output voltage is 9.95V V V V.5V V.7V. 7V R Vz V Vout fiziks, H.No., G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-6 Phone: / B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-6 Eail: fiziks.physics@gail.co 4

15 Q7. A F capacitor is connected in series with a k resistance and an AC source as shown in the figure. If V is the agnitude of the output voltage when a khzac signal of certain aplitude is applied at the input and V is the agnitude of the output voltage when a Hz AC signal of the sae aplitude is applied, then the ratio of V to V is approiately C F R k V out Q7. If light passes through a glass slab of c thickness and refractive inde.5 at an angle of o 45 with respect to the noral to the slab, then it deviates fro the original path by c.6c.6c.5c Q7. The output of light fro a laser source of W power passing through two crossed polarizers is zero. If another polarizer is introduced between these two at an angle of o 45 with respect to the optic ais of one of the, the output power at the detector is W.5W.75W.5W Q74. If the output fro a V source is attenuated by db, then the easured voltage will be.5v.v.v.v Q75. If. the actual wavelength of light eitted fro a luinous body is o 6, but is easured to be o 6, then its relative velocity with respect to the observer is 6 / sec.5 6 / sec 6 / sec 6 6 / sec fiziks, H.No., G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-6 Phone: / B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-6 Eail: fiziks.physics@gail.co 5

= T. Oscillations and Waves. Example of an Oscillating System IB 12 IB 12

= T. Oscillations and Waves. Example of an Oscillating System IB 12 IB 12 Oscillation: the vibration of an object Oscillations and Waves Eaple of an Oscillating Syste A ass oscillates on a horizontal spring without friction as shown below. At each position, analyze its displaceent,