1) The time constant for the current in the parallel circuit is 0.9 seconds and the steady state current through the battery is 6 amperes. 2) The final temperature of the water-ice mixture is 0°C. 3) Treating the sun as a black body, its surface temperature is approximately 5800 K.

1. IIT JEE –Past papersPHYSICS- UNSOLVED PAPER - 1989

2. SECTION – IFill in the blanksFill in the blanks in the following statements. Indicate the subdivision number and write down your answer corresponding to each blank strictly in the order in which it appears in the statement.

3. 01ProblemA uniformly wound solenoid coil of self inductance 1.8 X 10-4 H and resistance is broken up into two identical coils. These identical coils are than connected in parallel across a 12 V battery of negligible resistance. The time constant for the current in the circuit is ________ seconds and the steady state current through the battery is _________ amperes.

4. Problem02300 g of water at 25is added to 100 g of ice at The final temperature of the mixture of the mixture is _______.

5. Problem03The earth receives at its surface radiation from the sun at the rate of 1400 W m-2 . The distance of the center of the sun from the surface of the earth is 1.5 X 1011 m and the radius of the sun is m. treating the sun as a black body, it follows from the above data that its surface temperature is _________ K.

6. Problem04A point charge q moves from point P to points S along the path PQRS (Fig. 1989.1) in a uniform electric-field E pointing parallel to the positive direction of the x axis. The coordinates of the points P,Q,R and S are (a, b, 0) ,(2a, 0, 0, ) ( a, -b, 0 ) and ( 0, 0, 0) respectively . The work done by the field in the above process is given by the expression __________.

7. Problem05A point source emits sound equally in all directions in a non-absorbing medium. Two points P and Q are a distance of 9 m and 25 m respectively from the source. The ratio of the amplitudes of the waves at P and Q is ____________________.

8. SECTION – IIEach of which either true or FalseState whether the following statements are true of false. Give very brief reasons in support of your answers. Marks will be awarded only if correct. Reasons are also given.

9. 01ProblemA ring of mass 0.3 kg and radius 0.1 m and a solid cylinder of mass 0.4 kg and of the same radius are given the same kinetic energy and released simultaneously on a flat horizontal surface such that they begin to roll as soon as released towards a wall which is at the same distance from the ring and the cylinder. The rolling friction in both cases is negligible. The cylinder will reach the wall first.

10. Problem02Two particles of mass 1 kg and 3 kg move towards each other under their mutual force of attraction. No other force acts on them, When the relative velocity of approach of the two particles is 2 m/s, their centre of mass has a velocity of 0.5 m/s. When the relative velocity of approach becomes 3 m/s, the velocity of the centre of mass is 0.75 m/s.

11. Problem03The order of magnitude of the density of nuclear matter is

12. SECTION – IIISingle Correct Answer TypeIn each of the statements given below, several alternatives are given. In Some cases more than one alternative is correct. Select the correct alternative (s) in each case and write down the corresponding letter(s) (a), (b), (c) or (d), For each part marks will be awarded only if all the correct alternatives are written .

13. 01ProblemA conducting square loop of side L and resistance R move in its plane with a uniform velocity v perpendicular to one of its sides. A magnetic induction B, constant in time and space, pointing perpendicular to and into the plane of the loop exists everywhere (Fig. 1989.2) The current induced in the loop is:BL v/R clockwise 2BLv/R anticlockwiseBL v/R anticlockwiseZero

14. Problem02Two identical p-n junctions may be connected in series with a battery in three ways (Fig.1989.3). The potential drops across the two p-n junctions are equal in: Circuit 1 and circuit 2 Circuit 2 and circuit 3Circuit 3 and circuit 1Circuit 1 only

15. Problem03A beam of light consisting of red, green and blue colors is incident on a right tangled prism (Fig. 1989.4). The refractive indices of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. The prism will: Separate part of the red color from the green and blue colors Separate part of the blue color from the red and green colors Separate all the three coleus from one another Not separate even partially any color from the other two colours

16. Problem04Two rods of different materials having coefficients of thermal expansion a1, a2 and Young’s module respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If = 2 : 3, the thermal stresses developed in the two roads are equal provided is equal to : 2 : 31 : 13 : 24 : 9

17. Problem05Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T . If the gravitational force of attraction between the planet and the star is proportional to R-5/2, then: T2 is proportional to R2T2 is proportional to R7/2T2 is proportional to R3/2T2 is proportional to R3.75

18. Problem06A linear harmonic oscillator of force constant 2 x 106 N/m and amplitude 0.01 m has a total mechanical energy or 160 J. Its Maximum potential energy is 100 JMaximum kinetic energy is 100 JMaximum potential energy is 160 JMinimum potential energy is zero.

19. Problem07The decay constant of a radioactive sample is . The half-life and mean – life of the sample are respectively given by : 1/ and (In 2)/ (In 2)/ and 1 / (ln 2) and 1/ /(ln 2) and 1/

20. Problem08Capacitor C1 of capacitance 1 microfarad and capacitor C2 of capacitance 2 microfarad are separately charged fully by a common battery. The two capacitors are then separately allowed to discharge through equal resistors at time t = 0. The current in each of the two discharging circuits is zero at t = 0The currents in the two discharging circuits at t = 0 are unequal.The currents in the two discharging circuits at t = 0 are unequal. Capacitor C1 loses 50% of its initial charge sooner than C2 loses 50% of its initial charge

21. Problem09Velocity of sound in air is 320 m/s. A pipe closed at one end has a length of 1 m. Neglecting end corrections, the air column in the pipe can resonate for sound of frequency.80 Hz240 Hz320 Hz400 Hz

22. Problem10A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of – 3Q, the new potential difference between the same tow surfaces is V2V4V-2V

23. Problem11For an ideal gas:The change in internal energy in a constant pressure process from temperature T1 to T2 is equal to n C v(T2 - T2), where C v is the molar heat capacity at constant volume and n the number of moles of the gas. The change in internal energy of the gas and the work done by the gas are equal in magnitude in an adiabatic process. The internal energy does not change in an isothermal process.No heat is added or removed in an adiabatic process.

24. Problem12An astronomical telescope has an angular magnification of magnitude 5 for distance objects. The separation between the objective and the eyepiece is 36 cm and the final image is formed at infinity. The focal length f0 of the objective and the focal length fe of the eyepiece are = 45 cm and = 9 cm = 50 cm and = 10 cm = 7.2 cm and = 5 cm = 30 cm and = 6 cm

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