IIT JEE –Past papers PHYSICS- UNSOLVED PAPER - 1989

SECTION – I:

SECTION – I Fill in the blanks Fill 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.

Problem:

01 A 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 . Problem

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Problem 02 300 g of water at 25 is added to 100 g of ice at The final temperature of the mixture of the mixture is _______.

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Problem 03 The 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 10 11 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.

Problem:

Problem 04 A 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 __________.

Problem:

Problem 05 A 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 ____________________.

SECTION – II:

SECTION – II Each of which either true or False State 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.

Problem:

01 A 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. Problem

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Problem 02 Two 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.

Problem:

Problem 03 The order of magnitude of the density of nuclear matter is

SECTION – III:

SECTION – III Single Correct Answer Type In 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 .

Problem:

01 A 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 anticlockwise BL v/R anticlockwise Zero Problem

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Problem 02 Two 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 3 Circuit 3 and circuit 1 Circuit 1 only

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Problem 03 A 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

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Problem 04 Two rods of different materials having coefficients of thermal expansion a 1 , a 2 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 : 3 1 : 1 3 : 2 4 : 9

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Problem 05 Imagine 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: T 2 is proportional to R 2 T 2 is proportional to R 7/2 T 2 is proportional to R 3/2 T 2 is proportional to R 3.75

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Problem 06 A linear harmonic oscillator of force constant 2 x 10 6 N/m and amplitude 0.01 m has a total mechanical energy or 160 J. Its Maximum potential energy is 100 J Maximum kinetic energy is 100 J Maximum potential energy is 160 J Minimum potential energy is zero.

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Problem 07 The 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/

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Problem 08 Capacitor 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 = 0 The 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 C 2 loses 50% of its initial charge

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Problem 09 Velocity 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 Hz 240 Hz 320 Hz 400 Hz

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Problem 10 A 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 V 2V 4V -2V

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Problem 11 For an ideal gas: The change in internal energy in a constant pressure process from temperature T 1 to T 2 is equal to n C v (T 2 - T 2 ), 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.

Problem:

Problem 12 An 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 f 0 of the objective and the focal length f e 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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