This document contains an unsolved physics exam from 1995 containing 30 multiple choice problems. The problems cover topics in mechanics, thermodynamics, optics, electricity and magnetism, modern physics, and radioactivity. The full solutions are available online at www.vasista.net.

1. IITJEE –Past papers PHYSICS- UNSOLVED PAPER - 1995

2. SECTION – I Single Correct Answer Type Select the correct choice from the given alternative answers.

3. 01 Problem A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius (0.01) R. The period of the second satellite is larger than the first one by approximately. 0.7 % 1.0 % 1.5 % 3.0 %

4. Problem 02 Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed .The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum ,is located at a distance of 0.42 m from mass of 0.3 kg 0.70 m from mass of 0.7 kg 0.98 m from mass of 0.3 kg 0.98 m from mass of 0.7 kg

5. Problem 03 An object of specific gravity is hung from a thin steel wire. The fundamental frequency for transverse standing waves in the wire is 300 Hz.The object is immersed in water so that one half of its volume is submerged. The fundamental frequency in Hz is a. b. c. d.

6. Problem 04 Three rods of identical cross-sectional area and made from the same metal form the sides of an isosceles triangle ABC, right-angled at B. The points A and B are maintained at temperatures respectively. In the steady state, the temperature of the point .Assuming that only heat conduction takes place, is a. b. c. d.

7. Problem 05 A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential difference V. Another capacitor of capacitance 2C is similarly charged to potential difference 2V.The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is a. Zero b. c. d.

8. Problem 06 A battery of internal resistance 4Ω is connected to the network of resistances as shown .In order that the maximum power can be delivered to the network, the value of R in Ω should be 4/9 2 8/3 18

9. Problem 07 An isosceles prism of angle has a refractive index of 1.44. Two parallel monochromatic rays enter the prism parallel to each other in air as shown .The rays emerging from the opposite faces are parallel to each other are diverging make an angle 2 with each other make an angle with each other.

10. 08 Problem The focal lengths of the objective and the eye-piece of a compound microscope are 2.0cm and 3.0 cm respectively. The distance between the objective and the eye-piece is 15.0 cm. The final image formed by the eye piece is at infinity .The two lenses are thin. The distances in cm of the object and the image produced by the objective ,measured from the objective lens, are respectively 2.4 and 12.0 2.4 and 15.0 2.3 and 3.0 2.3 and 12.0

11. Problem 09 An energy of 24.6 eV is required to remove one of the electrons from a neutral helium atom. The energy (in eV) reqyured to remove both the electrons from a neutral helium atom is 38.2 48.2 51.8 79.0

12. Problem 10 The binding energy per uncleon of 16O is 7.97 MeV and that of is 7.75 MeV. The energy in MeV required to remove a neutron from is 3.52 3.64 4.23 7.68

13. Problem 11 The pair (s) of physical quantities that have the same dimensions is (are): Reynolds number and coefficient of friction Curie and frequency of a light wave Latent heat and gravitational potential Planck’s constant and torque

14. Problem 12 The temperature of an isotropic cubical solid of length L, density d and coefficient of expansion per degree kelvin, is raised by .Then at this ,at this temperature, to a good approximation length is total surface area is density is density is

15. Problem 13 A wave disturbance in a medium is desribed by ,where X and y are in metres and t in seconds. A node occurs at x=0.15m. An antinode occurs at x=0.3 m. The speed of the wave is 5.0 m/s. The wavelength is 0.2 m.

16. Problem 14 From the following statements concerning ideal gas at any given temperature T, select the correct one(s). The coefficient of volume expansion at constant pressure is the same for all ideal gases. The average translational kinetic energy per molecule of oxygen gas is 3 kT.(k being Boltzmann constant.) The mean-free path of molecules increases with decrease in the pressure. In a gaseous mixture, the average translational kinetic energy of the molecules of each component is the same.

17. Problem 15 Two point charges +q and –q are held fixed at (-d,0) and (d 0) respectively of a (X,Y) coordinate system. Then, the electric field at all points on the X-axis has the same direction at all points on the Y-axis is along . work has to be done in bringing a test charge from infinity to the origin. the dipole moment is 2qd directed along .

18. Problem 16 Two insulated rings, one of slightly smaller diameter diameter than the other , are suspended along their common diameter as shown. Initially the planes of the rings are mutually perpendicular. When a steady current is set up in each of them the two rings rotate into a common plane. the inner ring oscillates about its initial position. the outer ring stays stationary while the inner one moves into the plane of the outer ring. the inner ring stays stationary while the outer one moves into the plane of the inner ring.

19. 17 Problem A diminished image of an object is to be obtained on a screen 1.0 m from it. This can be achieved by appropriately placing a convex mirror of suitable focal length a concave mirror of suitable focal length a convex lens of focal length less than 0.25 m a concave lens of suitable focal length

20. Problem 18 Consider Fraunhofer diffraction pattern obtaind with a single slit illuminated at normal incidence. At the angular position of the first diffraction minimum the phase difference (in radinas) between the wavelets from the opposite edges of the slit is a. π/4 b. π/2 c.π d. 2 π

21. Problem 19 The probability of electrons to be found in the conduction band of an intrinsic semiconductor at a finite temperature increases exponentially with increasing band gap decreases exponentially with increasing band gap decreases with increasing temperature is independent of the temperature and the band gap

22. Problem 20 Which of the following statements concerning the depletion zone of an unbiased p-n junction is (are) true? The width of the zone is independent of the densities of the dopants (impurities). The width of the zone is dependent on the densities of the dopants. The electric field in the zone is provided by the electrons in the conduction band and the holes in the valence band. The electric field in the zone is produced by the ionized dopant atoms.

23. Problem 21 A set of n identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces at any two adjacent blocks is L. The block at one end is given a speed towards the next one at time t=0. All collisions are completely inelastic. Then. the last block starts moving at the last block starts moving at the centre of mass of the system will have a final speed the centre of mass of the system will have a final speed

24. Problem 22 A flat plate moves normally with a speed towards a horizontal jet of water of uniform area of cross-section. The jet discharges water at the rate of volume V per second at a speed of .The density of water is .Assume that water splashes along the surface of the plate at right angles to the original motion. The magnitude of the force acting on the plate due to the jet of water is a. b. c. d.

25. Problem 23 The motion of a body is given by the equation where is the speed in m/s and t in seconds. If the body was at rest at r=0. the terminal sped is 2.0 m/s the magnitude of the initial acceleration is 6.0 m/s2 the speed varies with time as the speed is 1.0 m/s when the acceleration is half the initial value

26. Problem 24 An X-rays tube is operating at 50 kV and 20 mA. The target material of the tube has a mass of 1.0 kg and specific heat capacity .One per cent of the supplied electric power is converted into X-rays and entire remaining energy goes into heating the target. Then, the average rate of rise of temperature of target would be the minimum wavelength of the X-rays emitted is about a suitable target material must have a high melting temperature a suitable target material must have low thermal conductivity.

27. Problem 25 Two metallic spheres S1 and S2 are made of the same material and have got identical surface finish. The mass of S1 is thrice that of S2 .Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of S1 to that of S2 is 1/3 1/√3 √3/1 (1/3)1/3

28. Problem 26 A sound wave of frequency travels v horizontally to the right .It is reflected from a large vertical plane surface moving to the left with a speed v .The speed of sound in the medium is c. The number of waves striking the surface per second is The wavelength of the reflected wave is The frequency of the reflected wave is The number of beats heard by a stationary listener to the left of the reflecting surface is .

29. Problem 27 In an interference arrangement similar to Young’s double-slit experiment ,the slits S1 and S2are illuminated with coherent microwave sources, each of frequency 106.Hz .The sources are synchronized to have zero phase difference. The slits are separated by a distance d=150.0 m. The intensity is measured as a function of θ,where is θ defined as shown .If Io is the maximum intensity I (θ),then is given by a. b. c. d. is constant for all values of θ

30. Problem 28 A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius and resistance R. One of the arcs AB of the ring subtends an angle at the centre. The value of the magnetic induction at the centre due to the current in the ring is Zero, only Zero for all values of θ proportional to inversely proportional to r

31. Problem 29 A proton of mass 1.67x10-27 and 10.6x10-19 charge is projected with a speed of 2X106m/s at an angle of to the X-axis. If a uniform magnetic field of 0.104 Tesla is applied along the Y-axis, the path of the proton is a circle of radius 0.1 m and time period a circle of radius 0.21 m and time period a helix of radius 0.1 m and time period a helix of radius 0.2 m and time period

32. Problem 30 A radioactive material decays by simultaneous emission of two particles with respective half-lives 1620 and 810 years. The time ,in years, after which one-fourth of the material remains is 1080 2430 3240 4860

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