NOTE: (i) Attempt FIVE questions in all including question No. 8 which is compulsory. All questions carry EQUAL marks.
(ii) Extra attempt of any question or any part of the attempted question will not be considered
(iii) Candidate must draw two straight lines (==================) at the end to separate each question attempted in Answer Books.

Q.1. (a) If α, ß, γ are the angles that vector r=xi+yj+zk makes with the positive directions of the coordinate axes, then show that cos 2 α + cos 2 ß + cos 2 γ = 1 . (6)
(b) Find ‘a’ such that the vectors 2i–j+k, i+2j–3k, and 3i+aj+5k are coplanar. (6)
(c) If Φ =3x2z–y2z3+4x3y+2x–3y–5, then find Div. grad F . (8)

Q.2. (a) State and explain Kepler’s laws of planetary motion. (12)
(b) A satellite is placed in a circular orbit with a radius equal to one half the radius of the moon’s orbit. What is its period of revolution in lunar months (the period of revolution of moon)? (8)

Q.3. State Bernoulli’s theorem and give all necessary conditions. Derive Bernoulli’s equation for moving fluids. (4,4,12)

Q.4. (a) What is simple harmonic motion (SHM)? Write the equation for SHM and solve it to find it’s time period. (2,4,8)
(b) A body oscillates with SHM according to equation: (6)
x=(6.12m)cos(8.38 rad/s)t+1.92 rad. Find its time period.

Q.5. (a) What do you understand by diffraction of light? Give all the necessary conditions. Explain diffraction through a single slit and derive an expression for the minimas in the diffraction pattern. (2,4,4,6)
(b) Monochromatic light of wavelength 44lnm falls on a narrow slit On screen 2.16m away, the distance between the second minima and the central maxima is 1.62cm. Find the width of the slit. (4)

Q.6. (a) Explain the terms isothermal and adiabatic processes and calculate the work done in each case. (7,7)
(b) Calculate the work done by an external agent in compressing 1.12 mole of oxygen from a volume of 22.4L and 1.32atm. pressure to 153 L at the same temperature. (6)

Q.7. Write notes on any TWO of the following: (10 each)
(a) Lorentz transformation
(b) Equivalence of mass and energy
(c) Production of low temperature

8. Write only the correct answer in the Answer Book. Do not reproduce the questions.

(1) A rock is thrown vertically upward with initial speed Vo. Assume a frictional force proportional to the velocity of rock V, and neglect the buoyant force exerted by air. The acceleration of the rock is?
(a) Always equal to “g”
(b) Equal to “g” only at the top of the flight
(c) Always less than “g”
(d) None of these

(2) In circular motion, the quantity mv²/r is:
(a) Momentum
(b) Acceleration
(c) Force
(d) None of these

(3) A ball is dropped from a height h. As it becomes off the floor its speed is 80 percent of what it was just before it hit the floor. The ball will rise to a height of most nearly.
(a) .80 h
(b) .75 h
(c) .64 h
(d) None of these

(4) A force is said to be conservative if:
(a) F.dA=0
(b) F.dr=0
(c) Force must be frictional
(d) None of these

(5) The kinetic energy of a particle of mass m and momentum p is given by”
(a) 2m/p
(b) p²/2m
(c) 2m/p²
(d) None of these

(6) Young’s Modulus is the ration between:
(a) Strain and stress
(b) Stress and strain
(c) Strain and longitudinal stress
(d) None of these

(7) In special theory of relativity the Time Dilation applies to:
(a) Atomic clocks only
(b) Mechanical clocks only
(c) Both clocks
(d) None of these

(8) A container has a small hole in bottom. Air can go through this hole, but water cannot. This can be best explained by the statement that:
(a) Water molecules are larger than molecules in the air
(b) Water is more viscous than air
(c) Surface tension of the water prevents it from escaping
(d) None of these

(9) Entropy of universe during any natural process:
(a) Remains constant
(b) Decreases
(c) Increases or remain constant
(d) None of these

(10) For an ideal gas PV=nRT, the SI units of Universal Gas Constant R is:
(a) Joule K-1 mole-1
(b) Newton K-1 mole-1
(c) Watt K-1 mole-1
(d) None of these

(11) If the higher temperature is double than the lower temperature of a Carnot’s engine, then its efficiency will be:
(a) 30%
(b) 60%
(c) 50%
(d) None of these

(12) The average translational kinetic energy of an atom of a gas is equal to:
(a) (1/2) kT
(b) (3/2) kT
(c) 3kT
(d) None of these

(13) Boltzmann law of distribution of energy among the gas atoms is:
(a) Linear
(b) Exponential
(c) Quadratic
(d) None of these

(14) By increasing the mass of bob of a simple pendulum by 3 times, the time period of the pendulum will:
(a) Increase 3 times
(b) Decrease 3 times
(c) Remains unchanged
(d) None of these

(15) The waves that cannot be plane polarized are:
(a) Radio waves
(b) Sound waves
(c) Infrared light waves
(d) None of these

(16) In sound frequency determines ‘Pitch’ and in light frequency determines:
(a) Speed
(b) Type of polarization
(c) Colour
(d) None of these

(17) The velocity of electromagnetic wave in free space is given by:
(a) C–2 = µo Eo
(b) C–½ = µo Eo
(c) C= µo / Eo
(d) None of these

(18) The speed of light in a certain transparent substance is two fifths of its speed in air. The index of refraction of this substance is:
(a) 1.4
(b) 2.0
(c) 2.5
(d) None of these

(19) A thin layer of oil on the surface of water appears coloured because of:
(a) Interference
(b) Polarization
(c) Diffraction
(d) None of these

(20) A man is 10 feet away from a plane mirror. His distance from his image is:
(a) 20
(b) 10
(c) 5
(d) None of these