117/1 I
2010
PHYSICS
Paper 1
Time: 3 Hours] Maximum Marks,' 300

INSTRUCTIONS
Each question is printed both in English and in Kannada.
Answers must be written in the medium specified (English or Kannada) in the Admission Ticket issued to you, which must be stated clearly on the cover of the answer book in the space provided for this purpose. In case ofany doubt in the Kannada text, please refer to English text.
This paper has four parts
A 20 marks
B 100 marks
C 90 marks
D 90 marks

Marks allotted to each question are indicated in each part.
All questions in Part Part B and Part C are compulsory. Answer any three questions in Part D.

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PART A 4x.5=20
Answer each question in about 50 words. Each question carries 5 marks.
1. A cord 3 m long is coiled around the axle of a wheel. The cord is pulled with a constant force of 40 N. When the cord leaves the axle, the wheel is rotating at 2 revolutions per second. Determine the moment of inertia of the wheel and the axle. Neglect friction.
An earth satellite of mass M circles the earth with speed v. By how much does its momentum change

as it goes half way around the earth


as it goes 3 th of the way around the earth 4


as it goes one full round about the earth
Ignore earth's rotation.
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What are adiabatic and isothermal changes? Give an example for each. Write the equations of state for each of the processes.
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PAJtT B 10x10=100 Answer each question in about 100 words. Each question carries lO'marks.
2. Obtain an expression for differential cross-section in Rutherford scattering of alpha-particles fired at target nucleus.

3. Show that for a conservative force field we can define a scalar

function VCr) such that FCr) DCr). Also show that curl Fcr) 0
for a conservative force field.
4. A solid sphere of mass m and radius r rolls down an inclined plane. Show
that its kinetic energy is rotational kinetic energy and translational
77
kinetic energy.

5.
What is a streamline State Bernoulli's theorem. Write the expression for velocity of efflux of a liquid from an orifIce of height h below the free surface of the liquid. Why is a rifle bullet cylindrical

6.
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7.
State Dulong and Petit's law. Give the Einstein's theory of specific heat of solids.

8.
Describe an experimental set-up to produce low temperature by adiabatic demagnetization.







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10.
Distinguish between progressive and stationary waves.

11.
Why does one get three dimensional image in holography? Explain the principle of construction of a hologram.


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PARTe 6x15=.90 Answer each question in about 150 words. Each question carries 15 marks.
12. Describe the general features of motion in a central force field.
State the Kepler's laws of planetary motion.
13. State the postulates of special theory of relativity.
Arrive at the velocity addition theorem. Show that the velocity of light remains the same for all observers.
14. Using Maxwell's thermodynamic relations, derive an expression for the difference in specific heats of a Van-der Waal's gas.
The entropy of an ideal gas increases by 420 J when it undergoes an isothermal expansion at 500 K. Calculate the amount of heat absorbed.
15. Define Helmholtz free energy and Gibbs free energy. Why are these functions called thermodynamic potentials
Arrive at the physical importance of these free energies.
16. Distinguish between. interference and diffraction.
Cb) Distinguish between Fresnel and Fraunhofer diffraction patterns.
17. What is stimulated emIssIOn? Describe population inversion optical pumping. Mention any three applications of Lasers. and
. Describe the construction and action of Ruby Laser.

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PAJiT D 3x30=90 Answer any three of the following questions, each m about 300 words. Each question carries 30 marks.
18. A simple harmonic oscillator is subjected to a damping force proportional to the velocity of the particle in addition to the restoring force necessary to produce oscillations. Obtain an expression for the displacement of a particle executing such a motion.

Discuss the motion of the particle when the oscillator IS overdamped, underdamped and critically damped.


What is logarithmic decrement Write the expression for logarithmic decrement.


19. Explain the principle underlying the construction of a rocket. Obtain an expression for velocity of a rocket when its weight is ignored.

What is a multistage rocket? Mention its advantage.


A rocket set for vertical launching has a mass of 50 kg and contains 450 kg of fuel. It can have a maximum exhaust speed of 1 km 8-1 Ifg 10 what should be the minimum rate of fuel consumption to just lift off the launching pad Also, find the maximum speed attainable.


20. Derive the Maxwell's thermodynamic relations. Give their physical interpretation.

Using the above relations, derive the Clausius -Clapeyron equation.


Find the temperature at which the rrns velocity of the molecules of a gas would become twice its value at 100oe.


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21. How are the three types of plane polarized light produced and detected?

What is resolving power Describe the Rayleigh's criterion for resolution of two point objects.


A narrow slit illuminated with monochromatic light of wavelength 589·3 nm is placed at a distance of 0·1 m from a straight edge. If the distance between the straight edge and the screen is 1-9 In, calculate the distance between the first and fourth dark bands.


22. Distinguish between elastic and inelastic collisions.
Show that in the case of an elastic and glancing collision between two particles of masses fil and ffi2 respectively, the maximum value of the scattering angle 81 in the laboratory frame corresponds to the scattering angle e in the centre of mass frame where
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117/2 I
2010
PHYSICS
Paper 2
Time: 3 Hours J Maximum Marks: 300

INSTRUCTIONS
Each question is printed both in English and in Kanncida.
Answers must be written in the medium specified (English or Kannada) in the Admission Ticket issued to you, which must be stated on the cover of the answer book in the space provided for this purpose. In case ofany doubt in the Kannada text, please refer to English text.
This paper has four parts:
A 20 marks
B 100 marks
C 90 marks
D 90 marks

Marks allotted to each question are indicated in each part.
All questions in Part Part B and Part C are compulsory. Answer any three questions in Part D.

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PART A
Answe-r each question in about 50 words. Each question carries 5 marks.
1. Two small balls each having equal positive charge q coulomb are suspended by two insulating strings of equal length I metre from the same point fixed to a stand, The whole set-up is taken in a satellite into space where there is no gravity. What is the angle between the two strings and the tension in each string
Obtain the equation of continuity from Maxwell's equation


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Calculate the de Broglie wavelength of an electron moving with a kinetic energy of 1 MeV.


Write a logic circuit to realize AND and OR gates usmg only NAND gates.



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PARTB 10,10=100 Answer each question in about 100 words. Each question carries 10 marks.
2.
Obtain an expression for impedance of a series LCR ae circuit where a sinusoidal emf is applied.

3.
Derive Poisson's equation and Laplace's equation in an electric field.

4.
Explain the concept of displacement current. Show that charging current is -equal to the displacement current in a capacitor.

5.
Assuming the energy of electron in the nth orbit of atom, obtain an expression for wave number of a spectral line emitted in H-atom on the basis of Bohr's theory of atomic model.

6.
Describe an experimental arrangement of the Stern -Gerlach experiment.

7.
What is Raman effect? Describe the quantum theory of Raman effect.

8.
What is superconductivity? Explain Meissner effect. Write an expression for critical magnetic field in terms of temperature of the material and their critical temperature. Mention three properties of superconductors and three applications of superconductors.

9.
Distinguish between p-type and n-type semiconductors.

10.
Describe the forward and reverse bias characteristics of a PN junction diode.

11.
Write the block diagram of a TV transmitter and receiver.


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PARTe 6x15=90 Answer each question in about 150 words. Each question carries 15 marks.
12. Define rms value, peak value and mean value of ac. Write an expression for mean value of ac voltage in terms of rms value.
Distinguish between series and parallel resonance.
13. What is self inductance? Write the expressions for self inductance of a solenoid and energy stored in the inductor.
State Gauss's law in electrostatics. Obtain an expression for Gauss' law in differential form.
14. State Biot -Savart's law.
Obtain an expression for magnetic field induction at a point due to current in a long straight conductor.
15. State the law of radioactive decay. Obtain the exponential decay equation.
It is proposed to use the nuclear fusion reaction H2 H2 in a nuclear reactor of 200 MW rating. If the energy from the above reaction is used with a 25% efficiency in the reactor, how many grams of deuterium fuel will be needed per day
Given: Mass ofH2 2·0141 amu and Mass ofHe4 4·0026 amu.
16. What is a thermistor Write an expression showing the variation of resistance of a thermistor with temperature. Also, write an expression for temperature coefficient of resistance,. Mention any three applications of thermistors.
Distinguish between strong and weak nuclear interactions.
17. Describe, with necessary circuit and waveforms, the working of a full wave rectifier.
Distinguish between half-wave and full·wave rectifier.
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PlURT D
Answer any three of the following questions. each in about 300 words. Each question carries 30 marks.
18. State and explain Kirchoffs laws.

Obtain the condition for balance in a Wheatstone's network.


Three 4 V batteries with internal resistances 0-2 .Q and 0·3 Q are connected in parallel and in series with a 2'045 Q resistor. Find


equivalent resistance for the current


equivalent voltage




current in the circuit

terminal voltage for equivalent cells


terminal voltage of each cell.


19. Explain para-, ferro-, antiferro-and ferri-magnetism on the basis of

their dipole moments,


behaviour in the presence of applied magnetic field, and


the cause of their magnetism.

Give an example for each class of the magnetic materiaL


Explain the concept of domains in ferromagnetic materials.


20. What are eigen values and eigen functions?

Obtain eigen functions and eigen values for a particle ill one dimensional box.


Find the probability that a particle in a one dimensional box of length L can be found between 0·4 L to 0·6 L for the ground stale.






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transitions arising from 2Pa 281 and 2Pl 281 in the

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presence of a weak magnetic field.

(The Lande g factor for 2Pt and 28, are and 2 22 2 respectively. Show the energy of each level in Lorentz units.)

Find the energy difference in Lorentz units between each Zeeman components.


The average life time of an electron in an excited state is about 10 ns. How many revolutions does the electron make before falling to n 1 state? Assume radius of first Bohr 0·53 A.


22. Describe with a circuit diagram the action of a Common-Emitter NPN transistor amplifier.
Cb) Obtain expressions for current gain and voltage gain of an amplifier.
The h-parameters of a transistor are hie 3·5 kQ, hfe 120, hie 1·3 x and hoe 8·5 If the load resistance is 1·06 kQ, calculate voltage gain, input impedance and current gain.
Use the following constants wherever required
Planck's constant, h 6·625 x 10-34 Js Mass of electron, m 9-1 x 10-31 kg 1 amu 931 MeV
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