LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034                                B.Sc. DEGREE EXAMINATION – MATHEMATICS

AC 03

THIRD SEMESTER – NOV 2006

PH 3100 – PHYSICS FOR MATHEMATICS

(Also equivalent to PHY 100)

 

 

Date & Time : 28-10-2006/9.00-12.00     Dept. No.                                                       Max. : 100 Marks

 

 

PART A

Answer ALL questions:                                                                 10 x 2 = 20 marks

 

1. State Principle of Conservation of angular momentum.
2. Give an expression for angular acceleration.
3. State Newton’s law of Gravitation.
4. What is parking orbit?
5. Define Poisson’s ratio.
6. Explain the term viscosity of a fluid.
7. State the fundamental postulates of the special theory of relativity.
8. Explain the term ‘frame of reference’.
9. What are beats?  How are they produced?
10. The driver of a car moving towards a factory with velocity 30 m/s sounds the horn with a frequency of 240 Hz.   Find the apparent frequency of sound heard by the watchman of the factory.

PART B

Answer any FOUR questions:                                                      4 x 7.5 = 30 marks

 

11. Prove that the oscillation of a liquid in a U-tube is simple harmonic.
12. Using Newton’s law of gravitation calculate (a) mass and density of earth (b) mass of sun [given G = 6.67 x 10^-11 Nm² Kg^-2; Radius of  earth = 6.38 x 10⁶ m and distance of earth from centre of the Sun = 1.5 x 10¹¹
13. Obtain Stoke’s law for the motion of body in a viscous medium from dimensional considerations. Also determine the Coefficient of viscosity of a liquid from Stoke’s formula.
14. On the basis of Lorentz transformation, derive an expression for length contraction.
15. Explain Doppler Effect. Derive a general expression for  the apparent frequency of a note when both the source and the listener are in motion.

 

PART C

Answer any FOUR questions:                                                    4 x 12.5 = 50 marks

 

1. Explain simple harmonic motion and discuss its characteristics.  Derive Simple Harmonic equations by calculus.
2. What is stationary satellite? Define escape velocity.  Show that the escape velocity from the surface of the earth is equal to 11 km/s.  Distinguish between orbital velocity and escape velocity.
3. Define Young’s modulus, modulus of rigidity and Poisson’s ratio.  Show that the bulk modulus of elasticity K = Y / [3(1-2σ)].
4. Describe Michelson-Morley experiment.  Discuss the results obtained.
5. What is resonance?  Explain the resonance column find the velocity of sound in air.

 

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                LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

SC 06

THIRD SEMESTER – APRIL 2007

PH 3100 – PHYSICS FOR MATHEMATICS

 

 

 

Date & Time: 28/04/2007 / 9:00 – 12:00 Dept. No.                                            Max. : 100 Marks

 

 

 

PART A

Answer ALL questions:                                                                 10 x 2 = 20 marks

 

1. Define Simple Harmonic motion.
2. A heavy fly wheel of moment of inertia 0.3 kg m² is mounted on a horizontal axle of radius 0.01 m and negligible mass compared with the flywheel. Neglecting friction, find the angular acceleration if a force of 40 N is applied tangentially to the axle.
3. State any two Kepler’s laws.
4. Define Gravitational Potential.
5. Explain the terms stress and strain.
6. Define Surface tension of a liquid.
7. State Einstein mass-energy relation.
8. Name the transformation under which Maxwell’s equations are invariant.
9. Explain Doppler Effect.
10. A tuning fork A of frequency 384 Hz gives 6 beats per second when sounded with another tuning fork B. On loading B with a little wax, the number of beats per second becomes 4.  What is the frequency of B?

 

PART B

 

Answer any FOUR questions:                                                      4 x 7.5 = 30 marks

 

11. Derive expressions for the periods of oscillation of the mass suspended when two springs are connected (i) in series (ii) in parallel.
12. Obtain an expression for the escape velocity of a body from the surface of the earth. Calculate its value.
13. Derive an expression for the work done in stretching a wire.
14. Obtain the time dilation formula of special theory of relativity.
15. Two trains traveling in opposite directions at 100 km/hr each, cross each other while one of them is whistling. If the frequency of the note is 800 Hz find the apparent pitch as heard by an observer in the other train: (i) before the trains cross each other (ii) after the train have crossed each other.

 

 

 

 

 

 

 

 

 

PART C

 

Answer any FOUR questions:                                                    4 x 12.5 = 50 marks

 

1. An object rolls without slipping down a smooth inclined plane find its acceleration.  Compare the acceleration of a solid cylinder with that of a hollow cylinder of the same mass.
2. State Newton’s law of gravitation.  With a neat diagram describe Boy’s experiment to determine G.  (2.5 + 10)
3. Define coefficient of viscosity and derive Poiseuille’s formula for the flow of a liquid through a capillary tube.
4. State the postulates of the Special Theory of Relativity.   On the basis of Lorentz transformation, derive an expression for length contraction.
5. State the laws of vibration of strings and describe experiments to verify the law concerning (i) length (ii) tension and (iii) linear density.

 

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

           B.Sc. DEGREE EXAMINATION – MATHEMATICS

FG 49

THIRD SEMESTER – APRIL 2008

PH 3100 (PHYSICS FOR MATHEMATICS)

 

 

 

Date : 07-05-08                  Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART A                             (10 x 2 m= 20 m)

 

• Draw graphs of kinetic and potential energies of simple harmonic motion as function of displacement.
• State the theorem of parallel axes of moment of inertia.
• State the Kepler’s laws of planetary motion.
• What is gravitational red shift?
• Define Poisson’s ratio.
• List any two phenomena which bring out the surface tension of water.
• Distinguish holonomic constraints from non-holonomic constraints.
• Two photons travel in opposite direction. Find the relative velocity of one with respect to the other.
• What are beats?
• How is a stationary wave formed?

 

PART B                               (4 x 7 ½ m = 30 m)

ANSWER ANY FOUR QUESTIONS

 

• Prove that a small oscillation of a liquid in a U-tube is simple harmonic.
• (a)State and explain the principle of equivalence of general theory of relativity. (b)Explain any one experiment in support of general theory of gravitation.
• Explain the torsional oscillation method of determining rigidity modulus of the material of a wire.
• (a) Write down the Lorentz transformation equations (b) Determine the velocity of a particle whose kinetic energy is equal to its rest mass energy.
• Determine the fundamental frequency and the first overtones of (i) open pipe and (ii) closed pipe

 

PART C                          (4 x 12 ½ m = 50 m)

ANSWRER ANY FOUR QUESTIONS

 

• (a) Find the moment of inertia of a thin rod about an axis perpendicular to its length and passing through one of its ends.(b)Obtain an expression for acceleration of a body rolling down an inclined plane
• (a) Determine the time period of an earth satellite which is orbiting near the surface of earth (b) Estimate the height of a geostationary satellite (c) What is escape velocity? Find an expression for it.
• Obtain an expression for the volume rate of flow of a liquid through a capillary tube by Poiseuilles method.
• Solve the problems of (i) Atwood’s machine and (ii) simple pendulum by Lagrangian dynamics
• What is Doppler effect? Find expression for the apparent frequency in the case of (i) source moving towards stationary observer and (ii) observer moving towards stationary source.

 

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

FIRST SEMESTER – NOVEMBER 2012

PH 1101 – PHYSICS FOR MATHEMATICS – I

 

 

Date : 03/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

 

PART – A

Answer ALL questions:                                                                                                        (10×2=20)

1. Draw distance – time and velocity – time graph for a particle moving with constant velocity.
2. What are generalized co-ordinates in Lagrangian formulation?
3. State Newton’s law of gravitation.
4. Calculate the mass of the earth from the following data. Radius of the earth = 6371 km
   G=6.66 x 10^-11 Nm²/kg²
5. State Hooke’s law of elasticity.
6. Define surface tension. Give its unit.
7. Draw a circuit diagram for the given function : F(A,B,C) = AB +
8. State two postulates of special theory of relativity.
9. What is meant by CMRR in op-amp?
10. The mean life of π meson is 2 x 10^-8 Calculate the mean life of a meson moving with the velocity of 0.8c.

PART – B

Answer any FOUR questions:                                                                                            (4×7.5=30)

11. Define centripetal force. Derive an expression for it.
12. Define escape velocity. Show that the escape velocity from the surface of the earth is 11km/s.
13. Derive Poiseuille’s formula for determining the coefficient of viscosity of a liquid.
14. With a neat circuit diagram and truth table, explain the working of a full adder.
15. Derive the Lorentz space-time transformation formulae.

 

PART – C

Answer any FOUR questions:                                                                                           (4×12.5=50)

16. Obtain the relation between the three moduli of elasticity.
17. Setup and solve Lagrange’s equation for i) Simple Pendulum ii) Atwood’s machine
18. a) State the postulates of general theory of relativity. (4)
    b) Show that the effect of gravitation is to introduce a curvature in space-time manifold. (8.5)   
19. a) With a neat circuit diagram, explain the working of an op-amp inverting amplifier. (8.5)
    b) Simplify using K-map : Y = F (A,B,C) = ∑ ( 1,2,3,5,7) (4)
20. Describe the Michelson –Morley experiment and explain the physical significance of negative results.

 

 

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