LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

FG 06

SECOND SEMESTER – APRIL 2008

PH 2501 – MECHANICS

 

 

 

Date : 23/04/2008                Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

SECTION – A

Answer all the questions.                                                                    10×2 = 20 Marks

 

1. State the law of conservation of angular momentum.
2. Find the center of mass of three particles of 1kg, 2kg, and 3kg placed at the three corners of an

equilateral triangle of 1metre side.

3. What are the conditions of equilibrium of a rigid body acted on by three coplanar forces?
4. Define: (i) Metacentre and (ii) Metacentric height.
5. What is meant by effusion of gases?
6. State Torricelle’s theorem.
7. What are generalized coordinates? What is the advantage of using them?
8. State the principle of virtual work.
9. What is a frame of reference? Distinguish between inertial and non-inertial frames.

10.Explain the law of addition of relativistic velocities.

SECTION B

Answer any four questions.                                                   4×7.5 = 30 Marks

 

11. What is a torsional pendulum? Derive an expression for the time period of oscillation of a

torsional pendulum.

12 (a)  Define center of gravity.

(b)  Determine the position of centre of gravity of a solid tetrahedron.

13. (a) State and explain Graham’s law of diffusion of gases.

(b) Obtain the equation of continuity for an incompressible fluid in streamline flow.

14. Apply Lagrange’s equation to determine

(a) motion of a single particle in space and

(b) time period of oscillation of a simple pendulum.

15. (a) Explain time – dilation with an example.

(b)  A π meson has a mean lifetime of 2×10^-8s when measured at rest.  How far does it go before

decaying into another particle if its speed is 0.99c?

 

SECTION C

Answer any four questions.                                                               4×12.5 = 50 Marks

 

16. What is a compound pendulum? Derive an expression for its time period of oscillation. Explain how the value of g is determined using it.
17. (a) Define centre of pressure. Determine the position of center of pressure of a rectangular lamina immersed vertically in a liquid with one edge in the surface of the liquid.

(b) Find the thrust on the rectangular end of a tank of width 0.8m and depth 0.5m filled

completely with water. Find the position where it acts.

18. State and prove Bernoulli’s theorem. Discuss any two applications of this theorem.
19. (a) State an explain D’Alembert’s principle.

(b) Derive Lagrange’s equations of motion from D’Alembert’s principle for a holonomic

conservative system.

20. (a) State the basic postulates of Einstein’s special theory of relativity.  Derive the Lorentz space –time transformation formulae.

(b)        A rod 5 metre long is moving along its length with a velocity 0.8c.  Calculate its length as it appears to an observer on the earth.

 

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      LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

XC 05

B.Sc. DEGREE EXAMINATION – PHYSICS

SECOND SEMESTER – April 2009

PH 2501 – MECHANICS

 

 

 

Date & Time: 23/04/2009 / 1:00 – 4:00      Dept. No.                                                       Max. : 100 Marks

 

 

PART A

Answer all questions.  All questions carry equal marks.                           (10 x 2 = 20 marks)

1. Define linear momentum. Give its unit.
2. Show points of suspension and oscillation are interchangeable.
3. Define center of gravity.
4. What are concurrent forces?
5. State Torricelli theorem.
6. A venturimeter has pipe diameter of 0.2m and a throat diameter 0.15m. The levels of water

column in the two limbs differs by 0.1m.  Calculate the amount of water discharged through

the pipe in one hour.  (Density of water 1000 kgm^-3).

7. Define the concept of Degrees of freedom.
8. State D’Alembert’s principle.
9. State the postulates of special theory of relativity.
10. How fast would a rocket have to go relative to an observer for its length to be contracted to

99% of its length at rest.

 

PART B

Answer any FOUR questions.                                                                     (4 x 7.5 = 30 marks)

11. Derive an expression for the period of oscillation of torsion pendulum.
12. Determine the location of the center of gravity of a solid cone.
13. Describe and explain working of pitot tube.
14. Explain the term “virtual displacement” and state the principle of virtual work.
15. Derive an expression for addition of velocities using Lorentz transformation.

 

PART C

Answer any FOUR questions.                                                                     (4 x 12.5 = 50 marks)

16. Explain how g can be determined using Compound pendulum.
17. State the laws of flotation. Discuss the experimental determination of the metacentric height

of a ship?

18. State and explain Bernoulli’s theorem. Discuss in detail two applications of this theorem.
19. State Lagrange’s equations of motion in generalized coordinates. Apply them to the

Atwood’s machine to find the acceleration of the system.

20. Derive the Lorentz transformation equations.

 

 

 

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      LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

XC 48

SECOND SEMESTER – April 2009

PH 2503 – MECHANICS

 

 

 

Date & Time: 23/04/2009 / 1:00 – 4:00  Dept. No.                                                   Max. : 100 Marks

 

 

 

PART – A

       Answer ALL questions:                                                                                (10×2=20 Marks)

 

1. Define centre of oscillation and centre of suspension.
2. What is a compound pendulum?
3. Explain concurrent forces.
4. Define centre of gravity.
5. Water flowing with a velocity of 2m/s in a 4cm diameter pipe enters a narrow pipe having a diameter of 2cm. Calculate the velocity in the narrow pipe.
6. State Torricelli’s theorem.
7. What are generalized coordinates?
8. Explain constraints with an example.
9. State Newton’s universal law of gravitation.
10. Calculate the escape velocity of a body from the moon’s surface, if the radius of the moon is 1.7×10⁶m and acceleration due to  gravity on the moon’s surface is 1.63m/s².

 

PART B

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

 

11. State and prove the law of conservation of angular momentum. (2+5.5)
12. Find out the location of the centre of gravity of a solid tetrahedron.
13. Explain the working of venturimeter.
14. Apply Lagrange’s equations of motion to the Atwood machine to find out the

acceleration of the system.

15. a)State Kepler’s laws of motion. (3)

b)Derive law of gravitation from Kepler’s law.                                                             (4.5)

 

PART C

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

 

16. a) Derive an expression for the period of oscillation of a compound pendulum. (7.5) b)Find out the condition for the minimum time period. (5)
17. Find the position of the centre of pressure of a triangular lamina immersed in a

liquid with its (i) vertex and (ii) base, touching the surface of the liquid.                (6+6.5)

18. a)State and prove Bernoulli’s theorem. (6)

b)Obtain the relation between time of diffusion and length of column.                        (6.5)

19. a)Explain the term ‘virtual displacement’ and state the principle of ‘virtual work’. (6.5)

b)State and explain D’Alembert’s principle.                                                                  (6)

20. Define and obtain expressions for (i)orbital velocity and (ii) escape velocity of a

satellite.                                                                                                                     (6+6.5)

 

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

SECOND SEMESTER – APRIL 2011

PH 2503 – MECHANICS

 

 

 

Date : 08-04-2011              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

PART – A

Answer ALL the questions.                                                                                   (10 × 2 = 20 Marks)

1. When will a compound pendulum have minimum period of oscillation?
2. Define centre of mass.
3. Define couple and moment of couple.
4. Find the position of centre of pressure of a rectangular lamina of width 1mm and height 0.6m

immersed vertically in a liquid with one edge in the surface of liquid.

5. What do you mean by equation of continuity?
6. State Graham’s Law of diffusion of gases.
7. What are generalized coordinates? What is the advantage of using them?
8. State the principle of virtual work.
9. Define Gravitation constant and mention its unit.
10. Define Gravitational potential.

PART – B

Answer any FOUR questions.                                                                         (4 × 7.5 = 30 Marks)

11. (a) Derive an expression for the period of oscillations of a torsional pendulum.               (5)

(b) Show that the speed of a rocket is twice its exhaust speed when the ratio of initial mass to the

instantaneous mass (M₀/M) is e².                                                                                        (2.5)

12. (a) Define metacentric height. (2)

(b) Explain how the metacentric height of a ship is determined experimentally.                   (5.5)

13. (a) Explain the working of a venturimeter. (5.5)

(b) A venturimeter has a pipe diameter of 0.2m and a throat diameter 0.15m.  The       levels of water column in the two limbs differ by 0.10m.  Calculate the amount of water discharged through the pipe in 30 minutes. Density of water is 1000kg m^-3.                                              (2)

14. (a) What are constraints? Give any two examples.                            (2+1)

(b) What is meant by configuration space?   How is this concept used to describe the motion of a system of particles.                                                                                                    (3+1.5)

 

 

 

15. (a) State and explain Newton’s law of gravitation. (4)

(b) How would you find the mass and density of earth using Newton’s law of gravitation?     (3.5)

 

PART – C

Answer any FOUR questions.                                                                        (4× 12.5 = 50 Marks)

 

16. Describe a Bifilar pendulum with non-parallel threads and discuss the theory to derive an

expression for its period of oscillations.

17. (a) Define centre of pressure.      (2.5)

(b) Determine the position of centre of pressure for a triangular lamina of height h

immersed vertically with (a) its apex and (b) its base in the surface of the liquid.       (5+5)

18. State and prove Bernoulli’s theorem. (2+10.5)
19. Derive Lagrange’s equations of motion from D’Alembert’s principle for a holonomic

conservative system.

20. (a) Derive an expression for the escape velocity of an artificial satellite and prove that it is

equal to √2 times its orbital velocity.                                                                                   (6+3)

(b)      Write a note on weightlessness.                                                                                  (3.5)

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

SECOND SEMESTER – NOVEMBER 2012

PH 2503 – MECHANICS

 

 

 

Date : 07/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

PART –A

Answer ALL  questons:                                                                                             (10×2=20Marks )

 

1. State the law of conservation of angular momentum . Give an example .
2. What is a rigid body?
3. Distinguish between couple and Torque with an example.
4. A ship of mass 2×10⁴ kg is displaced .A load of 30×10⁶ kg moved across 50 metres  across  the

deck makes the ship tilt through /100 radians.  Calculate the metacentric height.

5. What is the molecular weight of a gas which diffuses 1/50 as fast as hydrogen?
6. State Toricelli’s theorem.
7. Draw a neat diagram of a venturimeter.
8. State D’Alembert’s principle.
9. State and explain Kepler’s 2^nd law of planetary motion.
10. Explain weightlessness in a moving lift.

PART-B

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

 

11. Explain how the oscillations of a compound pendulum can be used to determine  the acceleration

due to gravity  in the laboratory .

12. a) What is meant by centre of pressure ?       (3marks)
13. b) Calculate the centre of pressure of a rectangular  lamina of sides a and b.                      (4.5marks)
14. State and prove Bernoulli’s theorem. (2+5.5 marks)
15. Discuss the motion of a simple pendulum from Langrange’s equations.
16. Distinguish between orbital and escape velocity.           (4marks)

Calculate the escape velocity of a body on the earth from the  given the following data:       (3.5 marks)

(Acceleration due to gravity g = 9.8 ms^-2 ;  radius of earth R_E = 6400 km)

 

PART-C

Answer any  FOUR questions:                                                                               (4X12.5 =50MARKS)

 

16. (a) Show that the time period of a torsion pendulum is given by 2 I/C.                        (8marks)

 

 

 

(b) A thin  uniform rod of length 1.2meter and breadth 0.12m is made to swing in a vertical plane

about an axis thro’ a point A at a distance  x from the centre of gravity. Find the value of  x  if the

period of oscillation is a minimum.                                                                                      (4.5marks)

 

17. a) Draw a diagram of a floating body to show meta centre and metacentric height.  (3 marks)
18. b) Discuss the stability of floating bodies with respect to the above terms.                            (3marks)
19. c) Explain how the metacentric height of a ship be determined .         (6.5marks)

 

18. a) State and explain the equation of continuity.         (5marks)
19. b)  Derive an expression for the terms potential head and kinetic head.                                  (4marks)
20. c) Water flowing with a velocity of 3m/s in a 4cm diameter pipe enters a narrow pipe having a

diameter  of only  2 cm. Calculate the velocity in the narrow pipe.                                     (3.5marks)

 

19. a) Define with an example the terms.       (6 marks)
20. i) degee of freedom
21. ii) constraints

iii) holonomic and non holonomic  systems

 

b)Derive Newton’s equation for force from  the Lagrangian.                                        (6.5 marks)

 

20. a) Explain gravitational potential. Hence derive an expression for gravitational potential at a

point, distant r from a body of mass  m.                                                                       (3+5 marks)

 

1. b) Assuming the earth to be a homogenous sphere and using the laws of gravity estimate the

density of the earth. G=6.6X10^-11  N( m/Kg )²  and radius of the earth is 6400 km.        (4.5marks)

 

 

 

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