LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

FIFTH SEMESTER – APRIL 2011

MT 5506/MT 4501 – MECHANICS – I

 

 

 

Date : 18-04-2011              Dept. No.                                                    Max. : 100 Marks

Time : 9:00 – 12:00

 

PART – A

Answer ALL Questions                                                                                           (10 x 2 = 20 marks)

 

1. Define parallelogram of forces.
2. What are coplanar forces?
3. State the theorem on polygon of forces.
4. Define moment of a force.
5. State newton’s laws of motion.
6. Define angle of friction.
7. Define relative angular velocity.
8. State the principle of conservation of linear momentum.
9. Write down the “horizontal range” for projectile (with usual notations).
10. Define Newton’s experimental laws on impact.

PART – B

 

Answer any FIVE Questions                                                                                                 (5 x 8 = 40 marks)

 

1. State and prove Lami’s Theorem.
2. A weight W hangs by a string and is drawn aside by a horizontal force until the string makes an angle 60^o with the vertical.  Find the horizontal force and tension in the string.
3. Find the resultant of two like parallel forces.
4. A uniform rod AB of length 2a and weight W is resting on two pegs C and D in the same level at a distance d apart.  The greatest weights that can be placed at A and B without tilting the rod are W₁ and W₂ respectively.  Show that .
5. A lift a ascends with constant acceleration f, then with constant velocity and finally stops under constant retardation f.  If the total height ascended is h and total time occupied is t, show that time during which the lift is ascending with constant velocity is .
6. Show that when masses P and Q are connected by a string over the edge of a table, the tension is the same whether P hangs and Q is on the table or Q hangs and P is on the table.
7. A particle projected upwards under the action of gravity in a resisting medium where the resistance varies as the square of the velocity.  Discuss the motion.
8. Two perfectly elastic smooth spheres of masses m and 3 m are moving with equal moments in the same st.line and in the same direction.  Show that the smaller sphere reduced to rest after it strikes the other.

PART – C

 

Answer any TWO questions                                                                                      (2 x 20 = 40 marks)

 

1. a) Three equal strings of no sensible weights are knotted together to form an equilateral triangle

ABC and a weight W is suspended from A.  If the triangle and the weight be supported with

BC horizontal by means of two strings at B and C each at an angle 135^o with BC.  Show that

the tension in BC is .                                                                                           (10)

1. b) Two like parallel forces P and Q (P > Q) act at A and B respectively. If the magnitudes of the

forces are interchanged,  show that the point of application of the resultant on AB will be

displaced through the distance  . AB.                                                                    (10)

20. a) A system of forces in the plane of ABC is equivalent to a single force at A; acting along the

internal bisector of the angle BAC and a couple of moment G.  If the moments of the system

about B and C are respectively G₂ and G₃ prove that (b+c) G₁ = b G₂ + c G₂.

 

1. b) A ladder which stands on a horizontal ground leaning against a vertical wall is so loaded that

its centre of gravity is at the distance a and b from the lower and the upper ends respectively.

Show that if the ladder is in limiting equilibrium, its inclination  to the horizontal is given by

where m and m¹ are the coefficients of friction between the ladder and the

ground and the wall respectively.

 

21. a) A body, sliding down a smooth inclined plane is observed to cover equal distances, each equal

to a, in consecutive intervals of time t₁, t₂.  Show that the inclination of plane to the horizon is

.                                                                                                             (8)

1. b) Discuss the motion of two particles connected by a string.                                                 (12)
2. a) Two smooth spheres of masses m₁ and m₂, moving with velocities u₁ and u₂ respectively in the

direction of line of centres impinge directly.  Discuss the motion.                                       (10)

 

1. b) Show that the path of projectile in a parabola.                                                                     (10)

 

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