LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – MATHEMATICS
FIFTH SEMESTER – APRIL 2008
MT 5500 - MECHANICS - II
Date : 28-04-08
Time : 1:00 - 4:00
Dept. No.
XZ 18
Max. : 100 Marks
PART – A
Answer ALL questions.:
(10 x 2 = 20)
1. Define centre of mass.
2. Define centre of gravity of a compound body.
3. State the principle of virtual work.
4. Define suspension bridge.
5. Define amplitude.
6. Define periodic time of S.H.M.
7. Write down the differential equation of the central orbit in p-r coordinates.
8. State the theorem of parallel axis.
9. Define equimomental system.
10. State D’Alemberts principle.
PART – B
Answer any FIVE questions.
(5 x 8 = 40)
11. A piece of uniform wire is bent in the shape of an isosceles triangle sides are ‘a’ ‘a’ and ‘b’. Show
a (2a  b)
that the distance of C.G from the base of the triangle is
.
2 (2a  b)
12. A regular hexagon is composed of six equal heavy rods freely jointed together and two opposite
angles are connected by string which is horizontal, one rod being in contact with a horizontal
plane; at the middle point of the opposite rod a weight W’ is placed. If W be the weight of each
3W  W 1
rod, show that tension in the string is
.
3
13. A particle moves in S.H.M in a straight line in the first second, after starting from rest, it travels a
distance a and in the next second, it travels a distance b in the same direction. Prove that the
2a 2
amplitude of motion is
.
3a  b
14. The velocity of a particle along and perpendicular to radius vector from a fixed origin are
2
3
1
and  r 2  2 2 .
r 2 
 c and components of acceleration are 2 2 r 2   2
r
r

15. An elliptic lamina of semi axes a and b swings about a horizontal axis through one of the foci in a
vertical plane. Find the length of the S.E.P.
16. Find the resultant of two simple harmonic motions of the same period in the same straight line.
17. Find the centre of gravity of a uniform solid right circular cone.
18. Find the components of the velocity and acceleration along radial and transverse directions.
1
PART – C
Answer any TWO questions.
(2 x 20 = 40)
19. a) Find the centre of gravity of the area enclosed by the parabolas y 2  ax and
x 2  by (a  0, b  0) .
b) A uniform chain, of length , is to be suspended from two points A and B, in the same
horizontal line so that either terminal tension is n times that at the lowest point. Show that the span
1
log n  n 2  1 .
AB must be
.......(10+10)
2
n 1
20. a) Define catenary and derive the equation of the catenary.
b) Four equal rods, each of length a, are jointed to form a rhombus ABCD and the points B and D
are joined by a string of length . The system is placed in a vertical plane with A resting on a
2w
horizontal pane and AC vertical. Prove that the tension in the string is
where W is the
4a 2  2
weight of each rod.
......(10+10)
d 2u
F
u  2 2 .
21. a) Obtain the differential equation of a central orbit in the form
2
d
hu
2
b) Show that the M.I about the x-axis of the parabola y  4ax bounded by the latus rectum
12
Ma 2 where M is the mass of
supposing the density at each point to vary as cube of the abcissa
11
the lamina.
......(10+10)





2