Annamalai University 2008-3rd Year B.Sc Mathematics " 750MECHANICS " ( - VIII ) ( PART - III ) ( ) 5240 - Question Paper
(b) Find the centre of gravity of a
quadrilateral lamina.
4
6. (a) State and prove the prinicple of virtual
work.
(b) State and prove Newtons laws of motion.
7. (a) Find the resultant of two simple harmonic
motions of the same period and in the same straight line.
(b) In a S.H.M., if / be acceleration and
V be the velocity at any time and T is the periodic time , prove that
f2 T2 + 4 K2 v2
parabola.
(b) If a particle is projected from a point O on a plane of inclination (3 with a velocity u making an angle a with the horizontal then find the range on the plane.
Name of the Candidate :
5 2 4 0 B.Sc. DEGREE EXAMINATION, 2008
(MATHEMATICS)
(THIRD YEAR)
(PART - III)
(PAPER - VIII)
750. MECHANICS December ] [ Time : 3 Hours
Maximum : 100 Marks
Answer any FIVE questions.
All questions carry equal marks.
1. (a) State and prove Zamis theorem.
(b) ABC is a given triangle. Forces P, Q, R acting along the lines OA, OB, OC are in eqilibrium.
(i) P : Q : R = a2(b2 + c2-a2)
= b2(c2 + a2 - b2) = c2(a2 + b2 - c2)
if O is the ortho center of the triangle.
ABC
(ii) P : Q : R = cos- : Cos : Cos
2 2 2
if O is the incenter of the triangle.
2. (a) OA, OB, OC are the lines of action of
two forces P and Q and their reslutant R respectively. Any transversal meets the line in L,M,N respectively: prove that P Q R
OL OM = ON '
(b) Forces of 2, VT, 5 {J 2 kgs wt. respectively act at one of the angular points of a regular hexagon towards the five others in order. Find the direction and magnitude of the resultant.
3. (a) Two unlike parallel forces P and Q acting
on a rigid body at A and B respectively by interchanged in position. Show that the point of application of the resultant
AB will be displaced along AB through a distance
P + Q
AB.
P - Q
(b) State and prove Varigons theorem of moments.
4. (a) Prove the resultant of any number of
couples in the same plane on a rigid body is a single couple whose moment is equal to the algebraic sum of the moments of the several couples.
(b) Derive the equation to the line of action of the resultant for a number of forces acting on a rigid body.
5. (a) A ladder AB rests with A resting on the
ground and B against a vertical wall, the co-efficients of friction of the ground and the wall being ji and |/ respectively. The centre of gravity G of the ladder divides AB in the ratio 1: n. If the ladder is on the point of slipping at both ends, show that its inclination to the ground by
1 - n jijil
9. A mass m after falling freely through a distance a begins to raise a mass M greater than itself and connected with it by means of an inextensible string passing over a fixed pully. Show that M will have returned to its original position at the end of time
2 m M - m
10. (a) Find the law of force towards the pole
underwhich the curve
2 2 O A
r = a cos 20
can be described.
(b) Show that the moment of inertia of triangular lamina of mass m about a side
is where h is the altitude from
6
the opposite vertex.
9. A mass m after falling freely through a distance a begins to raise a mass M greater than itself and connected with it by means of an inextensible string passing over a fixed pully. Show that M will have returned to its original position at the end of time
2 m M - m
10. (a) Find the law of force towards the pole
underwhich the curve
2 2 O A
r = a cos 20
can be described.
(b) Show that the moment of inertia of triangular lamina of mass m about a side
is where h is the altitude from
6
the opposite vertex.
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