LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – MATHEMATICS
SIXTH SEMESTER – April 2009
MT 6604 – MECHANICS – II
Date & Time: 21/04/2009 / 9:00 – 12:00 Dept. No. Max. : 100 Marks
PART – A
Answer ALL the questions: (10 x 2 = 20)
- Define centre of mass.
- Write down the formula for the C.G of a rigid body.
- State the principle of virtual work.
- Define suspension bridges.
- Define Simple Harmonic motion.
- Define second pendulum.
- Write down the components of the acceleration of a particle in polar coordinates.
- Define central orbit.
- State the theorem of perpendicular axes.
- State D’Alembert’s principle.
PART – B
Answer any FIVE questions: (5 x 8 = 40)
- A piece of uniform wire is bent in the shape of an isosceles triangle whose sides are a, a and b. Show that the distance of the C.G from the base of the triangle is .
- Find the C.G of a uniform solid right circular cone.
- A regular hexagon is composed of six equal heavy rods freely jointed together and two opposite angles are connected by a 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 rod, show that tension in the string is .
- Find the equation of the catenary in the Cartesian farm.
- A particle moves in SHM 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 amplitude of the motion is .
- Determine the maximum speed with which a car can turn round a level curve of radius 100 meters without slipping given that the coefficient of friction between the tyres and the track is 0.3.
- Derive the Pedal equation or p-r equation of a central orbit.
- Find the M.I of a hollow sphere.
PART – C
Answer any TWO questions: (2 x 20 = 40)
- (a) Find the C.G of the area enclosed by the parabolas .
(b) ABCDEF is a regular hexagon formed of light rods smoothly jointed at their ends with a
diagonal rod AD. Four equal forces ‘P’ act inwards at the middle points of the rods AB, CD, DE, FA and at right angles to the respective sides. Find the stress in the diagonal AD and state whether it is a tension or a thrust. (10+10)
- (a) A string of length 2l hangs over two small smooth pegs in the same horizontal level. Show
that if h is the sag in the middle, the length of either part of the string that hangs vertically is
(b) Find the resultant of two simple harmonic motions of the same period in the same straight
- (a) State and prove the theorem of parallel axis.
(b) Find the M.I of the square lamina about a diagonal of length l. (10+10)
- (a) A particle acted on by a central attractive force is projected with a velocity at an
angle of with its initial distance ‘a’ from the centre of force. Show that the path is the equiangular spiral .
(b) A square lamina of side 2a rotates in a vertical plane about a horizontal axis passing through
one of the vertices and perpendicular to its plane and a weight equal to that of lamina is placed at the opposite vertex. Find the length of S.E.P. (10+10)
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