PAH Dynamics B.Sc Question Paper : ideunom.ac.in

University : University of Madras
Degree : B.Sc
Department :Mathematics
Subject :PAH Dynamics
Document type : Question Paper
Website : ideunom.ac.in

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PAH Dynamics Model Question Paper :

OCTOBER 2011 U/ID 4708/PAH
Time : Three hours
Maximum : 100 marks
SECTION A — (10 ´ 2 = 20 marks)
Answer ALL questions.

Related : University of Madras PAP Historiography & Historical M.A Question Paper : www.pdfquestion.in/6851.html

Each question carries 2 marks.
1. What is the resultant of two velocities u, v along the same line and in the same direction?
2. The line OP turns through two right angles in one second, what is the angular velocity of P?
3. What is the Simple Harmonic period of x = a coswt + bsinwt ?
4. What is the acceleration of Transverse component?
5. What is Impulsive force?
6. What is the horizontal range of a projectile?
7. What is the velocity of central orbit?
8. What is the value of du\dq at an apse point?
9. Define Moment of inertia.
10. What is meant by angular momentum of a rigid body?

SECTION B — (5 ´ 16 = 80 marks)
Answer ALL questions.
Each question carries 16 marks.
11. (a) Find the angular velocity of a particle moving along a circle with uniform speed.
(b) A ship is sailing due west and the apparent direction of the wind is from the north. If the
wind is known to be blowing from a point 30° east of north, show that its velocity is double that of the ship.
Or
(c) The speed of a train increases at a constant rate ‘a ’ from O to V, and then remains constant for an interval and finally decreases to O at a constant rate b . If l be the total distance described, prove that the total time occupied is 1/v=1/u

12. (a) Derive Simple Harmonic Equation.
(b) Two bodies of masses M and M¢ are attached to the lower end of an elastic string whose upper end is fixed and hang at rest; where a is the unstrected length of the string, and b and c are the distances by which it would be stretched when supporting M and M¢ respectively.

13. (a) A shot of mass m penetrates a thickness t of a fixed plate of mass M. If M were free to move and the resistance supposed to be uniform show that the thickness penetrated  is mt/M=m
(b) Derive the direct impact of two smooth spheres.
Or
(c) Show that the path of a projectile is a parabola.
(d) Show that, for a given velocity of projection the maximum range down an inclined plane
of inclination a bears to the maximum ranger up the inclined plane the ratio 1 + sina : 1 – sina .

14. (a) A particle C of mass m is attached by strings CA, CB to two fixed points A, B in the same vertical line, A being above B; and the whole rotates about AB with angular velocity ‘w’
show that in order that the strings may be stretched w=g/b cos a
(b) Derive Pedal equation of the central orbit.
Or
(c) A particle moves in an ellipse under a force which is always directed towards its focus. Find the law of force the velocity at any point of the path and its periodic time.
(d) A particle moves with a central acceleration equal to 5 m ¸ (distance) and is projected from an apse at a distance a with a velocity equal to ‘n’ times that which would be acquired in falling from infinity. Show that the other apsidal distance is a/n-1

15. (a) State and prove the theorem of parallel axes.
(b) A uniform rod of length 2a can turn freely about one end. If it is let fall from a horizontal position, show that its angular velocity when it is first vertical is 3g/2a
Or
(c) Show that the moment of a uniform triangular lamina of mass M about a line
through one vertex of the lamina is M/6 if the distances of the line from the other two vertices are b and g.

(d) A heavy uniform rod AB of length 2l and mass M has a mass m attached to it at B. The  whole oscillates freely about a horizontal axis through A. Show that the time of a small oscillation is 4Q.