LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

**B.Sc.** DEGREE EXAMINATION – **MATHEMATICS**

SIXTH SEMESTER – **APRIL 2012**

# MT 6604/MT 5500 – MECHANICS – II

Date : 18-04-2012 Dept. No. Max. : 100 Marks

Time : 1:00 – 4:00

**PART – A**

**Answer ALL the questions: (10 x 2 =20)**

** **

- State the conditions for non-existence of centre of gravity.
- Mention the differences between center of gravity and centre of mass.
- Define the work done by the tension in an elastic string.
- Define Suspension bridge.
- A particle executing simple harmonic motion makes 100 complete oscillations per minute and its maximum speed is 15 ft/sec. What is the length of its path and maximum acceleration?
- Define Centripetal force.
- Define Central Orbit.
- An insect crawl at a constant rate u along the spoke of a earth wheel of radius a starting from centre, the wheel moving with velocity v. Find the accelerations along and perpendicular to the spoke.
- State Parallel axis theorem.
- Write down the formula for Moment of Inertia of a solid sphere and hollow sphere.

__PART –B__

** Answer any FIVE questions: (5 x 8 = 40)**

** **

- Find the Centre of gravity of a uniform circular angle.
- Derive the intrinsic equation of the catenary.
- A particle executing simple harmonic motion in a straight line has velocities 8,7,4 at three points distant one foot from each other. Find the period.
- ABCD is a trapezium in which AB and CD are parallel and of lengths a and b. Prove that the distance of the centre of mass from AB is where h is the distance between

AB and CD.

- A particle describes the orbit
*r*=Acos^{n}*nθ*-Bsin*nθ*under a central force, the pole being the centre. Find the law of force. - Derive the p-r equation of a central orbit.
- Find the moment of Inertia of a thin uniform parabolic lamina bounded by the parabola
*y*^{2}=4*a*(*h*–*x*) about the*y*-axis. - State and prove D’Alemberts Principle.

__PART –C__

**Answer any TWO questions: (2 x 20 = 40)**

** **

- a) Find the centre of gravity of a hollow hemisphere.
- b) Find the centre of gravity of the arc of the cardiod r = a(1+cos
*θ*) lying above the initial

line. (8+12)

- State and prove Principle of virtual work for a system of coplanar forces acting on a body.

- a) Find the resultant of two simple harmonic motions of the same period in the same

straight line.

- b) The speed
*v*of a particle moving along the x-axis is given by

Show that the motion is simple harmonic with centre at *x* = 4*b* and amplitude 2*b*.

Find the time from *x* = 5*b* to *x* = 6*b*. (12+8)

- a) If the law of acceleration is and the particle is projected from an apse

at a distance *c* with velocity , prove that the equation of the orbit is

- b) Find the moment of inertia of an elliptic lamina. (10 + 10)

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