LOYOLA COLLEGE ( AUTONOMOUS ) , CHENNAI – 600 034

#### BSc DEGREE EXAMINATION -MATHEMATICS

# V SEMESTER – NOVEMBER 2006

Date : Max : 100 Marks

### Duration: Hours: 3 hours

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SUB.CODE:*MT5500*** ** SUB.NAME **: MECHANICS-II**

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Answer ** ALL** the questions and each question carries 2 marks [ 10 X 2 = 20 ]

01.State the cases of non existence of center of gravity

02.State the forces which can be ignored in forming the equation of virtual work.

03.Define Neutral equilibrium with an example

04.Define Span of a Catenary

05.A particle is performing S.H.M. between points A and B. If the period of oscillation is

2p, show that the velocity at any point is a mean proportional between AP and BP.

06.Define Apse

07.If the angular velocity of a particle moving in a plane curve about a fixed origin is

constant, show that its transverse acceleration varies as radial velocity.

08.Find the M.I of a thin uniform rod.

09.Define radius of gyration.

10.State D’Alembert’s principle.

Answer any ** FIVE** of the following [ 5 X 8 = 40 ]

- A uniform solid right circular cylinder of height l and base radius r is sharpened at

one end like pencil. If the height of the resulting conical part be h, find the distance

through which the C.G is displaced, it being assumed that there is no shortening of the

cylinder.

12.Find the C.G. of a uniform hollow right circular cone.

13.A uniform chain, of length l, 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 AB must be

14.A uniform string hangs under gravity and it is such that the weight of each element of

it is proportional to the projection of it on a horizontal line. To determine the shape of

the string.

15.Show that the composition of 2 simple harmonic motions of the same period along 2

perpendicular lines is an ellipse.

16.A particle executing S.H.M in a straight line has velocities 8,7,4 at three points distant

one foot each other. Find the period.

17.Derive the radial and transverse components of velocity and acceleration.

- A circular disc of radius 5cms. Weighing 100 gms. is rotating about a tangent at the

rate of 6 turns per second. Find the frictional couple which will bring it to rest in one

minute

Answer any ** TWO** of the following [ 2 X 20 = 40 ]

19.i.Discuss the stability of a body rolling over a fixed body

ii.A body consisting of a cone and a hemisphere on the same base rests on a rough

horizontal table. Show that the greatest height of the cone so that the equilibrium may

be stable is times the radius of the sphere.

20.i.State and prove the principle of virtual work for a system of coplanar forces acting on

a rigid body.

ii.A solid hemisphere is supported by a string fixed to a point on the rim and to a point

on a smooth vertical wall with which the curved surface of the hemisphere is in

contact. If and are the inclination of the string and the plane base of the

hemisphere to the vertical, prove that

21.A point moves with uniform speed v along the curve r = a (1+ cosq ). Show that

- Its angular velocity w about pole is
- Radial component of acceleration is constant and equal to numerically

iii. Magnitude of resultant acceleration is

22.i.State and prove the theorem of parallel axes

- Find the moment of inertia of a hollow sphere.