# CUSAT Previous Question Papers

# June 2008

# Engineering Mechanics ** **

**Max marks:100**

**PART A**

1. (a) Explain principle of transmissibility of force and law of superposition.

b) State and prove Pappus theorem.

c) Derive an expression for polar moment of inertia of a circle of

diameter‘d’ with respect to its centre.

d) Explain principle of Virtual work.

e) Prove that the trajectory of a projectile is parabolic.

f) Explain principle of conservation of momentum in case

of impact of bodies.

g) Derive a formula for equivalent length of a compound pendulum.

h) What is “centre of percussion”? Obtain an expression for

distance b/w centre of percussion and rotating axis of a rigid body,

considering x-axis through the centre of gravity of the rotating body.

**PART B**

2. A semicircular disc of radius ‘r’ and weight ‘w’ rests on

a horizontal surface and is pulled at right angles to its geometric axis

by a horizontal force ‘P’. Find the angle that the flat surface

of disc will make the horizontal just before sliding begins.

The weight ‘w’ is acting at the centre of gravity.

**OR**

3. A beam AB is hinged at ‘A’ and supported at B

by a vertical cord which passes over a frictionless pulley at C

and carries at its end a load P as shown. Determine the distance

‘x’ from ‘A’ at which a load Q must be placed on the

beam if it is to remain in equilibrium in a horizontal position.

Neglect the weight of beam. If proportion of

distance x:l is 1:6 and P=10N, find load at ‘Q’.

4. A particle is projected from origin ‘O’ with

a velocity of 120m/s at an elevation of 60

degree to the horizontal. At some position P it has a

velocity in a direction making an

angle of 30 degree with the horizontal.

Determine the velocity of the particle at P

coordinates of P and the distance OP.

**OR**

5.A car traveling at 40km/hr sights a distant signal at 150m

and comes uniformly to rest

at the signal. It remains at rests for 20s.

As allowed by the signal, it uniformly

accelerate and attain 40km/hr in 250m.

Calculate time lost due to signal

6. A steam turbine is running at 2400 revolutions/minute.

On shutting off steam it slows down & comes to rest in 4 minutes.

If the angular retardation is uniform,

find its m magnitude in radians per second square & also the

no.of revolutions made by the turbine before coming to rest.

**OR**

7. A slender prismatic bar of weight W=36 N is free to rotate

in a vertical plane about a fixed axis through’ O’.

The bar is released from rest in the unstable position of

equilibrium & falls into the horizontal position A’B’,

where it is brought to rest by 2 identical springs having constant K.

If the spring A is compressed 1.27 cm before the

bar comes to rest , what is the spring constant?