Cochin University of Science and Techology (CUST) 2008-1st Year B.E Mechanical Engineering BTECH ENGINEERING MECHANICS - Question Paper

BTECH DEGREE 1st YEAR exam JUNE 2008

ENGINEERING MECHANICS

Max marks:100

Time: three Hrs

PART A

1. a) discuss principle of transmissibility of force and legal regulations 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) discuss principle of Virtual work.

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

f) discuss 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”? find 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’. obtain the angle that
the flat surface of disc will make the horizontal just before sliding starts. 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, obtain 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 a few 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. compute 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 four minutes. If the angular retardation is uniform,find its m
magnitude in radians per 2nd 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 two 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?

Earning:   Approval pending.