# B Tech 1st Sem Dec 2005

The questions are of equal value.
The figures in the margin indicate full marks.
Candidates are required to give their answers in their own words as far as practicable.
Note: Answer Question No. I which is compulsory and any six from the remaining.
1. Choose the correct answers with proper justification : 5×2=10 a)
First area moments (of a plane surface area) about centroidal axes is equal to
i)          zero
ii)         non-zero. b)
For a two-dimensional equilibrium ( static ) problem,
the maximum number of unknowns that can be evaluated using equilibrium equations are I)
one ii) three ill) six. c)         Thermal stress is induced within a material due to
i)          free expansion , ii)         free contraction Hi) free expansion or contraction
iv)        restricted expansion or contraction v)          none of these*
d)         When a body slides down an inclined siirface ( of inclination 0 ) the acceleration ’f of the body is
i)          /= 9 II)        f = g sin Q ill) /= g cos 0 iv) /= g tan 0
. e)         The kinetic energy of a body rotating with an angular speed co depends on 0 co only
ii)         co2 only ill) mass only iv)        the distribution of mass and angular speed v)          all of these.

State and prove perpendicular axis theorem of area moment of inertia. Locate the centroid of the quadrant of a circle of radius r (Jig. 1 )

a) State the laws of static friction.

b) A block of weight Wj = 1290N rests on a horizontal surface and supports another block of weight W2 = 570 N on top of it as shown in Jig.
2. Block of weight W2 is attached to a vertical wall by an inclined string AB. Find the force P applied to the lower block, that will be necessary to cause the slipping to impend. Given : Coefficient of friction between blocks (1) and (2) = 0-25 Coefficient of friction between
(1) and horizontal surface = 0-40.                  7   Fig . 2

1. a) State and prove Lami’s theorem, b) Define free body diagra
2. 5  Two cylinders of diameters 60 mm and 30 mm weighing 160 N and 40 N respectively are placed as shown. Assuming all the contact surfaces to be smooth, find the reactions at A, B and C.                 ^

1. a) State the principle of virtual work.
b) Using the principle of virtual work, find the value of the angle 0 defining the configuration of equilibrium of the system as shown in Jig. 4. The balls D and E can slide freely along the bars AC and BC but the string DE connecting them is

inextenslble.                                                                                            

6
State Coulomb’s Law of friction. A block of weight Wl = 500 N rests on a horizontal surface and supports on top of it another block of weight W2 = 100 N. The block W2 is attached to a vertical rtU buJh.G I”011,11611Sng ABFind the magnitude of the horizontal force p applied to the lower block as shown In Jig. 6 that will be necessary to cause slippkig to impend. The co-efficient of static friction for all contiguous surfaces 1S * ~ °’3– 2 + 8=10 iV- c 1: w; V—►P

1 >’T~

Fig. A particle moving in the x-y plane undergoes a displacement S = (4l + 6j)m
^C°.nStf?t f°rCe l= (57 + I0 J ) N actln^ on lt– Calculate the work done, magnitude of force and magnitude of displacement. *                                                                      5 A 5 kg block slides from rest at point A along a frlctionless inclined plane making an angle 25 with horizontal. Determine the speed of the block at B at a distance of 3 m from A.         g Distinguish between particle and rigid body.

2 A baH is dropped vertically on to a 20* inclined plane at A. The direction of rebound forms an angle of 35‘ with vertical. Knowing that the ball strikes the inclined plane at B, determine i) the velocity of rebound at A. U) the time required for the ball to travel from A to B.                                  g

6.     a) Define Hooke s law.

)          A bronze bar 3 m long with a cross-sectional area of 320 mm 2 is placed between two rigid walls as shown in Jig. 5. At a temperature of – 20’C. the gap A = 2-5 mm. Find the temperature at which the compressive stress in the bar will be o = 35 MPa. Use a = 18 x 10“« m/^C and E = 80 GPa.                                                                      7