# WBUT Question Papers CS Engineering Mechanics

# B Tech Ist Sem 2011 12

Time Allotted.; 3 Hours Full Marks .- 70

The figures in the margin indicate full mark

Candidates are required to give their answers in their own words

as far as practicable.

GROUP – A ( Multiple Choice Type Questions )

1. Choose , the correct alternatives for any ten of the following :

10x 1 = 10

i) Coloumn friction is between .

■ . . %

a) solids and liquids

b! dry surfaces

c) between bodies having relative motion

d} ^{1} none of these. . .

ill The velocity of a simple wheel and axle, with D and d as the diameters of effort respectively is

■ a) (D + d) ^ b) (D – d)

d D

c) — d) —

D d

iii) For stable equilibrium the potential energy will be

a) maximum

b) minimum

c) zero

d) equal to kinetic energy.

iv) The centroid of a semicircular area of radius r from the

c) — d) r.

2k

v) Materials having same elastic properties in all directions

are called .

a) Isotropic b) Orthotropic

c) Composite d) Elastic.

vi) The work done against any conservative force is stored

. f

in the body in the form of

a) energy b) potential energy

c) elastic energy d) strain energy.

vii) A pair of a force and a couple in the same plane upon a rigid body

a) balance each other

b) cannot modify each other

c) produce a moment

d) none of these .

Hooke’s law is valid up to

a) yield point c) proportiona

xii) Couple is a

a) bound vector

c) sliding vector

free vector none of these.

xiii) Angle between the vectors (i + j) and {i-j) is

a) 90° b) 45°

^{c) }0 d) none of these.

[ Turn over

GROUP -B

( Short Answer Type Questions )

Answer any three of the following. .

3×5=15

2*. a) Define moment.

b) In the given figure 1 weight of the block is 1600N and p0.2 • Find the value of F for impending motion. 2 + 3

6, a) State & Prove Lame’s theorem,

b) Two equal loads of 2500 N are supported by a flexible string ABCD at points B and D as shown in figure 2. Find the tensions in the portions AB. BC, CD of the string.2 + 3

GROUP -C ( Long Answer Type Questions )Answer any three of the following. 3 x 15 = 45

- a) A block of weight, Wj=200kgf resis on a horizontal surface and supports on top of it another block of weight U2 = 5p kgf. The block W
_{2}is attached to a

vertical wall ^{r<}by the inclined string AB. Find the magnitude of the horizontal force P applied to the lower block as shown, that will be necessary to cause slipping to impend. The coefficient of static friction for all contiguous surfaces is \x = 0.3 ■ 7

b) A shot is fired with a bullet yrith an initial velocity of 40m/s from a point 20m iivfront of a vertical wall 10m high. Find the angle of projection with horizontal to enable the shot to just clear the wall. 8

stress there is to be limited to 140 N/Mm^{2}, Find also the length of the middle portion of the total elongation of

the bar is to be 0.16mm. Take E = 2 x 2xl0^{5}mm^{2}. 10

^{1} Figure 5

b) Determine the co-ordinate of the centroid with respect to the given axis of the shaded area as shown in figure 6. 5

a) State principle of transmissibility.

b) Given a force F = 1 Of + 5j + A kN. If this force is to have a rectangular component of 8N along a line having unit vector r = 0,6i + 0.8 k, what should be the value of A ? What is the angle between F and r ?

c) Two identical blocks A and B each having weight W are connected by rigid link and supported by a vertical wall and a horizontal plane having same co-efficient of friction (|i) as shown in figure. If sliding impends for 0=45° , calculate (a. 2 + 5 + 8

- a) If the string
^{f}AN is horizontal, find the angle that the string AC makes with the horizontal when the ball is in a position of equilibrium. Also find the pressure R between the ball and the plane.

b) A Toller of radius r = 12 cm and Q = 500 kgf is to be rolled oyer a curb of .height h = 6 cm by a horizontal force F applied to the end of a string wound around the circumference of the roller. Find the magnitude of P required to start the roller over the curb. There is sufficient friction between the roller surface anu the edge of the curb to prevent slip at A.

. Figure 9

‘ 7 + 8

1 j _{a}| State parallel axis and perpendicular axis theorem -oi moment of inertia.,. .

b) Define radius of gyration. How Is it related to mass moment of inertia ? _

c) Determine ^{f}the centre of a quarter circular arc ol

3. The position co-ordinate of .a particle which is confined to move in a straight line is given by S-2(^{3}-24t_{+}6. where S is in m and t is in sec.

Determine,

a) the time required for the particle to reach a velocity of 72 m/s from its initial condition at t = 0.

b) the acceleration of the particle when v = 30 m/s.

c) the net displacement of the particle during the inteival from t =1 sec to t = 4 sec.

4. Define (i) Malleability (ii) Resilience ini) Toughness (iv) Ductility and (v) Proof Resilience.

5. A force F =3/ – 4/’ + 12k acts at a point A whose co-ordinates are (1, – 2, 3). Compute.

a) moment of force about origin,

b) moment of force about point (2.12)