West Bengal Institute of Technology (WBIT) 2010 B.Tech Computer Science Information Technology Semester 1 - ENGINEERING MECHANICS - Question Paper
West Bengal University of Technology (WBUT)
FIRST SEMESTER B.TECH. exam
10 DECEMBER 2010
ENGINEERING MECHANICS (SUBJECT CODE: ME 101)
Time: three hours Max. Marks: 70
Name:......................................................................
RollNo.: ..................................;...............................
Invigilators Signature: v.............................................
CS/B.TECH (NEW)/SEM-1 /ME 101/2010-11
Time Allotted : 3 Hours Full Marks : 70
' - . . '
The figures in the margin indicate full marks. , 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 the following : 10 x 1 = 10
i) Mass moment of inertia of body is
a) moments of its inertia
b) rotational analogue of mass
c) Inertial moment about the centroidal axis
d) none of these.
ii) the centre of percussion of a rigid body is a point , a) through which resultant of all forces acts
b) where minimum external force acts
c) where impact is made
d) all of these.
iii) Two coplanar couples having equal and opposite moments
a) balance each other '
b) produce a couple and an unbalance force
c) an equivalent t
d) all of these.
iv) The moment of inertia of a rectangle having base b and height h with respect to its base is
a) \h2h2 b) -b3h
3 3
C) | bh3 d) b2h2.
. ' . ' /,
v) The D' Alembert's principle
a) is based upon the presence of inertia force
b) provides advantage over Newtons law
c) is purely a hypothetical principle
d) allows a dynamic problems to be treated as a static one
vi) Centroid of a line segment .
a) must lie on the line
b) may not lie on the line
c) must be same as the cetre of gravity.
d) none of these.
vii) Volumetric strain of a rectangular body subjected to an axial force, in terms on terms of linear strain e and Poisson's ratio V is given by
a) e (1 + 2V) b) e (1 - 2V)
c) e (1 + V) . d) e(l -V).
viii) Poisson's ratio is defined as
a) lateral stress and lateral strain
b) longitudinal stress and longitudinal strain ,
c) lateral stress and longitudinal stress
d) none of these.
' ' > . - > . .
ix) Relative velocity of A with respect to B is defined as
a) Va/b = Vb -Va b) Va/b =VA - V
> > > .
c) Va/b =Vb +Va d) None of these.
x) When a change in length takes place, the strain is known as t.
a) Linear strain b) lateral strain
c) shear strain d) volumetric strain.
GROUP-B ( Short Answer Type Questions)
Answer any three of the following.
3x5= 15
The position vector of a particle moving in the x-y plane at time t = 3 60s is 2-76 j m. At t = 3-62s its position vector has become 2 79i-3 33 j m. Determine the magnitude v of its average velocity during this interval and the angle 0 made by v with je-axis. .
3 [ Turn over
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What do you mean by a free body diagram ? Draw the FBD |
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If two equal tensions T in the pulley cable are 400-N, cable as shown in Fig. 2 express in vector notation the force JR exerted on the pulley by the two tensions. Determine the magnitude of R.
i) State and prove Lami's theorem. -
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T* 400KJ |
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Fig. 2 | |
ii) Define free-body diagram. 3 + 2 A bullet of mass m, moving with a horizontal velocity v, hits a stationary block of mass M, suspended by a massless string of length L. The bullet gets embedded in the block after impact and the two together swings up. Show that the maximum angle of Swing (i.e. angle made by the string with the vertical), is
m2v2
1
0 = cos-
1-
2gL(M + m)
GROUP -G ( Long Answer Type Questions)
Answer any three of the following.
3x 15 = 45
7. a) A 50 N block is released from res on an inclined plane which is making an angle of 35 to the horizontal (Fig. 3). The block starts from 'A' slides down a distance
of 12 m and strikes a spring with a stiffness of 8 kN/m. The co-efficient of friction between the inclined plane and the block is 0 25. Determine (i) the amount the spring gets compressed and (ii) distance of the block will rebound up the plane from the compressed position.
8
b) A reinforced concrete column having cross-section 300 mm x 300 mm is provided with 9 bars of 20 mm diameter (Fig. 4). The column carried a load of 300 KM. Find the stress developed in the steel bars and concrete. Take Es = 2-1 x 105 N/irnn2 and Ec = 014 x 105 N/mm2.
SXbi
8. A rigid bar AB is hinged to a vertical wall and supported horizontally by a tie rod CD as shown in Fig. 5. The cross-
CS/B.TECH (NEW)/SEM-1/ME 101/2010-11
sectional area of GD is A = 0-5 sq.cm and its allowable stress in tension is ow = 1,500 kg/sq, cm. Find the safe value of P and the corresponding vertical displacement AB of B. Modulus of elasticity of tie rod E = 2 x 106 kg/sq. cm.
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Fig. 5 |
9. a) A block of weight W1 = 200 N rests on a horizontal surface and supports on top of it, another block of , weight W2 = 50 N. The block W2 is attached to a vertical
wall by the inclined string AB. Find the magnitude of
the horizontal force P applied to the lower block as
shown in Fig. 6, that will be necessary to cause slipping to impend. The coefficient of static friction for all
7
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Fig. 6 |
b) . Two smooth circular cylinders, each of weight W= 100N and radius r = 6 cm are connected at the centres by a string AB of length 1 = 16 cm and rest upon a horizontal plane, supporting above them a third cylinder of weight Q = 200 N and radius 1 = 6 cm as show in Fig. 7. Find the force S in the string AB and pre&sure produced on the floor at D and E. 8
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Q |
 |
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Fig. 7 |
10. a) Two rollers of diameters 60 mm and 30 mm weighing
200 N and 150 N respectively. They are supported by an inclined plane and vertical walls as shown in Fig. 8. Assuming smooth surfaces, determine the reactions at
the contact surfaces.
b) Find out the moment of inertia about centroidal axes of an area as shown in Fig. 9.
20mm
100mm
Calculate the Increase in stress for each segment of the compound bar shown in Fig. 10. If the temperature increases by 100F, assume that the supports are unyielding and that the bar is suitably braced against buckling,
11. a)
8
4 = 2.0 la* = 29X106psi
a -12.8 X l<r/*F A 15
b)
 |
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Fig. 10 |
In Fig. 11 a lever is attached to a spindle 2 5 cm in diameter by means of a square key 6 mm x 6 mm if the average shear stress in the key not to exceed 700 N/cm2. What is the safe value of the load P applied to tiie end of the lever, . 7
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Fig. 11 |
,1215 8
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Attachment: |
| Earning: Approval pending. |
