Monday, 7 December 2009


Vivekanand Institute of Technology & Science; Ghaziabad
B.Tech…first Semester

Sub Name: Engineering Mechanics Max. Marks: 100
Sub Code: EME-102 Max. Time: 3: 00 Hr

(i) This paper is in three sections, section A carries 20 marks, section B carries 30 marks and section C carries 50 marks.
(ii) Attempt all the questions. Marks are indicated against each question
(iii) Assume missing data suitably if any.

Group A

Q.1 Answer the following questions as per the instructions 2x20=20
Choose the correct answer of the following questions:

(i) The magnitudes of the force of friction between two bodies, one lying above the another depends upon the roughness of the
(a) Upper body;                 (b) Lower body
(c) Both the bodies               (d) The body having more roughness

(ii)The moment of inertia of a circular section of diameter D about its centroidal axis is given by the expression
(a) π(D)4/16               (b) π(D)4/32
(c) π(D)4/64               (d) π(D)4/4

Fill in the blanks in the following questions:

(iii)The distance of the centroid of an equilateral triangle with each side(a) is …………. From any of the three sides.
(iv)Poisson’s ratio is defined as the ratio between ……………………. and
………………………… .
(v)If two forces of equal magnitudes P having an angle 2Ө between them,
then their resultant force will be equal to ________ .

Match the following columns for the following two parts:

(vi) Match the column I to an entry from the column II:
(i) BMD of an UDL(a) stored strain energy per unit volume
(ii) Resilience is(b) brittle materials
(iii) Bulk Modulus (c) parabolic in nature
(iv) Yield Point (d) volumetric stress & strain
(e) Ductile materials
(f) Shear stress

(vii) Match the Following columns:
(i) Square of side (b) (p) π b4 / 64
(ii) Equilateral Triangle of side (b)(q) b4 / 12
(iii) Circle of diameter (b)(r) b4/ 36
(iv) Isosceles right angle triangle of base (b) (s) b4/(32√3)
(e) Ductile materials
(f) Shear stress

Column II gives the value of Moment of Inertia Ixx about a centroidal axis.

Choose correct answer for the following parts:

(viii) Statement 1:
In the yielding zone, strain increases even if stress is decreased.

Statement 2:
At yielding point, the deformation becomes plastic by nature.

(i) Statement 1 is true, Statement 2 is true.
(ii) Statement 1 is true, Statement 2 is true and they are unrelated with
each other
(iii) Statement 1 is true, statement 2 is false.
(iv) Statement 1 is false, Statement 2 is false.

(ix) Statement 1:
For two identical mass, one of which lies on a horizontal plane and another is kept at an inclined plane having same co-efficient of friction, still frictional forces differs from each other.

Statement 2:
Frictional force always depends upon the magnitude of the normal force.

(i) Statement 1 is true, Statement 2 is true.
(ii) Statement 1 is true, Statement 2 is true and they are unrelated with
each other
(iii) Statement 1 is true, statement 2 is false.
(iv) Statement 1 is false, Statement 2 is false.

Choose the correct word/s.
(x) In a truss if the no.of joints (j) is related with no. of links (m) by the equation m > 2j- 3, then it is an example of (redundant/ deficient/ perfect) Truss.


Q.2: Answer any three parts of the followings: 10X3=30
(a) Find the shear force and moment equation for the beam as shown in the figure. Also sketch SFD (shear force diagram) and BMD (bending moment diagram)

(b) Explain and prove “the parallel axis theorem of moment of inertia.”
Also find the centroid of the following composite area.

(c) Find the centroidal Moment of Inertia of the following shaded area.
(d) Two cylinders P and Q rest in a channel as shown in fig. below. The cylinder P has a diameter of 100 mm and weighs 200 kN, where as the cylinder Q has a diameter of 180 mm and weighs 500 kN. Find the support reactions at all the point of contact.

Two blocks A and B of weights 1 kN and 2 kN respectively are in equilibrium as Shown in the figure.
If the co-efficient of friction everywhere is 0.3, find the force P required to move the block B.


(3) Answer any two parts of the following 5X2=10

(a) A simply supported beam of circular cross section of radius 4 cm having a length 2 m long in concentrated load of 5 kN (acting perpendicular to the axis of beam) at a point 0.75 m from one of the supports. Determine
(i) the maximum fiber stress (σb)max); (ii) the stress in a fiber located at a distance of 1 cm from the top of the beam at mid-span.

(b) Describe the procedure of Truss Analysis by Section method.

(c)A flywheel is making 180 rpm and after 20 second it is running at 120 rpm.
How many revolutions will it make and what time will elapse before it stops, if the retardation is constant.

(4) Answer any one part of the following: 1X10=10

(a) Explain the terms polar moment of inertia and radius of gyration.
Derive the area moment of inertias for a quarter circle of radius R.

(b) Analyse the following truss:

(5) Answer any three question;                           3X10=30

(a) Compare the stress – strain diagrams of a ductile material to that of a brittle Material. Also explain the term poisson's ratio and modulus of rigidity.

(b) Explain and prove the “Torsion Equation” (T/J)=(τ/r)=(Gθ/L). What is
called as Section Modulus?

(c) A cylinder of radius R, length L and total mass M is suspended vertically
from the floor, if the modulus of elasticity of the cylinder be E, find the total
deflection and maximum stress induced due to self weight.

(d) A cylinder of 200 mm diameter is subjected to a twisting moment of
250 kN-m, the length of the cylinders is 1 m, if the modulus of rigidity of the
cylinder material be 150 GPa, find the maximum shear stress induced in the
cylinder. Also find the total angular deformation.

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