Mechanical Question and Answer with explanation: March 2013

Que: Two tapering bars of the same material are subjected to tensile load P. The larger diameter of each of the bar id D. The diameter of the bar A at its small end is D/2 and bar B is D/3. If both the bar are the same length, then what is the ratio of elongation of bar A to bar B. (Engg Services-2006)

(a) 3 : 2
(b) 2 : 3
(c) 4 : 9
(d) 1 : 3

Ans: (b)
Explanation: For a tapering rod,
ΔL = 4WL / π d1 d2 E

ΔL for A bar = 4WL / (π D D/2 E) = 8WL / (π D² E)

ΔL for B bar = 4WL / (π D D/3 E) = 12WL / (π D² E)

So, Ratio of ΔL for A bar to ΔL for B bar = 8 / 12 =2 / 3

Que: Two identical circular rod of the same diameter and same length are subjected to same magnitude of axial tensile force. One of the rod is made out of mild steel having the modulus of elasticity of 206 Gpa. The other rod is made out of cast iron having modulus of elasticity of 100 Gpa. Both the material are homogeneous and isotropic and the axial force causes the same amount of uniform stress in them. if the stresses developed are within the proportional limit of respective materials, then which of the following statement are correct (Gate-2007)

(a) Both rods elongate by the same amount
(b) Mild steel rod elongates more than Cast iron rod
(c) Cast iron rod elongates more than Mild steel
(d) As the stresses are equal, strain are also equal in both the rods

Ans: (c)
Explanation: Stress are equal in both materials
Length of the both rods are same
From equation of Modulus of elasticity = stress / strain = (force * length) / (area * change in length)
here force, length and area remain same so modulus of elasticity are directly proportional to change in length
So
For Mild steel 206 ≈ 1 / change in length
change in length for mild steel ≈ 1 / 206 ≈ 0.0048

For Cast iron 100 ≈ 1 / change in length
change in length for Cast iron ≈ 1 / 100 ≈ 0.01
so (elongation) change in length are higher in Cast iron

Que: The total area under the stress-strain curve of a mild steel specimen tested upto failure under tension is a measure of its (Gate-2002)

(a) Breaking Strength
(b) Toughness
(c) Hardness
(d) Stiffness

Ans: (b)
Explanation: Breaking strength is the maximum stress that a material can withstand while being stretched or pulled before failing or breaking so its not related with strain only stress are considered,
Hardness is the resistance of a material to localized deformation so hardness is propositional to accepted load before any deformation at here strain = change in length / original length are not consider.
Toughness is the ability of a material to absorb energy and plastically deform before fracturing and absorb energy per unit volume calculated by area under the stress-strain curve.

Engineering Mechanics example (Gate-2005)

Que: A time variation of the position of a particle in rectilinear motion is given by x = 2t³ + t² + 2t If v is the velocity and a is the acceleration of particle in constant units, the motion started with (Gate-2005)

(a) v = 0, a = 0

(b) v = 0, a = 2

(d) v = 2, a = 2

Ans: (d)

Explanation:

x = 2t³ + t² + 2t So,

Velocity v = dx/dt = 6t² + 2t +2

Acceleration a = 12t + 2

At the start of motion t = 0, Then

v = 0 + 0 + 2 = 2

a = 0 + 2 = 2

Que: a car moving with uniform acceleration covers 450 m in a 5 second interval, and covers 700 m in the next 5 second interval. the acceleration of the car is (Gate-98)

(a) 7 m/s²
(b) 10 m/s²
(c) 25 m/s²
(d) 50 m/s²
^{Ans: (b)}
^{Explanation: Here}
^{u = initial velocity}
^{v = final velocity}
^{a = acceleration}
^{t = time}
^{s = distance}
^{using the relation}s = ut + 1/2 at² and v=u + at, for the first 5 second interval,we have

450 = 5u + 25/2 a ___(i)

v = u + 5a

for the next 5 second interval (v=u + 5a) will be the initial velocity, then

700 = (u + 5a) 5 + 25/2 a

700 = 5u + 25a + 25/2 a ___(ii)

From equations (i) and (ii), we get

700-450 = (5u +25a + 25/2 a) – (5u + 25/2 a)

250 = 25a

a = 250/25

a =10 m/s²

Que: Which one of the following is correct in respect of Poisson's ratio (µ) limits for an isotropic solid? (Engg Services-2004)

(a) - ∞ ≤ µ ≤ ∞

(b) ¼ ≤ µ ≤ 1/3

(d) - ½ ≤ µ ≤ 1/2

Ans: (b)

Explanation: Poisson's ratio always lies between 0.25 and 0.33 for most of the engineering materials.

Que: A solid uniform bar of diameter d and length l is hanging vertically from its free end. The elongation of the bar due to self weight is (Engg Services-2005)

(a) Proportional to l and inversely Proportional to to d²
(b) Proportional to l² and inversely proportional to d²
(c) Proportional to l but independent of d
(d) Proportional to l² but independent of d

Ans: (a)
Explanation: Extension due to self weight (W) is
Here E = Modulus of elasticity
d = Diameter of rod
L = Length of rod
ΔL = Elongation

From equation of modulus of elasticity of self weighted rod = E = (W x L) / 2(π/4 d² x ΔL)
ΔL = (W x L) / 2(π/4 d² x E)
From above equation concluded that Elongation (ΔL) are directly Proportional to l and inversely Proportional to to d²

HPCL Mechanical engineering questions with answers

Engineering Service 2011 question paper

Que: A thermodynamic system is considered to be an isolated one if (Engg Services-2011)

(a) Mass transfer and entropy change are zero
(b) Entropy change and energy transfer are zero
(c) Energy transfer and mass transfer are zero
(d) Mas transfer and volume change are zero

પ્રશ્ન: થર્મોડાયનેમિક સિસ્ટમ આઇસોલેટેડ ગણવામાં આવે છે જો
(a) માસ ટ્રાન્સફર અને એન્ત્રોપી ફેરફાર શૂન્ય છે
(b) એન્ત્રોપી ફેરફાર અને ઊર્જા ટ્રાન્સફર શૂન્ય છે
(c) ઊર્જા ટ્રાન્સફર અને માસ ટ્રાન્સફર શૂન્ય છે
(d) માસ ટ્રાન્સફર અને વોલ્યુમ ફેરફાર શૂન્ય છે

Ans: (c)
Explanation: A system is called isolated if there are no mass and energy transfer between system and surrounding,so answer is (c)

Que: In case of pressure vessels having open ends, the fluid pressure induces

(a) longitudinal stress
(b) circumferential stress
(c) shear stress
(d) none of these

પ્રશ્ન: પ્રેસર વેસલના ખુલ્લા છેડાના કિસ્સામાં, પ્રવાહી દબાણના તણાવની દિશા
(a) સમાંતર તણાવ
(b) પરિધીય તણાવ
(c) કર્તનમાં તણાવ
(d) આમાંથી કંઈ નહિં

Ans: (b)

Que: A pressure vessel is said to be a thin cylindrical shell, if the ratio of the wall thickness of the shell to its diameter is

(a) equal to 1/10
(b) less than 1/10
(c) more than 1/10
(d) none of these

પ્રશ્ન: પાતળો નળાકાર શેલ એ પ્રેસર વેસલ કહેવામાં આવે છે, જયારે શેલમાં દિવાલની જાડાઈ અને તેના વ્યાસનો ગુણોત્તર
(a) 1/ 10 બરાબર
(b) 1/10 કરતાં ઓછો
(C) 1/10 કરતાં વધુ
(ડી) કોઈપણ નહિ

Ans: (b)

Que: Stress and Strain Multiple choice question test.

Que: Machine Design consideration Multiple choice question test.

Que: Material Technology Multiple choice question test.

Que: Bending Stress general equation

M = Bending moment acting at the given section,
σ = Bending stress,
I = Moment of inertia of the cross-section about the neutral axis,
y = Distance from the neutral axis to the extreme fibre,
E = Young’s modulus of the material of the beam, and
R = Radius of curvature of the beam.

Que: The maximum shear stress developed in a beam of rectangular section is ........ the average shear stress.

(a) equal to
(b) 4/3 times
(c) 1.5 times

પ્રશ્ન: મહત્તમ કર્તન દબાણમાં લંબચોરસ વિભાગમાં એક બીમમાં તણાવ સરેરાશ કર્તન દબાણમાં તણાવ કરતા_______ ગણો છે.
(a) સમાન
(b) 3/4 ગણું
(c) 1.5 ગણું

Ans: (c)

Induce Shear Stress due
to shear force

Que: At the neutral axis of a beam, the shear stress is

(a) zero
(b) maximum
(c) minimum

પ્રશ્ન: બીમની તટસ્થ ધરી પર, કર્તન દબાણમાં તણાવ
(a) શૂન્ય
(b) વધુમાં વધુ
(c) ન્યૂનતમ

Ans: (b)

Que: Guest’s theory is used for

(a) brittle materials
(b) ductile materials
(c) elastic materials
(d) plastic materials

પ્રશ્ન: ગેસ્ટ સિદ્ધાંત________માટે વપરાય છે
(a) બ્રિટલ મટીરીયલ

(b) ડક્ટાઇલ મટીરીયલ

(d) પ્લાસ્ટિક મટીરીયલ

Ans: (b)

Que: Rankine’s theory is used for...

(a) brittle materials
(b) ductile materials
(c) elastic materials
(d) plastic materials

પ્રશ્ન: રેંકિન સિદ્ધાંત________માટે વપરાય છે
(a) બ્રિટલ મટીરીયલ
(b) ડક્ટાઇલ મટીરીયલ
(c) ઇલાસ્ટિક મટીરીયલ
(d) પ્લાસ્ટિક મટીરીયલ

Ans: (a)

Que: When a machine member is subjected to a tensile stress (σt) due to direct load or bending and a shear stress (τ) due to torsion, then the maximum shear stress induced in the member will be

Ans: (a)

Que: A solid shaft transmits a torque T. The allowable shear stress is τ. The diameter of the shaft is

Ans: (a)

Que: Two shafts under pure torsion are of identical length and identical weight and are made of same material. The shaft A is solid and the shaft B is hollow. We can say that

(a) shaft B is better than shaft A
(b) shaft A is better than shaft B
(c) both the shafts are equally good

પ્રશ્ન: શુદ્ધ ટોર્શન હેઠળ બે શાફ્ટ સમાન લંબાઈ અને સમાન વજનના છે અને તે જ સામગ્રીના બનેલા છે. શાફ્ટ A ઘન છે અને શાફ્ટ B હોલો છે. તો આપણે કહી સકિયે કે
(a) શાફ્ટ B એ શાફ્ટ A કરતાં વધુ સારો છે
(b) શાફ્ટ A શાફ્ટ B કરતાં વધુ સારો છે
(c) બંને શાફ્ટ સમાન છે

Ans: (a)

Que: If di and do are the inner and outer diameters of a hollow shaft, then its polar moment of inertia is

Ans: (a)

Que: If d = diameter of solid shaft and τ = permissible stress in shear for the shaft material, then torsional strength of shaft is written as

Ans: (c)

Que: The maximum bending stress, in a curved beam having symmetrical section, always occur, at the

(a) centroidal axis
(b) neutral axis
(c) inside fibre
(d) outside fibre

Ans: (c)

Que: The bending stress in a curved beam is

(a) zero at the centroidal axis
(b) zero at the point other than centroidal axis
(c) maximum at the neutral axis
(d) none of the above

Ans: (b)

Que: At the neutral axis of a beam,

(a) the layers are subjected to maximum bending stress
(b) the layers are subjected to tension
(c) the layers are subjected to compression
(d) the layers do not undergo any strain

Ans: (d)

Que: The neutral axis of a beam is subjected to

(a) zero stress
(b) maximum tensile stress
(c) maximum compressive stress
(d) maximum shear stress

Ans: (a)

Que: The torsional shear stress on any cross-section normal to the axis is ......... the distance from the center of the axis.

(a) directly proportional to
(b) inversely proportional to

Ans: (a)

Que: When a machine member is subjected to torsion, the torsional shear stress set up in the member is

(a) zero at both the centroidal axis and outer surface of the member
(b) Maximum at both the centroidal axis and outer surface of the member
(c) zero at the centroidal axis and maximum at the outer surface of the member
(d) none of the above

Ans: (b)

Que: Torsional Shear Stress general equation?

τ = Torsional shear stress induced at the outer surface of the shaft or maximum
shear stress,
r = Radius of the shaft,
T = Torque or twisting moment,
J = Second moment of area of the section about its polar axis or polar moment of
inertia,
C = Modulus of rigidity for the shaft material,
l = Length of the shaft, and
θ = Angle of twist in radians on a length l.

Que: How much force is required to lift the weight?

A) 40 lbs

B) 50 lbs

C) 60 lbs

D) 70 lbs

Ans: (C)
Solution: 60 lbs is needed to lift the weight. It can be calculated like this:

f = (w x d1)/d2
f = (80 x 9)/12
f = (720)/12
f = 60 lbs

Que: The notch sensitivity q is expressed in terms of fatigue stress concentration factor Kf and theoretical stress concentration factor Kt, as

Ans: (b)

Que: If the size of a standard specimen for a fatigue testing machine is increased, the endurance limit for the material will

(a) have same value as that of standard specimen
(b) increase
(c) decrease

Ans: (c)

Que: The ratio of endurance limit in shear to the endurance limit in flexure is

(a) 0.25
(b) 0.40
(c) 0.55
(d) 0.70

Ans: (c)

Que: When a material is subjected to fatigue loading, the ratio of the endurance limit to the ultimate tensile strength is

(a) 0.20
(b) 0.35
(c) 0.50
(d) 0.65

Ans: (c)

Que: Factor of safety for fatigue loading is the ratio of

(a) elastic limit to the working stress
(b) Young's modulus to the ultimate tensile strength
(c) endurance limit to the working stress
(d) elastic limit to the yield point

Ans: (c)

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