I B.Tech Supplementary Examinations, November 2009 MATHEMATICAL METHODS

Code No: Z0224/R07 Set No. 1
I B.Tech Supplementary Examinations, November 2009
MATHEMATICAL METHODS
( Common to Electrical & Electronic Engineering, Mechanical Engineering,
Electronics & Communication Engineering, Computer Science &
Engineering, Electronics & Instrumentation Engineering, Bio-Medical
Engineering, Information Technology, Electronics & Control Engineering,
Mechatronics, Computer Science & Systems Engineering, Electronics &
Telematics, Electronics & Computer Engineering, Production Engineering,
Instrumentation & Control Engineering and Automobile Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Express the following system in matrix form and solve by Gauss elimination
method.
2x1 + x2 + 2x3 + x4 = 6; 6x1 - 6x2 + 6x3 + 12x4 = 36,
4x1 + 3x2 + 3x3 - 3x4 =- 1; 2x1 + 2x2 - x3 + x4 = 10.
(b) Show that the system of equations 3x + 3y + 2z = 1; x + 2y = 4;
10y + 3z = - 2; 2x - 3y - z = 5 is consistent and hence solve it. [8+8]
2. Determine the eigen values and the corresponding eigen vectors of the matrix A,
where A =
2
4
1 0 −2
0 0 0
−2 0 4
3
5 [16]
3. Reduce the quadratic form 3x2+5y2+3z2-2yz+2zx-2xy to the canonical form and
specify the matrix of transformation. [16]
4. (a) Find a positive root of the equation by bisection method: x3 - 4x - 9 = 0
(b) Find the positive root of x3 = 2x + 5 by False Position method. [8+8]
5. (a) It is known that x, y are related by y =a
x + bx and the experimental values
are given below:
x: 1 2 4 6 8
y: 5.43 6.28 10.32 14.86 19.5
Obtain the best values of a and b.
(b) Find the first two derivatives of the function tabulated below at x=0.6
x: 0.4 0.5 0.6 0.7 0.8
y: 1.5836 1.7974 2.0442 2.3275 2.6511
[8+8]
6. Find y(0.1), y(0.2), z(0.1), z(0.2) given dy
dx = x + z, dz
dx = x − y2 and y(0) = 2, z(0)
= 1 by using Taylor’s series method. [16]
7. (a) Find the Fourier sine transform of e−ax cosx.
(b) Find the Fourier cosine transform of x.e −ax. [8+8]
1 of 2
Code No: Z0224/R07 Set No. 1
8. (a) Solve (x+y)p+(y+z)q=(z+x).
(b) Solve the difference equation, using Z-transform y(k+2)-2cos.y(k+1)+y(k)=0,
given y(0)=1, y(1)= 1. [8+8]
? ? ? ? ?
2 of 2
Code No: Z0224/R07 Set No. 2
I B.Tech Supplementary Examinations, November 2009
MATHEMATICAL METHODS
( Common to Electrical & Electronic Engineering, Mechanical Engineering,
Electronics & Communication Engineering, Computer Science &
Engineering, Electronics & Instrumentation Engineering, Bio-Medical
Engineering, Information Technology, Electronics & Control Engineering,
Mechatronics, Computer Science & Systems Engineering, Electronics &
Telematics, Electronics & Computer Engineering, Production Engineering,
Instrumentation & Control Engineering and Automobile Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Express the following system in matrix form and solve by Gauss elimination
method.
2x1 + x2 + 2x3 + x4 = 6; 6x1 - 6x2 + 6x3 + 12x4 = 36,
4x1 + 3x2 + 3x3 - 3x4 =- 1; 2x1 + 2x2 - x3 + x4 = 10.
(b) Show that the system of equations 3x + 3y + 2z = 1; x + 2y = 4;
10y + 3z = - 2; 2x - 3y - z = 5 is consistent and hence solve it. [8+8]
2. For the matrix A =2
4
4 1 0
1 4 1
0 1 4
35
, determine matrix P such that P−1 AP is a
diagonal matrix. [16]
3. (a) Show that every square matrix can be expressed as a sum of Hermitian and a
skew Hermitian matrix.
(b) If A=2
4
2 + 3i 1 − i 2 + i
−2i 4 2i
−4i −4i i
35
, then find a skew Hermitian matrix. [8+8]
4. (a) Find a positive root of x4 - x3 - 2x2 - 6x - 4 =0 by bisection method.
(b) Find an approximate root of x log10x - 1.2 = 0 by Regula False method.
[8+8]
5. (a) Fit a second degree parabola to the following data:
x: 0 1 2 3 4
f(x): 1 1.8 1.3 2.5 6.3
(b) The velocity v of a particle moving in a straight line covers a distance x in
time t. They are related as follows: Find f0 (15).
x: 0 10 20 30 40
v: 45 60 65 54 42
[8+8]
6. Find y(0.1) and y(0.2) from dy
dx = xy + y2, y(0) = 1 by using Runge-Kutta method
and hence obtain y(0.4) using Adam’s method. [16]
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Code No: Z0224/R07 Set No. 2
7. Find the Fourier Transforms of f(x) = a2 − x2; |x| < 1
0; |x| > 1
Deduce that
1
R0
sin t−t cos t
t3 dt =
4. Using Parseval’s identity prove that
1
R0
( sin t−t cos t
t3 )2dt =
15 . [16]
8. (a) Form the partial differential equations by eliminating the arbitrary constants
i. x2 + y2 + (z − c)2 = a2
ii. z=(x2+a)(y2+b)
(b) Find the Z-transform of the sequences {x(n)} where x(n) is
i. !1
3 n
ii. (3)n cosn
2 . [8+8]
? ? ? ? ?
2 of 2
Code No: Z0224/R07 Set No. 3
I B.Tech Supplementary Examinations, November 2009
MATHEMATICAL METHODS
( Common to Electrical & Electronic Engineering, Mechanical Engineering,
Electronics & Communication Engineering, Computer Science &
Engineering, Electronics & Instrumentation Engineering, Bio-Medical
Engineering, Information Technology, Electronics & Control Engineering,
Mechatronics, Computer Science & Systems Engineering, Electronics &
Telematics, Electronics & Computer Engineering, Production Engineering,
Instrumentation & Control Engineering and Automobile Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Find the rank of
0BB@
2 −4 3 −1 0
1 −2 −1 −4 2
0 1 −1 3 1
4 −7 4 −4 5
1CCA
(b) Solve the system of equations 3x+y+2z =3, 2x-3y-z= -3, x+2y+z=4. [8+8]
2. (a) Determine the eigen values and eigen vectors of the matrix A= 5 4
1 2
(b) If A = 2 0
0 1 , find A100 [8+8]
3. Reduce the quadratic form 3x2 - 2y2 - z2 + 12yz + 8zx - 4xy to canonical form by
an orthogonal reduction and state the nature of the quadratic form. [16]
4. (a) Find a positive root of the following equation by bisection method
x3 - x2 - 1 = 0
(b) Find the interpolating polynomial f(x) from the table
x 0 1 4 5
f(x) 4 3 24 39
[8+8]
5. (a) Fit a curve of the form i(d) = adn for the data:
d: 1720 2300 3200 4100
i(d): 655 789 1000 1164
(b) Evaluate
3
R0
dx
1+x3 using Simpson’s one-third rule, by dividing the range by
choosing h=0.5. [8+8]
6. Evaluate the values of y(1.1) and y(1.2) from y00 + y2y0 = x3; y(1)=1, y0 (1)=1 by
using Taylor series method. [16]
7. Find the Fourier Transforms of f(x) = e−| x| and deduce that
1
R0
cos xt
1+t2 dt =
2 e−|x | .
Hence show that F(xe−|x | )=i q2

2s
(1+s2)2 . [16]
1 of 2
Code No: Z0224/R07 Set No. 3
8. (a) Form the partial differential equations by eliminating the arbitrary constants
i. x2 + y2 + (z − c)2 = a2
ii. z=(x2+a)(y2+b)
(b) Find the Z-transform of the sequences {x(n)} where x(n) is
i. !1
3 n
ii. (3)n cosn
2 . [8+8]
? ? ? ? ?
2 of 2
Code No: Z0224/R07 Set No. 4
I B.Tech Supplementary Examinations, November 2009
MATHEMATICAL METHODS
( Common to Electrical & Electronic Engineering, Mechanical Engineering,
Electronics & Communication Engineering, Computer Science &
Engineering, Electronics & Instrumentation Engineering, Bio-Medical
Engineering, Information Technology, Electronics & Control Engineering,
Mechatronics, Computer Science & Systems Engineering, Electronics &
Telematics, Electronics & Computer Engineering, Production Engineering,
Instrumentation & Control Engineering and Automobile Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Express the following system in matrix form and solve by Gauss elimination
method.
2x1 + x2 + 2x3 + x4 = 6; 6x1 - 6x2 + 6x3 + 12x4 = 36,
4x1 + 3x2 + 3x3 - 3x4 =- 1; 2x1 + 2x2 - x3 + x4 = 10.
(b) Show that the system of equations 3x + 3y + 2z = 1; x + 2y = 4;
10y + 3z = - 2; 2x - 3y - z = 5 is consistent and hence solve it. [8+8]
2. (a) Find the eigen values and eigen vectors of the matrix A =2
4
3 1 4
0 2 6
0 0 5
35
(b) If A = 1 0
0 3 , find A256. [8+8]
3. Reduce the quadratic form 3x2 - 2y2 - z2 + 12yz + 8zx - 4xy to canonical form by
an orthogonal reduction and state the nature of the quadratic form. [16]
4. (a) Using Lagrange’s formula, fit a polynomial to the data
X: 0 1 3 4
Y: -12 0 6 12
Also find y at x =2.
(b) If the interval of differencing is unity, prove that tan−1 n−1
n = tan−1 1
2n2 .
[8+8]
5. (a) Fit a curve of the form i(d) = adn for the data:
d: 1720 2300 3200 4100
i(d): 655 789 1000 1164
(b) Evaluate
3
R0
dx
1+x3 using Simpson’s one-third rule, by dividing the range by
choosing h=0.5. [8+8]
6. (a) Using Euler’s method, find y(0.2), y(0.1) given y0= x2 + y2, y(0)= 1
1 of 2
Code No: Z0224/R07 Set No. 4
(b) Evaluate y(0.8) using R - K method given y0= (x+y)
1
2 , y = 0.41 at x=0.4.
[8+8]
7. (a) Find the Fourier sine transform of e−ax cosx.
(b) Find the Fourier cosine transform of x.e −ax. [8+8]
8. (a) Solve xp - yq=z
(b) Solve the difference equation, using Z-transform x(k+1)-2x(k+1)=1, given
x(0)=0. [8+8]
? ? ? ? ?
2 of 2
Code No: Y0821/R07 Set No. 1
I B.Tech Supplementary Examinations, November 2009
INTRODUCTION TO CHEMICAL ENGINEERING
(Chemical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) What is the role of chemical engineer in food processing industry.
(b) Explain briefly ideal solution.
(c) Write short notes on flotation. [6+4+6]
2. (a) Define heat capacity and explain how to calculate mean heat capacity for
gases.
(b) Differentiate between Cp and Cv and also write the relation between these two
for ideal gases.
(c) Write short notes on equivalent mass. [6+6+4]
3. (a) Describe the boundary layer formation on a flat plate for a fluid stream.
(b) State and explain the equation of continuity. [12+4]
4. (a) Explain the mechanism of heat transfer by conduction, convection and radia-
tion.
(b) Write the equation for the rate of heat flow by conduction. Explain the terms
in it?
(c) Write brief note on conductivities of solids, liquids and gases. [6+4+6]
5. (a) Explain mass transfer coefficient in terms of film coefficient.
(b) Discuss about the flux equation for diffusion in gases and diffusion in liquids.
[16]
6. (a) Explain with the help of suitable equations how to estimate the vapour and
liquid composition for flash distillation.
(b) How many ways the azeotropes are classified and how to separate them.[8+8]
7. (a) Write short notes on the fields of applications of liquid-liquid extraction.
(b) In a ternary extraction system, what are the solute, solvent, and carrier?
(c) What you understand about solute and raffinate?
(d) Define and explain distribution coefficient. [4+4+4+4]
8. (a) Explain briefly adsorption equipment.
(b) Write expressions for Freundlich and Langmuir isotherms. [16]
? ? ? ? ?
1 of 1
Code No: Y0821/R07 Set No. 2
I B.Tech Supplementary Examinations, November 2009
INTRODUCTION TO CHEMICAL ENGINEERING
(Chemical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Differentiate between frothers and Depressors.
(b) What are the mixers used for mixing of dry powders.
(c) Differentiate between Dodge crushers and Blake crusher. [6+4+6]
2. (a) Explain a combined detailed flow diagram of process.
(b) State the different forms of energy associated with mass.
(c) What are the steps to follow in energy balance calculations? [4+4+8]
3. Explain the physical significance of Reynold’s number and describe Reynold’s ex-
periment. [16]
4. (a) Explain: convection, forced convection, Natural convection and heat transfer
coefficient
(b) Write the relation between overall heat transfer coefficient and individual heat
transfer coefficients. Also mention the meaning of various terms in it. [9+7]
5. (a) Name the two mass transfer operations for the following phases in conact:
i. liquid-liquid
ii. solid-vapour.
(b) Mention the similarities between various mass transfer operations.
(c) Mass diffusion exists between various mass transfer operations. Explain with
examples. [4+6+6]
6. Describe the criteria of selection of equipment for gas-liquid operation. [16]
7. Write the advantages or uses of:
(a) Mixer settlers
(b) Pulse column
(c) Spray column
(d) Rotating disc contactors. [4×4]
8. (a) Explain rotary drier with neat sketch.
(b) Explain process of humidification and dehumidification with suitable example.
[10+6]
? ? ? ? ?
1 of 1
Code No: Y0821/R07 Set No. 3
I B.Tech Supplementary Examinations, November 2009
INTRODUCTION TO CHEMICAL ENGINEERING
(Chemical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. Discuss briefly:
(a) Flotation
(b) Screening. [2×8=16]
2. Give details about humidity and saturation. [16]
3. (a) Differentiate between pseudo-plastic and Dilatant fluids with suitable example.
(b) What are the time dependent fluids and explain with suitable examples.
(c) Write salient points of one dimensional flow. [6+6+4]
4. Write about types of evaporators in details. [16]
5. (a) What are three main problems that exists when a gas and liquid flow through
a packed bed? Discuss indetail about their effect on mass transfer and suggest
ways of reading them.
(b) Write overall mole balance at steady state for designing a packed absorption
column, and explain the terms involved. [9+7]
6. Explain briefly:
(a) Venturi scrubber
(b) Spray column. [8+8]
7. (a) Write short notes on selection of liquid-liquid contactors.
(b) Write short notes on selection of disperse phase. [8+8]
8. (a) Define molecularity, order and rate of a reaction.
(b) Distinguish between elementary and non elementary reactions with suitable
examples. [9+7]
? ? ? ? ?
1 of 1
Code No: Y0821/R07 Set No. 4
I B.Tech Supplementary Examinations, November 2009
INTRODUCTION TO CHEMICAL ENGINEERING
(Chemical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Explain the electro mechanical operation.
(b) Differentiate between Geometric and Kinematic Similarities. [8+8]
2. (a) How do you classify energy associated with mass.
(b) Derive Kirchoff’s equation for effect of temperature on heat of reaction.[6+10]
3. (a) With the help of a neat figure discuss about the development of a boundary
layer on a flat plate.
(b) Write the expression for thickness of boundary layer if the boundary layer is
laminar and turbulent, respectively. [12+4]
4. (a) Define capacity and economy.
(b) Explain forward feed triple effect evaporator with suitable sketch. [6+10]
5. (a) Mass transfer may occurs in different ways, name any five.
(b) What are phenomena that must exists in a mass transfer opeartion.
(c) There are many similarities and differences between various mass transfer
operations mention them. [5+3+8]
6. (a) What is differential distillation? Derive Rayleigh equation.
(b) Explain briefly classification of gas-liquid contact equipment. [8+8]
7. Explain in detail about classification of industrial liquid-liquid contactors. [16]
8. (a) How many ways the crystallization takes place.
(b) What are the steps involved for crystallization to takes place?
(c) Write short notes on classification of crystallization equipment. [4+4+8]
? ? ? ? ?
1 of 1
Code No: Z1821/R07 Set No. 1
I B.Tech Supplementary Examinations, November 2009
ENGINEERING MECHANICS
( Common to Metallurgy & Material Technology and Aeronautical
Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. A 300 N vertical force is applied at the end of a lever which is attached to shaft at
O as shown in figure 1. Determine
Figure 1
(a) The moment of the 300 N force about O.
(b) The magnitude of the horizontal force applied at A which creates the same
moment about O.
(c) The smallest force applied at A which creates the same moment about O. [16]
2. A block of mass 200 kg resting on a horizontal surface supports another block of
100 kg as shown in figure 2. The smaller block is attached to string from the wall.
Find the horizontal force P just to move the 200 kg block to the left. μ = 0.35 for
all rubbing surfaces. [16]
Figure 2
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Code No: Z1821/R07 Set No. 1
3. Determine the width of a 9.75 mm thick leather belt required to transmit 15 kW
from a motor running at 900 r.p.m. The diameter of the driving pulley of the
motor is 300 mm. The driven pulley runs at 300 r.p.m. and the distance between
the centre of two pulleys is 3 meters. The density of leather is 1000 kg/m3. The
maximum allowable stress in the leather is 2.5 MPa. The coefficient of friction
between the leather and pulley is 0.3. Assume open belt drive and neglect the sag
and slip of the belt. [16]
4. A hemisphere of diameter 30 cm is symmetrically placed on top of a circular cylinder
of diameter 20 cm and height 30 cm. locate the center of gravity of the composite
volume. [16]
5. (a) Starting from the first principles determine the moment of inertia of a triangle
with respect to its base.
(b) Determine the radius of gyration for rectangle
i. about x axis and
ii. about its base. [8+8]
6. The horizontal component of velocity of a projectile is twice its vertical component.
Find the range on the horizontal plane through the plane of projection if the pro-
jectile passes through a point 18 m horizontally and 3 m vertically above the point
of projection. Determine also initial velocity of the projectile. [16]
7. Two blocks are joined by an inextensible cable as shown in figure 7. If the system
is released from rest, determine the velocity of block A after it has moved 2 m.
Assume that μ equals to 0.25 between block A and the plane and that the pulley
is weightless and frictionless. [16]
Figure 7
8. A shaft 1.5 m long is supported in flexible bearings at the ends and carries two
wheels each of 50 kg mass. One wheel is situated at the center of the shaft and
the other at the distance of 0.4 m from the towards right. The shaft is hollow of
external diameter 75 mm and inner diameter 37.5 mm. The density of the shaft
2 of 3
Code No: Z1821/R07 Set No. 1
material is 8000 kg/m3. The Young’s modulus for the shaft material is 200 GN/m2.
Find the frequency of transverse vibration. [16]
? ? ? ? ?
3 of 3
Code No: Z1821/R07 Set No. 2
I B.Tech Supplementary Examinations, November 2009
ENGINEERING MECHANICS
( Common to Metallurgy & Material Technology and Aeronautical
Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Two forces are acting at a point O as shown in figure 1a. Determine the
resultant in magnitude and direction.
Figure 1a
(b) Three forces of magnitude 40 KN, 15 KN and 20 KN are acting at a point O
as shown in figure 1b. The angles made by 40 KN, 15 KN and 20 KN forces
with X-axis are 600, 1200 and 2400 respectively. Determine the magnitude and
direction of the resultant force. [8+8]
Figure 1b
2. (a) A wooden block weighing 30 N is placed on a horizontal plane. A horizontal
force of 12 N is applied and the block is on the point of moving. Find
i. Coefficient of friction
ii. Angle of friction and
iii. The resultant reaction.
(b) A block of weight 80 N is placed on a horizontal plane where the coefficient of
friction is 0.25. Find the force that should be applied to the block at an angle
of 300 with the horizontal to attain the condition of limiting equilibrium.[8+8]
3. The power transmitted between two shafts 3.5 metres apart by a cross belt dive
round the two pulleys 600 mm and 300 mm in diameters, is 6 kW. The speed of the
1 of 3
Code No: Z1821/R07 Set No. 2
larger pulley (driver) is 220 r.p.m. The permissible load on the belt is 25 N/mm,
width of the belt is 5 mm thick. The coefficient of friction between the smaller
pulley surface and the belt is 0.35. Determine necessary length of the belt, width
of the belt and necessary initial tension in the belt. [16]
4. Find the centroid of the shaded area shown in figure 4. All dimensions are in mm.
[16]
Figure 4
5. (a) Starting from the first principles determine the moment of inertia of a triangle
with respect to its base.
(b) Determine the radius of gyration for rectangle
i. about x axis and
ii. about its base. [8+8]
6. A bus starts from rest at point A and accelerates at the rate of 0.9 m/s2 until is
reaches a speed of 7.2 m/s. It then proceeds with the same speed until the brakes
are applied. It comes to rest, at point B, 18 m beyond the point where the brakes
are applied. Assuming uniform acceleration, determine the time required for the
bus to travel from A to B. Distance AB = 90 m. [16]
7. A spring is used to stop a 60 kg package which is sliding on a horizontal surface.
The spring has a constant k = 20 kN/m and is held by cables so that initially it is
compressed to 120 mm. Knowing that the package has a velocity of 2.5 m/s in the
position shown in the figure 7 and that the maximum additional deflection of the
spring is 40 mm, determine.
Figure 7
(a) The coefficient of kinetic friction between the package and the surface.
2 of 3
Code No: Z1821/R07 Set No. 2
(b) The velocity of the package as it passes again through the position shown. [16]
8. A shaft 1.5 m long supported in flexible bearings at the ends carries two wheels
each of 50 kg mass. One wheel is situated at the centre of the shaft and the other at
a distance of 375 mm from the centre towards left. The shaft is hollow of external
diameter 75 mm and the internal diameter 40 mm. The density of shaft material is
7700 kg/m3 and its modulus of elasticity is 200 GN/m2. Find the lowest whirling
speed of the shaft, taking into account the mass of the shaft. [16]
? ? ? ? ?
3 of 3
Code No: Z1821/R07 Set No. 3
I B.Tech Supplementary Examinations, November 2009
ENGINEERING MECHANICS
( Common to Metallurgy & Material Technology and Aeronautical
Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. A 300 N vertical force is applied at the end of a lever which is attached to shaft at
O as shown in figure 1. Determine
Figure 1
(a) The moment of the 300 N force about O.
(b) The magnitude of the horizontal force applied at A which creates the same
moment about O.
(c) The smallest force applied at A which creates the same moment about O. [16]
2. (a) A wooden block weighing 30 N is placed on a horizontal plane. A horizontal
force of 12 N is applied and the block is on the point of moving. Find
i. Coefficient of friction
ii. Angle of friction and
iii. The resultant reaction.
(b) A block of weight 80 N is placed on a horizontal plane where the coefficient of
friction is 0.25. Find the force that should be applied to the block at an angle
of 300 with the horizontal to attain the condition of limiting equilibrium.[8+8]
3. Determine the width of a 9.75 mm thick leather belt required to transmit 15 kW
from a motor running at 900 r.p.m. The diameter of the driving pulley of the
motor is 300 mm. The driven pulley runs at 300 r.p.m. and the distance between
the centre of two pulleys is 3 meters. The density of leather is 1000 kg/m3. The
maximum allowable stress in the leather is 2.5 MPa. The coefficient of friction
between the leather and pulley is 0.3. Assume open belt drive and neglect the sag
and slip of the belt. [16]
1 of 3
Code No: Z1821/R07 Set No. 3
4. In a rectangular plate 10 cm × 12 cm, as shown in figure 4 a rectangular opening
PQRS 3 cm × 12 cm, is made. Find the centroid of the plate after the opening is
made. [16]
Figure 4
5. Calculate the mass moment of inertia of thin plate shown in figure 5 with respect
to the axis X-X.Take mass of the plate as m. [16]
Figure 5
6. A bus starts from rest at point A and accelerates at the rate of 0.9 m/s2 until is
reaches a speed of 7.2 m/s. It then proceeds with the same speed until the brakes
are applied. It comes to rest, at point B, 18 m beyond the point where the brakes
are applied. Assuming uniform acceleration, determine the time required for the
bus to travel from A to B. Distance AB = 90 m. [16]
7. Two blocks are joined by an inextensible cable as shown in figure 7. If the system
is released from rest, determine the velocity of block A after it has moved 2 m.
Assume that μ equals to 0.25 between block A and the plane and that the pulley
is weightless and frictionless. [16]
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Code No: Z1821/R07 Set No. 3
Figure 7
8. A cantilever shaft 50 mm diameter and 300 mm long has a disc mass 100 kg at its
free end. The young?s modulus for the shaft material is 200 GN/m2. Determine
the frequency of longitudinal and transverse vibrations of the shaft. [16]
? ? ? ? ?
3 of 3
Code No: Z1821/R07 Set No. 4
I B.Tech Supplementary Examinations, November 2009
ENGINEERING MECHANICS
( Common to Metallurgy & Material Technology and Aeronautical
Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. Find the reaction at the supports A, B of the beam shown in figure 1. [16]
Figure 1
2. The cutter of a broaching machine is pulled by square threaded screw of 55 mm
external diameter and 10 mm pitch. The operating nut takes the axial load of 400
N on a flat surface of 60 mm internal diameter and 90 mm external diameter. If
the coefficient of friction is 0.15 for all contact surfaces on the nut, determine the
power required to rotate the operating nut, when the cutting speed is 6 m/min.
[16]
3. An open belt running over two pulleys 240 mm and 600 mm diameter connects
two parallel shafts 3 metres apart and transmits 4 kW from the smaller pulley that
rotates at 300 r.p.m. Coefficient of friction between the belt and pulley is 0.3 and
the safe working tension is 10 N per mm width. Determine the minimum width of
the belt, initial belt tension and length of the belt required. [16]
4. Determine the centroid of the section shown in figure 4. [16]
Figure 4
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Code No: Z1821/R07 Set No. 4
5. (a) Starting from the first principles determine the moment of inertia of a triangle
with respect to its base.
(b) Determine the radius of gyration for rectangle
i. about x axis and
ii. about its base. [8+8]
6. A bus starts from rest at point A and accelerates at the rate of 0.9 m/s2 until is
reaches a speed of 7.2 m/s. It then proceeds with the same speed until the brakes
are applied. It comes to rest, at point B, 18 m beyond the point where the brakes
are applied. Assuming uniform acceleration, determine the time required for the
bus to travel from A to B. Distance AB = 90 m. [16]
7. A spring is used to stop a 60 kg package which is sliding on a horizontal surface.
The spring has a constant k = 20 kN/m and is held by cables so that initially it is
compressed to 120 mm. Knowing that the package has a velocity of 2.5 m/s in the
position shown in the figure 7 and that the maximum additional deflection of the
spring is 40 mm, determine.
Figure 7
(a) The coefficient of kinetic friction between the package and the surface.
(b) The velocity of the package as it passes again through the position shown. [16]
8. Determine the natural frequency of the free longitudinal vibrations of a contilevel
beam by equilibrium method and Rayleigh’s method. [16]
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