Physics Stream (2012-July) Question Papers

USN fiPHYtA22

FirsUSecond Semester B.E. Degree Examination, Jtne 2Ol2
Engineering Physics

Time: 3 hrs. Max. Marks: 100

Note: 1. Answer any FIVE questions, choosing at lcast two frorn each part.
full
I L Answer all objective type questions only on OMR sheet page 5 of the answer booklet.
3. Answer to objective type questions on sheets other than OMR will not be valued.
o; 4. Constants to be given, ma.ss of electron = 9.11 x lT3tkg, e = 7.6 x IUIeC,
c =3 xldm/s, h=6.626 xlo'3alS, k= 1.38 x1a23 J/k, t,=8.854 xlat2 F/m,
":tt
Na = 6.022 x 1d6/K mole.
PART -A
I a. Choose your answers for the following : (04 Marks)
i) U(traviolet catastrophe is the failure of Rayleigh-Jeans law in explaining the
oB black-body radiation for wavelength.
A) equal to that in visible range B) longer than that of violet light
C) shorter than that of violet light D) None of these
iD Photo-electriceffectestablishes
A) wave nature of light B) particle nature of Iight
.9r! C) dual nature of light D) None of these
iiD Ifthe group velocity of the de-Broglie waves associated with a particle is 3 x l0a m/s,
the velocity of the particle is
-bB A) 3 x 108 m/s B) 3 x l0r2 m/s
C) 3 x 104 m/s D) None of these
iv) The Compton wavelength is giv.en by
d. 8_
A; h/moc2 B) h2lm.c2 C) h/moc D h2l2m,c
,n9
b. State de-Broglie hypothesis. Using the de-Broglie wavelength expression, show that an
d=
AE
.
alectron accelerated by a potential difference V vott is tr" = 'l.ZZ6 x lO-etJi (05 Marks)

EE c. Define group velocity and obtain expression for the same. (06 Marks)

6,Y d. Find the de-Broglie wavelength of an electron accelerated through a potential difference of
182 volts and object of mass 1 kg moving with a speed of (l m/s) compare the results and
comment. (05 Marks)

itr 2 a. Choose your answers for the following : (04 Marks)
o{ i) Ifthe uncertainity in momentum is large, the uncertainity in wavelength is
";.i A) Small B) Large C) Tero D) None of these
ii) Ifthe wave packet is narrow then there is
z A) Large uncertainity in momentum B) Small uncertainity in momentum
C) No uncertainity in momentum D) None of these
iii) An electron, a proton and an a-particle are enclosed in three one dimensional boxes of
the same width. The energy levels will be closer together for
A) Electron B) Proton C) Alpha particle D) None of these
iv) If the electron moves in one-dimensional box of length 2nm, the normalization
constant is
A) l(nm)-r12 B) 2(nm)
1
q kz,,l' D) None of these

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L0PIIYt2t22

b. State Heisenberg's uncertainity principle. Using uncertainity principle explain the
non-existence ofelectron in the nucleus. (07 Marks)
c. Set up time independent Schrodinger wave equation for free particle in one-dimension using
complex variables. Write the expression for zero point energy. (05 Marks)
d. A particle,moving in one-dimension box is described by the wave function
v=xp:l for o<x<t and
V=0 elsewhere

Find the probability of finding the particle within the interval
|
0.; I . (04 Marks)

3 a. Choose your answers for the following : (04 Marks)
i) In classical free electron theory, the electric field due to ion cores.
A) is neglected B) is assumed to be periodic
C) constant
is assumed to be D) None ofthese
ii) Mobility of electron is
A) reciprocal of electrical conductivity
B) acceleration ofelectron per unit ele. field
C) average drift velocity per unit electric field
D) None of these
iiD IfEF is the Fermi energy at absolute zero, then mean energy ofthe electron at absolute
zero is

elE=r.sr, srE=ie,
355 oE=3e, otE=]e"
iv) The resistivity of metals is due to scattering of electron by
A) phonons B) lattice imperfection
C) impurities D) All of these
b. Explain the terms
i) Relaxation time; ii) Mean collision time; iii) Drift velocity (06 Marks)
c. Define Fermi energy. Discuss the Fermi factor f(o) for cases E < Ee, E > Er at T = 0, E =Ee
at T + 0. (05 Marks)
d. Calculate the conductivity of sodium given r. = 2 x 10-raS. Density of sodium is 971
kg/mt3. its atomic weight is 23 and has one conduction electrorl/atom. (05 Marks)

i) The electric dipole moment per unit volume is
A) Magnetization B) Dipole moment
polarization
C) Electric D) Electric susceptibility.
iD The comparatively, high value oft, for water suggests that it is
A) Semi conductor B) Conductor
C) Di-electric D) Superconductor
iii) All materials have
A) Diamagnetic property B) Ferrimagnetic property
C) Ferromegnetic property D) Paramagnetic property
iv) In ionic solid dielectric as the temperature increases the ionic polarization
A) Increases B) decreases
C) remain constant D) None of these

2ol 4

I'
l

l

|$PHYt2t22

b. Derive Clausius-Mossotti equation. (05 Marks)
c. Describe any tkee polarization mechanisms with example. (06 Marks)
d. x
An elemental solid containing 2 lO28 atoms/mt3 shows an electronic polarizability of
x
2 '1040 Fmt2. Assuming a Lorentz force field to be operative, calculate the di-electric
constant ofthe material. (05 Marks)

PART-B
i) Spontaneous emission of light produces
A) coherent light B) incoherent light
C) unidirectional light D) None of these
ii) The He-Ne laser is a
A) high power continuous laser B) high power pulsed laser
C) low power continuous laser D) low power pulsed laser
iii) The life time of an atom in a metastable state is of the order of
A) a few seconds B) unlimited time
C) a nanosecond D) few milliseconds.
iv) From a broken hologram which is '10Vo of the original, if reconstruction of image is
being done, then
A) onty l07o of information of the object can be obtained.
B) complete information of the object is obtained.
C) no information of the object can be obtained.
D) None of these
b. Explain the terms
i) Resonant cavity; ii) Metastable state; iii) Stimulated emission. (06 Marks)
c. Describe the construction and working of He-Ne laser with the help of energy level diagram.
(06 Marks)
d. The ratio of population of two energy levels is 1.059 x 10-30. Find the wavelength of light
emitted at 330K. (04 Marks)

i) In a superconductor in superconducting state critical magnetic field
A) increases if temperature decreases B) increase with increase in temperature
C) does not depend on temperature D) remain content
iD If the optical fibre is kept in a medium of p > 1 instead of air, the acceptance angle
A)increases B) decreases
C) remains same D) None of these
iii) Attenuation in optic fibre is due to
A) absorption B) scattering
C) radiation loss D) all the above
iv) Numerical aperture ofan optical fibre depends on
A) acceptance angle B) 1 of cladding
C) q"o," of material D) AII of these
b. Discuss the different tlpes of optical fibres with suitable diagrams. (06 Marks)
Write a short note on Masslex vehicles. (05 Marks)
d. Calculate the N.A., V-number and number of modes in an optical fibre of core diameter
50pm, core and cladding refractive indices 1.41 and 1.4 at wavelength 820 nm.
(05 Marks)

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toPHYt2t22

7 a- Choose your answers for the following : (04 Marks)
i) A crystal oftetragonal lattice has
A) a=b=c B)a*b+c C)a--b+c D)a+b=c
ii) The relation between atomic radius r and lattice constant a in FCC structure is

A)a=2R nya=zJIR qu=4n
4J: ora=+n
iii) Packing factor of diamond crystal is
A) 34Ea B)527o C)68Vo D) 747o
iv)
Which of the following unit cells is a primitive cell?
A) Simple cubic B) bcc C) FCC D) None of these
b. Derive an expression for interplanar spacing in a cubic system. (05 Marks)
c. Explain how Bragg's spectrometer is used for determination of interplanar spacing in a
crystal. (06 Marks)
d. Calculat'e the energy of electron that produces Bragg's diffraction of first order at glancing
angle of 22o when incident on crystal with interplanar spacing of 1.8 Ao. (05 Marks)

i) The nanostructure reduced in only one direction is known as
A) quantumdot B) quantum wire
C) quantum well D) film
i, Fullerene is a
A) molecule B) atom
C) chemical mixture D) nano particle
iii) Testing ofa product without causing any damage is called
A) minute testing B) destructive testing
' testing
C) non-destructive D) random testing
iv) The signal due to a reflected wave is called
A) transmitted wave B) longitudinal wave
C) echo D) peaco
b. With simple illustration describe the two methods of preparation of nano materials.
(05 Marks)
c. What are the potential applications of carbon nanotubes? (05 Marks)
d. Describe in brief a method of measuring velocity of ultrasonic waves in a liquid. (06 Marks)

***r(*

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USN O6MAT11

First Semester B.E. Degree Examination, Jane 2Ol2
Engineering Mathematics - I
Time: 3 hrs. Max. Marks:100

E Note:l. Answer FIVE full questions choosing d.t least two from each pafi.
2. Answer all objective type questions only on OMR sheet page 5 of the Answer Booklet.
3. Answers to objective type questions on sheets other than OMR will not be valued.
I

I a. Choose the correct answer : (04 Marks)

o- i) The nth derivative of log[(3x + I )ee* * s] is
ri
3'(-l)*r(n - l)!
(A)
(3x + l)"
,",3"t-l)"nl
' (3x + I )"*'

(C) n!(-l)"
' (3x + 1)' (D) Zero.
o>
ii) If $ is the angle between radius vector and tangent to the curve r : f(0), then tan $ is
(A) 1 do (B) r !9 tCrr!! (D) 1g
rdr dr de rd0
iii) If r = e0 at 0 = 0, then the slope ofthe curve is
.ed (A) 0 (D% (C) I (D) I
2
iv) The angle between the radius vector and tangent for the curve r = o e0 'ot
o
is

(A) {B (C) r (D) a
o, 6-
I
l+a
3*
b. Find the nth derivative ofe cos2 6x. (04 Marks)

c. If y = tog11a tr[a (1+x2)y,*z + (2n+l )xy,+r * n2yn = g.
prove that (06 Marks)
^1 ,
d. Find the pedal equation ofthe curve r* = a'(cos m 0 + sin m 0). (06 Marks)

2a. Choose the correct answer : ((M Marks)

it Ifu=x2+y2then i'' ;. aqrr, ,o
' A*6y
(A) 2 (B) 0 (C) 2x+2y (D) x +y
.-.i c.j
iir ltu=,", fLl.,n.n*
"(yl 1*v9
0x'6y isequat ro
z (A) 2u (B) u (c) 0 (D) I
a iii) Ifx: r cos 0, y = r sin 0, then
(A) 9t=-!
dr */a*
(B) 9t=q
& dx
(C) 4=0
Ar
tD) None ofthese

iv) Ifan error of l7o is made in measuring its length and breadth, the percentage error in
the area of a rectangle is
A) .2?o (B) 2qo (C) (D l7o
'027o
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O6MAT11

u. Ir, = t""'($) n.ou" ttut *4*rfr =]'i, 2,. (04 Marhs)

c. tf z=f1x, yr. x = e'+ e' and y = e-'+ eu, show that ' ?-?--?-r* 106Mar&sr
au dv dx 'Ay
d. If u= x+y+z.v=x2+ y2+r' . * =xy +yz+zx. findl[u.''w). (06 Marksr
I J
^,y..
a. Choose the correct answer : ((X Marks)
n/
i) The value of f ' cos, xdx is
-h
(A) 14
35
(s) i2
35
(c) Zero e) l:1
128

ii.1 The value of f' n.
,, dx is
b 1l + x, )/2

(A)
G
4
l5
(B)2
l5 2
(c) :1 @) l:
iii) If the equation ofthe curve remains unchanged after changing 0 by -0, the curve
r: f(0) is symmetrical about
(A) Initial line (B) the pole
(c) Symmetry does not exist (D) None of these.
iv) J
I tant odo =
0

/r
(A) 2loe2 (B) 2 log 2-1 1Ct 1t2log 2-ly tD)loslal
'[e/
b. Obtain the reduction formula for Jsec"
xdx. ((N Ma*s)

c. Evaluate I x,J2ax-*, dx. (06 Marks)
f)

d. 'Trace the curve a2y2 = x21g,2 - x.z). (06 Marks)

a. Choose the correct answer: (04 Marks)

i) lfr = f(0) be the polar curve. th"n S i,
dr
(A' (D) None of these
[,,.(edJ
ii) The area bounded by the curve y = f(x), the x - axis and the ordinate x = a and x = b is
ta) Iyav rnr (O (D) None of these
frax fvo*
iii) The length of the cuwe y = y *)'4 b"t*""nx = I andx=4is

5.1*rr.1 6 -2xl Gt ?st
(A) ?g,t ?$z @)
:r Zzt
g
i9 If
r1-,"px] iseeualto

(A) f 9rt*, ora* (B) .l
lan*. ou*
t dcl da
to fartx,clao
(D) None of these.

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O6MAT11

b. If x =aeisint, y= ae'cost,find ((X Marks)
*.
c. Find the surface ofthe solid formed by revolving the cardiode r = a(1+cos 0) about the
initial line. (06 Marks)

d. Evaluatef,g'(l-e "-)dx,whenc > -1 by differentiating under the integral sign. (06 Mart<s)

PART. B
a. Choose the correct answer: (04 Mad(s)
i) The general solution ofxdy- ydx = 0 is
(A) x+y=s (B) xy=c (C) y=xc (D) None of these
ii) !I
The integrating factor of the differential equation
'dx *' +y= l is

(A) +
x
(B) toe x (C) e t*
1/
(D) None of these
iii) The homogeneous differential equation M(xy) dx + N(xy) dy = g san be reduced to a
differential equation in which the variables are separated by the substitution
(A) x+y=v (B) x = v/y (C) y=vx (D) y-x=v
iv) The equation y - 2x = c represents the orthogonal trajectories of the family
(A) y=ae2* (B) x+2y=c (C) xy=a (D) x2+2y2=a
b. Solve cos(x+y+l) dx - dy = 0. (M Marks)

c. Solve (l+ (t - *ty) oy -- u. (06 Marks)
d. "%1dx+ "t
Show that the orthogonal trajectories of the family of cardiode r = a c osz (f) is another
family of cardiod e r =b sin2 (%). (06 Marts)

a. Choose the correct answer : (04 Marks)

i) Let Iu, be a series of +ve terms. Given that Iun is convergent and u;.o 1i.14g1is6s
n_- Un

. then the said limit is
(A) Necessarily equal to one(B) Necessarily greater than one
(C) May be equal to one or less than one (D) Necessarily less than one.
.)1t5
lll I ne Serles :*-:+----a+ '""' ls
lj ,j ']r 4:
(A) Conditionally convergent (B) Absolutely convergent
(C) Divergent (D) None of these.
iii) Which one of the following series is not convergent?
tnr -L+-L*-L*..... (B) 1-1+1-q+.....
2.12 3J3 4J4 2345
tcl l-1-1-1.
23 4 5
(D) x + x2 + x3+ .... where lxl < l.
iv) If Iun is +ve term infinite series and if lim u, = 0, then Iu, is
(A) Convergent (B) Divergent
(C) Either convergent or divergent (D) Oscillatory.
b. Find the nature ofthe series 2* 4* 6 *..... (04 Marks)
1.2.3 2.3.4 3.4.5

c. Test for convergence of the ss1;gs ; 1a
1
1i 6 x211!2*3....... , 1v g.
x (0,6 Marks)
7 7.tO .4.5 7

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O6MAT11

Define absolute convergence and conditional convergence. Is the series
,- | - |
' |-
conditionallyconvergenl.? (06 Marks)
zTz-iTt-iTq-'
Choose the conect answer : (04 Marks)
i) Ifcos o , cos B , cos y be the direction ratios ofthe line, then sin:a + sin2p + sin2y =
(A) z (B) 6 (c) 4 (D) 8
ii) The angle between the two planes 2x y
- - 32 = 5 and x +3y-22+6=0is
(A) 600 (B) 9oo (C) cos '1 s ; (D) None of these
t4
iii) The angle between any two diagonals ofa cube is
(N % 181 tan't( /r'1 G)
cot't(
N) @) colt1/y
iv) The equation ofa straight line parallel to the x - axis is given by
(A) x-a-y-b-z-c 13)
x-a Y-b z-c
-
llt 0ll
rCr x-l y-b z-c rllt x-a _ y-b z-c
loo 001
b. Find the value ofk, such that the set of four points (l,l,0), (1,2,1), (4,5,6) and (3,0,k) are
coplandr. (04 Ma*s)
c. Find the equation of the plane passing through the line of intersection of the plane
2x+y-z= l,5x-3y+ 4z+3 x-l-v-2-z-3. (06 Mart<s)
=O and parallel to the 11n"
234
Find the shortest distance and its equation between the lines *O
*=5=i
x _y-9 z-2 (06 Marks)
-3 2

8 a. Choose the correct answer : (04 Marks)
i)The angle between the two surfaces $ (x,y,z) and ry(x,y,z) at any point (xr,yt,zr) is 0 -
141 51n-r(v6.vv) (B) Cos-r f vo.vv l
l.lvolivql ll"dF',ll
',",,un-r1v6.vy)
(D) None of these
li"oli"ti]
iD A unit tangent vectortothe surface x = t, y = 12. t= l.
z = tJ at
(A) (y, y,l (r : r.)
x 1g1
1.,'i' fi fil
(C) (."6, ,.,6.,./[) (D) None of these
iii) If A = 2x2i - 3yzj + xz2 k, then V.A is
(A) 4x-32+2xz (B) xi+yj+zk
(C) z(xi+4yj+3zk) (D) None of these.
iv) For any scalar $(x,y,z), the value of VxV{ is
(A) I (B) 0 (C) 2 (D) None of these
b. Find the directional derivative of{ = x2yz + 4xz2 at the point (1, -2, -l) in the direction of
the vector 2i-j - 2k. (M Marks)
c. If A is a vector function and Q is a scalar function then prove that
Curl (Q.I)=0(curl I)+gradSx L (06 Marks)

d. Find the constants a and b, so that F = laxy + z3)i + (3x2 - z)j + (bxz2 - y)k is irrotational
and find $ such that F= V0. (06 Marks)

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irl,rlfr<

USN 1OMAT2l

Second Semester B.E. Degree Examination. Jane 2Ol2
Engineering Mathematics - II
Note: 1. Answer FIVE full questions choosing at least two from each part.
Z Answer all objective type questions only on OMR sheet page 5 of the answer booklet.
3. Answer to objective tjpe questians on sheets other than OMR will not be valued.

PART-A
1. a. Select the correct answcr : (04 Marks)
i) We say that the given differential equation is solvable for x, if it is possible to
express x interms of
A) andy
x B) -xandpC) yandp D) x,yandp
ii) The general solution of P2 - 7P + 12=0is
A) (y+3x-c)(y+4x-c)=0 B) (y-3x-c)(y-4x-c)=0
C) (y-4x)(y+3x)=0 D) None of these
iii) The general solution of the equation y = 3x + log P is
A) Y=:x+3+ceY B) y=3x+log(3+ceY)
C) y+3x= 3+cey D) None of these
iv) The general solution of the equation (y - Px)2 = 4P2 + 9 is
A) y=cx+ 4c2 +9 B) Y="+ 4c2 +9
C) y=c x+.[aS-g D) y-c x=4c2+9
b. Solve: p2+ 2pycotx=y2. (05 Marks)
c. Solve : p2 + 4 xsp - l2xa y = 9, q61a1, the singular solution also. (05 Marks)
d. . Solve the equation (px - yt (py + x) = 2p by reducing into Clairaut's form, taking the
substitution X= x'. Y =y". (06 Marks)

2. a. Select fte correct answer : (04 Marks)
i) P.L of y" - 3y' +2y 12is :
I
A) 6 B)y=cre*+c2e2* C) |
ii)
'12
The complementary function of (Da - aal y = 6 ;5
D)
i
A) y = c r eu' + c2 e-u* + ca cos x +c4sin x
B) Y = cr e-u* + c2 e"*
C) y = c, eut + c2 e-u* + ca cos ax + c4 sin ax
D) None of these
iii.) If F(D) = D2 + 5, I s,in 2x= .......
f (D)

A) -cos2x B) cos 2x C) sin 2x D) cos 2x
22
iv) The solution of the differential equation y" - 3y' + 2y : s3* it
A) y=cr e-*+c2e2*+ !;* B) v=c,e'+c,e2*+ lei*
2

C) v = c, e-* + c, e2* + 1eJ*
-2 D) v=cre'*+cre2*+ 1el*
2
l of 5

lOMAT2T

b. Solve : (D -2)2 y=8(e2'+sin2x). (0s Marks)
c. Solve : y" - 2y' + y : x cos x. (05 Marks)

d. Solve *-Zy =.o"Zt, $+2x =sin 2t,giventhatx= l,y=0atr=0. (06 Marks)
dr"dt
3. a. Select the correct answer : (04 Marks)
i) The Wronskian of x and e* is
A) e*(1-x) B) xe* C) e-x(x-l) D) e- (x-l)
ii) In the equation sint+ 1, 9I* * ="o, t, if y= sin t+ I + e'r, then x = ....
#* r=
A) 0 B) e-t C) x e-t D) e'
iii) In homogeneous linear differential equation whose auxiliary equation has roots
l, -l is
A) y" +y:o B) x2y"-xy'-y=0
C) x2y"+xy'- y=Q D) y"-y':o
iv) The solution of x2 y" + xy' = 0 is
A) y=cr+c2 logx B) y=atogx+6 C) y=gr D) y=e-t
b. Using the method of variation of parameters solve y" + 4y = tan 2x. (05 Marks)
c. Solve: (l+x)2y"+ (1+x)y'+y=2 sin flog(1 +x)]. (0s Marks)
d. Solve by Frobenius method, the equation

4* d'X*2dY*r=t.t. (06 Marks)
dx' dx


of - ;
6'z
i)
' The solution ^
= sin (xy) is
Dv'

A) z= -x2.int*Vl * yf(x)+g (x) B) z= 99s(ID.+ y f(x) + Q (x)
x-
C) z=- sin( Iy) + y f(x) + 0 (x) D) None ofrhese
x-
ii) A solution of (y-zp+(z-x)q=x-yis
A) x2+ Vi+z!= f (x+y+z) B) x'- y'-r'=f (x-y+z)
C) x'-y'-z'=f(x-y-z) D) None ofthese
iii) The partial differential equation obtained form z = ax + by + ab by eliminating a
and b is
A) z=px+qy B) z=px+qy+pq
C) z=px+qy-pq D) z=px-qy-pq
iv) The partial differential equation obtained from z = f(x + y) + g(x - y) by
eliminating the arbitrary functions is
A) r+t=0 B) r-t=0 C) r-a2t=0 D) r+a2t=0
b. Solve !1*r=g,giurnthatwhenx =Q,2=gt N6
" I =1. (05 Marks)
0x' dx
c. Solve : (x2 - yz) p + (y2 - zx) q-- z2 - xy. (05 Marks)

d. Solve by the method of variables + $ * Idy = .lr, given that u(0, y) = 2 esv.
ax
(06 Marks)

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1OMAT21

PART -B

i) The vatue of .t.ll' * n' o* o, i,
l'
A)0 B)l c) ll
'2 D) 13

ii) The integral dx afterchangingtheorderof integration is
f i ;*
-6 .v
t[lao*o, f fl:]*0,
A) -_v
B)
"0 y t'y y
p p
D) | | :ax
.@ -! 6-y
C) I I :-dx dy
-,
ay
tb y tt y

iii, s [1.])=.....
' l) )l
.T
A) G ,, * c) 3.1416 D) -n

iv) In terms of Beta tunction
f .,"'rJ* d0 = ........

A) p@,1) u )o<+,lt c) pe,})
"> f,o<r,|t
)
b. Change the order ofintegration in y'dx dy and hence evaluate the same.
I
'o {*
(05 Marks)

c.' Evaluate e**Y*'dzdydx. (05 Marks)
{ f f.'
d. Showthat
fJsine
* fJ*,, or=,. (06 Marks)

a. Select the correct answer : (04 Marks)
i) In Green's theorem in the plane dx +n dy= ......
{m
A) r^r[ , e ]a* a,
' filf. ox "' B) ti[!ln-4')d. o,
ay )"" ay a* "'
lrl )""
., I(*-#).. * c) lfF. a o.

ii) The area of the eltipse = t by emptoying Green's theorem is
i. #
A)0 B)1 C)n D) r ab
iii) A necessary and sufficient condition that the line integral
JF. dR
forevery closed
L
curve C is
A) curlF=0 B) divF=0 C) curlF=O D) divF-0
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1OMAT21

iv) If V is the volume bounded by a surface S and F is continuously differentiable
vector tunction rhen
fff Oi" F dv = .....
A) { F.di
. J B) JJ n a, c)
[[F. fftv*n).n
)J'
os D) Noneof these
ess
b. If F = 2x y i + yz2 j + x z k and s is the rectangular parallelepiped bounded by x = 0,
y=0,2=0, x=2,y=1,2=3,evahate lJF. n O'. (05 Marks)
s

c. Using Green's theorem, evaluate Jt(V - sin x)Ox + cos x dy J, where C is the plane
c

triangleenclosed by the lines y =0. x =
I*Ot = ?. (05 Marks)

d. VeriSr Stoke's theorem for fr =1x2+ y21i-Zxy l taken around the rectangle
bounded bY the lines x = + n, Y = Q, Y = [. (06 Marks)

i) L {e2o-1)1 ='...
A) s-2I B, s-2 c)l s+2 ,,
' "-'
;',
ii; I 1th1 =.......
-r J;
A)g
./,
rl,21:
,/,
c)
,G o) rr_
2s/2
.... - [sin tl
ur) L<->= ......
trl
A) I+tan-r s B) 1 - .ot-' , C) cot-1 s D) tan-1 s
22
iv) L {6 (t+ 2)} = ......
A) e-u' B) e2' c) e-2' D) eu'

b. Find the value of l" C.-' sin t dt using Laplace transforms. (05 Marks)
+
Draw the graph of the periodic function
I t O<t<rr
f(tl = i and find its Laplace trans [orm. (05 Marks)
|.n-t. ,r<t<2rr
d. Prove thatL [6[t-a)J =e''. . (06 Marks)

8. Select the correct answer : (04 Marks)
^.
i, t,l--Ll,=
las' - 36J

A) lcos h 6t B) I
'4 sin 3t c) *to'n r' D) asin h: t
12

ii) Ir{l+e"}=
Is')
A) t+(t-3)u(t-3) B) (t-3)u(t-3)
C) t-(t-3)u(t-3) D) t+(t+3)u(t+3)
4of5

1OMAT21

iii)
' L'l lcor' 1I=
t a)

O, sin t B) .in, I t' sin h a t ,, sinh t
t , t
iv) L[{ rtrts(t-u)du]
A) f(t)g(t) B) f(s)g(s) c) f(s)-g(s) ,,
H
b. Find'{ed:*-} (osMarks)

c. Apply convolution theorem to evaluate
-,1 s2 I
(osMarks)
' {5';,x;-g}
d. Solve (D3 - 3D2 + 3D - 1) y = t2 e'. y(0) = l. y'(0) = 9, y" (O) = -2by Laplace
transform method, (06 Marks)

5 of 5

USN 10crvl3/23
FirsUSecond Semester B.E. Degree Examination, Jane 2Ol2
Elements of Givi! Engineering and Engineering Mechanics
Note: 1. Azsyer FIVE full questions choosing at least two Irom each part-
2. Answer all objective type questions only on oMR sheet page 5 of the answer booklet.
3. Answer to objective qpe questions on sheets other than oMR will not be valued.

PART-A
l. a. Select the correct answer : (04 Marks)
i) A Bascule bridge is a
A) Floating bridge B) Arch bridge
C) Suspension bridge D) Movable bridge
ii) Geotechnical engineering involves the study of
A) Water B) Soil c) Air D) All of rhese
iii) Pick up a structure in which an inspection gallery is formed
A) Dam B) Bridge C) Harbour D) Airporr
iv) The part ofcivil engineering which deals with waste water and solid waste is called
A) Transportation Engineering B) StructuralEngineering
C) SanitaryEngineering D) Surveying
b. Explain the role ofcivil engineer in the infra structural development ofa nation.
-
(06 Marks)
c. Explain different types ofroads. (06 Marks)
d. Give the difference between Earthen dam and gravity dam. (04 Marks)

2. a. Select the correct answer : ((X Marks)
i) The moment of a force about a moment centre is a measure of its
A) Translatory effect B) Rotational effect
C) Both A and B D) None of these
ii) Effect of force on a body depends on
A) Magnitude B) Direction C) Position D) All of these
iii) Couple means two forces acting parallel and
A) Equal in magnitude and in same direction
B) Not equal in magnitude but in same direction
C) Equal in magnitude but opposite in direction
D) None of these
iv) The magnitude of the moment is _ when a force is applied perpendicular to
a lever
A) Maximum B) Minimum C) Zero D) Negative
b. State and explain principle of transmissibility ofa force. (04 Marks)
c. Explain equivalent force - couple system. (04 Marks)
d. Determine angle 0 ( 0 < 0 < 1800) for the force F = 200N shown in fig.e2(d), so that it
produces (a) maximum moment about .A, and (b) minimum moment about .A,.
Determine maximum and minimum moments. (08 Marks)
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t0ctvt3t23

i) The process offinding the resultant ofa system of forces is called
A) Resultant B) Resolution C) Composition D) None of these
ii) If two forces P and Q (P > Q) act on the same straight line but in opposite direction
their resultant is

A) P+Q u, c) Q-P D) P_Q
;
iii)
Component of a force at a right angles to its line of action is
A) Tero B) Positive C) Negative D) None of these
:
iv) In a coplanar concurrent force system if XH 0, then the resultant is
A) Horizontal B) Vertical C) Moment D) None of these
b. The 26kN force is the resultant of two forces, one of which is shown in fig.Q3(b).
Determine the other force. (08 Marks)

Y^f 'l
I
Fie.Q3(b) l.2or,(

I
I
nie.e:t"r
'f-
5;olor

c. A rigid plate is subjected to the forces as shown in fig.Q3(c), compute resultant of
forces and position of resultant force with respect to centroid point '0' of the plate.
(08 Marks)

i) Centroid of semicircle of radius 'R' about its centroidal axis parallel to diametric
axis is
3R B)E 4R
c) _4R
D)
A)
4x 8t It J7T
;-
ii) An axis over which one half of plane figure is just mirror image of the other
half is
A)
Axis of symmetry B) Unsymmetrical axis
C) Bottom most axis D) None of these
iii) Moment oftotal area about its centroidal axis is
A) Twice the area B) Three times the area
C) Z,ero C) None of these
iv) The centroid ofa triangular lamina of height 'h' is situated at a distance from
its apex.
-
A)
h
3
B)?!
5L
c) ! ,r+
2of5

tocrvt3t23
b. Locate the centroid ofthe shaded area shown in fig.Q4(b), with respect to point '0'.
(08 Marks)
I*'k
ry
I
I

t",
r
I

Ir
rl
F_6oc Fie.Q4(c)

c. The centroid of the rectangular area requires to be shifted from point '0' to 01 (2 cms).
This is accomplished by removing hatch portion which is l2cm deep and symmetrical
about X X-axis. Determine area of hatched portion shown in fig.Q4(c). (08 Marks)

PART. B
i) The force which is equal and opposite to resultant is
A) Resultant force B)
Moment
C) Equilibrant D) None of these
ii) A particle acted upon by the two forces of equal magnitude is in equilibrium. The
angle between the forces is
A) 0o B) 9oo c) r800 D) 450
iii) The necessary condition of equilibrium of a coplanar concurrent force system is
algebraic sum of must be zero.
A) Horizontal and Vertical forces B) Moment of forces
C) Horizontal vertical and moment of forces
D) None of these
iv) Lami's equation can be applied when number of unknown forces are _
A) TWO B) Five C) Four D) Three
b. Determine the angle 0 for the system of strings ABCD in equilibrium as shown in
(08 Marks)

Fig.Qs(c)
Fie.Qs(b)

A cylinder of weight 600N rests on smooth surfaces as shown in fig. Q5(c). Determine
the reactions at contact points. The contact surfaces are perpendicular to each other.
(08 Marks)

6. a. Select the correct answer: (04 Marks)
i)A cantilever beam is one in which
A) Both ends are fixed B) Both ends are hinged
C) One end is fixed and other end is simply supported
D) One end is fixed and other end is free.
3 of 5

t0crYt3t23
ii) A truss is perfect when
A) m=2j-3 B) 2j=rna3 C) m=3j-Z D) 2j=6-3
iii) The minimum number of members to form a perfect truss is
A)l B)2 c)3 D)4
iv) The number of reaction components at an hinged end of a beam
A) zero B) 2 c)3 D)l
b. A pin joined truss is loaded and supported as shown infig.Q6(b). Determine forces in
members BC, GF and CG and nature of forces. Use method of section. (08 Marks)

ri KN
IOKN

5lr

I Fie.Q6(b) Fig.Q6(c)
Ir
E
c. Find the reactions for the beam supported and loaded as shown in fig.Q6(c).(0s Marks)

1 Select the correct answer : (M Marks)
i) Compared to static friction, kinetic friction is
A) greater B) smaller C) very large D) zero
ii) Frictional force acts _to the surfaces in contact
A) Tangential B) Normal C) Inclined D) None of these
iii) The force of fiiction depends on
A) Area of contact B) Roughness of surfaces
C) Both area of contact and roughness of surfaces
D) None of these
iv) At the point of impending motion, the static flictional force is
A) Zero B) Maximum C) Minimum D) Infinite
b. State laws of static friction. ((X Marks)
c. Briefly explain i) Angle of repose ii) Cone of ftiction. (04 Marks)
d. A ladder 7m long weighing 300N is resting against a wall at an angle of 600 to the
horizontal ground. A man weighing 700N climbs the ladder, at what position does he
induce slipping. Take p = 6.25 for all contact surfaces. (08 Marks)

8. Select the correct answer : (04 Marks)
i)Moment of inertia of a square of side 'b' about an axis through its centroid is

A)4
t2
B){8 c){
36
D){
l2
ii) Moment of inertia of a triangle of base 'b' and height 'h' about its base is

A) lli
36
B) !4
36
c)q
l2
D) Bh,
t2
iii)
The unit ofradius of gyration is
A)
mm B1 mmz C) KN- m D) mma
iv) Which of the following equation relating to radii of gyration is correct?
A) K-=K*+Kyy B) K--=&v+K-
q K'z- = rl-+ r'z, D) None of these
4of5

4i ,

t0crvt3t23

b. State and prove parallel axis theorem. (06 Marks)
c. Determine moment of inertia and radius of gyration of the area shown in fig.Q8(c),
about base AB and centroidal axis parallel to AB. (10 Marks)

Fie.Q8(c)

5 of 5

06cl-t3t23

FirsUSecond Semester B.E. Degree Examination, June 2Ol2
Elements of Givil Engineering and Engineering Mechanics
a Note: l. Answer any FIVE full questions, choosing at least two frorn each part.
Z Answer all objective Epe questions only OMR sheet, page 5, of the answer booklet.
3. Answers for objective type questions on sheets other than OMR will not be valued.
4. Missing data if any may be suitably assumed.

t:e PART -A
I a. Choose your answers for the following : (04 Marks)
o.. tt i) Temporary dams are called as
H"o
.E c't A) Earth dam B) Gravity dam
C) Coffer dam D) Diversion dam.
iD Boundary between carriage way and foot paths are
A) Traffic seperators B) Kerbs C) Shoulders D) Fencing
ctr
o,
iiD Bascule bridge is a
A) Deck bridge B) Through bridge
C) Semi-through bridge D) None of these
=.9
9?E
iv) Geo-technical engineering is also called as
A) Structural engineering B) Inigation engineering
C) Soil mechanics D) Hydraulics
.gd b. Explain impact of infrastructural facilities on socio - economic development of a country.
(06 Marks)
c. Explain briefly with neat sketches, gravity dam and earth dam. (06 Marks)
->a d. Draw simple sketch ofany two types ofbridges. (04 Marks)

o, 6-
6.J 2 a. Choose your answers for the following : (04 Marks)
i) An object which has only mass, but no size is called
qE A) Continuum B) Point force C) Particle D) Rigid body
;E
iD Moment of a force about a point is a measure of its
A) Rotational effect B) Translational effect
C) Irrotational effect D) None of these.
6i iii) A body which does not under go any deformation on application of force is
A) Deformable body B) Rigid body C) Elastic body D) Plastic body
iv) Two equal and opposite, parallel and non-collinear force constitute a
o< A) Point force B) Couple C) Both A and B D) None ofthese.
-i di b. Write any two Newton's laws of motion. What are the characteristics of a couple?
(05 Marks)
z c. State and explain the principle of transmissibility of a force. (03 Marks)
d. A system of forces is acting on a rigid body as shown in Fig. Q2(d), reduce this system to
E
i) a single force
ii) a single force and a couple at A
iii) a single force and a couple at B. (08 Marks)

Fig. Q2(d)
I of 4

06ctYt3t23
3 a- Choose your answers for the following : (04 Marks)
i) Lines of action of all forces pass through a single point and all forces lie in the same
plane. Such forces are called
A) Coplanar concurrent forces B) Coplanar non concurrent forces
C) Non coplanar concurrent forces D) Collinear forces.
iD The method to resolve a single force in two mutual perpendicular directions is called
A) Composition of forces B) Resolution of forces
C) Moment D) All of the above
iii)
Resultant of two forces shown in Fig. Q3(a) is
A) 1000 kN B) l400kN c) llo0kN D) l200kN

t'op.'oortx
A

Fig.Q3(a) Fig. 3(b) Fig. Q3(c)
iv) Two forces of equal magnitude P act at angle '0' to each other. What will be their
resultant?
A)Pcos 0/2 B) 2Pcos0 C) 2Pcos 0/2 D) Pcos0.
h. Two forces acting on a body are 500 N and 1000 N as shown in Fig. Q3(b). Determine the
third force F such that the resultant of all three forces is 1000 N directed at 45o to the
x-axis. (06 Marks)
c. Find the equilibrant with respect to A as origin for the system of forces shown in
Fig. Q 3(c). (10 Marks)

4a. Choose your answers for the following : (04 Marks)
i) Point where the whole weight of body acts at
A) Centroid B) Centre of gravity
C) Axis of reference D) Second moment of area
iD The distance of centroid of quarter circle from its diameters are

iii)
A)g )71
B)r
",+
Height of centroid ofa triangle ofheight 'h' from its base is
D)
3r
4tr

o,+ nr]rr ., 1 ,,+
iv) The centroid of a plane lamina will not be at its geometrical centre if it is a
A)Circle B) Right angled triangle
C) Rectangle D) Equilateral triangle
b. Locate the centroid of a semicircle by the method of integration. (06 Marks)
c. Locate the centroid of the shaded area shown in Fig. Q4(c). (10 Marks)

Fie. Q4(c)
2of4

06ctvt3t23
PART - B
i) Relation between action and reaction force is
A)They are equal in magnitude and opposite in direction
B) They have common line of action
C) Act perpendicular to the line of contact
D) All the above
ii)The non-applied forces are
A)Selfweight B) Reaction C) Both A and B D) None ofthese
iii) A force which nullifies the effect of forces is called
A) Equilibrium B) Equilibrant C) Resultant D) None of these
iv) A system that possesses a resultant
A) Will be in equilibrium B) Will be under rest
C) Not be in equilibrium D) None of these
b. State Lami's theorem. (02 Marks)
c. A sphere of weight 5 kN is supported by the Pully 'P' and 2 kN weight passing over a
smooth pully as shown in Fig. Q5(c). If o = 30', calculate the value of P and 0.
(06 Marks)

Fig. Q5(c) Fie. Qs(d)

, 4nu
d. A string is subjected to the forces 4 kN and P as shown in Fig. Q5(d). Determine the
magnitudes of P and tension forces induced in various portions of the string. (08 Marks)

i) A beam which has one end fixed and other end simply supported is called
A) Fixed beam B) Simply supported beam
C) Propped cantilever beam D) Cantilever beam
iD Ifthe intensity of load increases linearly along the length ofbeam, it is
A) Uniformly distributed load B) Uniformly varying load
C) Moment D) General loading
iii) A statically indelerminate beam is a
A) Cantilever beam B) Simply supported beam
C) Double over hanging beam D) Continuous beam
iv) A support, where two reaction components exist which are mutually perpendicular, is
A) Simple support B) Roller suppot C) Hinge support D) Fixed support.
b. Find the suppo( reaction for the cantilever beam loaded as shown in Fig. Q6(b). (os urarts)

k 5h;+- 5m _?k* 4m -r+ _ _4h , k-1m
k_1m _r+-_
+- 3llr-----,r+-, t,5mJ
3n______?t_, r,5mJ
Fig. Q6(b) Fie. e6(C)
Q6(C)
c. Determine the reaction at the supports A and B for a beam loaded as shown in Fig. e6(c).
(08 Marks)
3 0f 4

06crYt3t23
i) Friction acting on a body which isjust on the point or verge of sliding is called
A) Limiting friction B) Sliding friction
C) Co-efficient of friction D) Cone friction
iD Friction acting on a body when the contact surfaces are completely separated by
lubricant is called.
A) Non viscous fiiction B) Film fiiction c) Viscous friction D) Dry friction
iii) Friction force always acts
A) Opposite to the motion of the body B) Along the motion of the body
C) Peryendicular to the motion D) None of these
iv) The coefficient of friction is equal to
A) The tangent ol cone of fliction B) The tangent of angle of fiiction
C) The tangent of angle of repose D) The ratio of resultant to normal.
b. State the laws of fiiction (04 Marks)
c. Define: i) Angle of fiiction ii) Co-efficient of striction. (02 Marks)
d. A block weighting l0 kN is to be raised by means of 20o wedge as shown in Fig. Q7(d).
Find the horizontal force P, which will just raise the block. Assume co-efficient of friction
for all surfaces of contact is 0.3. Neglect weight of wedge. (10 Marks)

Fie. Q7(d)

8 a. Choose your answers for the following : ((X Marks)
i) Area moment of inertia is
A) First moment of area B) Second moment of area
C) Radius of gyration D) Area of cross section
iD Radius of Gyration is given by

A) K=# B)K=F c) K= D) K=IxA
iii) Moment of inertia of a triangle about its base is

A) Dn
36
B) bhl
t2
oq
'48 D)u
iv) - -16
Algebraic sum of first moment of elemental areas of plane figures about centroidal
axis is always
A) Unity B) 7,ero
C) Total area of elements D) Moment of inertia.
b. State and prove perpendicular axis theorem. (04 Marks)
c. Determine the second moment ofarea and radius of gyration about the horizontal centroidal
axis for the shaded area shown in Fig. Q8(c). (12 Marks)

1
Rr = 20 mm,
I Rz = 50 mm,
Rr = Radius of circle,
+
Rz = Radius of semi circle
Fie. Q8(c)

4of4

lmDo.lml Note : l. On compleLiig you eswqs, compul$rily dEs diagonal aos! lincs on rhe maining blMk pages,
I Any Ev€aling ol idenlif4alion, appeal lo evalualor od /or equations wrnLen eg. 42+8 = 50. wil be rreated as malprctice,

9.a a. =t =' :?
: ,,8 I 5ll I
-
z

"r
q9 r'O>UO>> o "a

iii
@ !] r=;-.lEa
q : H! eLq
5 s-zAitrdx
F=g
:6
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4 = e i6;? -#.;q;es!': Zi x.i.q st
6 P,
?3
ro { df
f ::,:3 6 9:-6
La
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P-d ,=
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f
?.
;
e+'d5- 2 3 iB
*-a Etir e *? "$si :*
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a : it:-S
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? ':se d,i
E,sE sE ui0 e P = yse.vs* tS$
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56 =
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odE
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