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14 TRIBHUVAN TJNIVERSITY
INSTITUTE OF ENGINEERING
Examination Control Division
2075 Ashwin
BEL,BEX,BCT, I
eailin n6. e. ni.i "P^ Marks
(sH402)
Candidates are required (^) to give their answers in their own words (^) as far as practicable.
Attempt All questions.
Thefigures in tlw margin indicate Full Morks.
Assume suitable data if necessary.
l) (^) Deduce dre time penod of a simple harmonic vibration. Explain why a loaded bus is more .comfortablc than^ an^ empty^ bus.^ (3+2)
- (^) Explain forced oscillation with its (^) differentiat equation.:Write the relation for the frequency dependent amplitrde and hence give (^) a rough sketch of trc resonance curve. (3+z)
Or
Calculate the average arnplitude of a sinusoidal sound wave in air of a frequency of 1.5 KFlz
and average intensity (^) l0-5Wcm2, where density of air is l.29kglm3 (i)
- (^) Give (^) ?n account of bad acoustic properties of a hall (^) and discuss tlre method to improve these defects. (^) (j)
- Explain the physical (^) meaning of Dispersive and resolving powers (^) of a (^) Grating Two spectral
lines have wavelengths x. and }u+Al respectively where al, <<L Show that their angular
separation A0 in (^) a grating (^) spectrometer ;5 (^69) $, where'd' dnd (^) 'rn' are grating J(#'-t' elements and no. oforder respectively. 0r
1z+3)
In newton's ring experiment, "Central spot is (^) dark in (^) reflected system' and (^) "Fringes get closer as the no. of order increased" explain. Is it possible to make central spot bright in reflected system? lf so how? (3+2)
A soap film (^) 5*10-s cm thick is viewed at an angle of 35o to the normal. Find the wavelength of the visible light which will be absent from (^) the reflected lighr (5)
Light of wavelength 580nm falls on a calcite crystal ofcertain thickness. Thg emerging light is bircularly polarized. What must be the thickness of such crystal? (5)
Calculate the focal length sf combination oftwo thin lenses of focal length fr and fz separated by a distance'd'. Find the position of two principal points. (5) t
8) Trace the ray diagiarn that shows the propagation of light.through the step and graded index
optical fiber. Write the importance of self-focusing in an^ optical fiber. (3+2)
,'i
- Ctrarge (^) of uniform (^) deirsity p=3.2pClm2 (^) fills a non+o.nducting (^) solid (^) sphere ofradius of 5. cm.What (^) is the magnitude (^) of the electric (^) field a) at 3.5 crh (^) U) S.O cm irom (^) the sphere's center
Or
Two large parallel (^) ptates are (^) separatd by (^) a distance of Scm.The ptates have (^) equal but opposite (^) charges (^) that create an electric fietd (^) in the region between (^) the plates. An alpha particle (^) (q= 3.2+10'le.C, ttl= 6.68*10'2?kg) (^) is reteased from the positivbty'charged it ilate,^ and
strikes the negatively charged plate 2* 106 sec tater. Assuming that the etectric field .
between (^) plates is (^) uniform and perpendicular to the plateq whatis (^) the strength (^) of electrie field?
(5)
(s)
l0) Calculate (^) the potential (^) at a point (^) due to a uniform line (^) of charge of (^) length L at a distance D fmm (^) its one end which (^) lies in (^) the perpondicular (^) line. -^ :^ (S)
I l) Explain how electric energy is stored in (^) a capacitor and derive (^) an expression for energy density (^) of electric field.
e+3)
- Explain (^) super conductivity (^) and its types with (^) examples. Write (^) the differenc{s) (^) betrveen superconductorandperfect gonductor.
e+Z)
t3) (^) If a test charge (^) revolves round a (^) circuiar path of radius 8.5cm where the magnetic (^) field increases (^) at steady rate (^) 0. | 3Tls, calcufate the magnitude of induced electric field (^) at a point 12.5 cm? (^) (5)
t4) Derive expression (^) for inductances (^) of a solenoid and toroid. Then show that inductance is the propefty (^) of the coil. (^) (5)
Or
lvhat is Hall Effect? write its importance. show that the hall coeflicient Rs = -l/ne, where
the symbols (^) have their own (^) meanings. (^) (l+l+3)
l5)The Sun (^) delivers about l03Wm2 of energy to the earth's (^) surface through EM radiation calculate a) the total power incident on a roof of dimensions 8m.*20 (^) m. b; Radiation pressure and (^) force exerted on the rooq assuming roof (^) is perfect (^) absorber. (^) (2+3)
l6) Abeamofelectronshavingenergyofeach3evisincidentonapotentialbagierofheight4ev
.lf the width of the barrier is (^) 20nm, calculate the percentage (^) transmission (^) of the beam through the barrier. (^) (5)
'r
- Define the three electric vectors E,P,D and develop a (^) relation between them.
OR
A cylindrical capacitor has radii 'a'and 'b'. Show that halfthe energy stored lies within the
cylinder whose radius is r = Jab
11. What will be the conductivity of'sodium metal having atomic weight 22.9 and density
1.013 grnlcm-3? Th" relaxation time of sodium metal is 1" 1O-la sec.
- What type of particles can be (^) accelerated by a cyclotron? Explain the working (^) of
cyclotron (^) and synchrotron with their differences. OR Differentiate between electromagnetic (^) induction and self-induction. Develop an
expression for self-inductance ofa teroid.
- Using Ampere's law, calculate the magnetic field inside, outside and on the surface of a
long current carrying conductor and hence plot (^) a graph (^) between the magnetic field versus
distance from the center ofthe conductor.
- (^) Determine the energy stored in an inductor. Also, determine the energy density (^) in
magretic field. l5.A radio wave transmits (^) 25 Wm2 of power (^) per unit area. The flat surface area (^) is perpendicular to the direction of propagation of the wave. Calculate the radiation pressure
on it and maximum electic and magnetic field associated with the wave.
- What are the significances of wave-function? Using the wave function derive and
expression for the time dependent Schrodinger wave (^) equation.
'/
,I 24 ,IRIBHUVAN^ UNIVERSITY INSTITUTE (^) OF ENGINEERING Examination (^) Control Division
2074 Ashwin
Sabject: - Engineering Physics (5H402)
Candidates are reguired to give (^) their answerS in their (^) own words as far as practicable.
Attempt AII questions..
AII questions earry equal marks.
Assume suitable data if necessarv.
Define centers of suspension and oscillation of a compound pendulum and show that they
are interchangeable. what length of the pendulum has its minimum time period?
OR
Define sHM- Derive the expression for energy of SHM. Show that the KE and pE of
simple harmonically oscillating object changes with time however the total energy is
invariant.
l.
- What is LC oscillation? Derive the (^) differential equation (^) of free oscillation and (^) compare
its solution with mass spring system.
3' What (^) is piezoelectric effect? (^) Describe the construction (^) of a piezoelectric oscillator
the production of ultrasonic waves.
4- Explain"how interference (^) fringes are formed by a thin wedge (^) shaped film examining normally reflected light. (^) Derive a relation (^) for the fringe width on (^) such.system interference fringes.
OR What (^) is double refraction? (^) Explain how would you (^) use the phenornenon to produce (^) linear
polarized light and circularly polarized light.
- (^) A diffraction grating (^) used at normal incidence gives (^) a line (540 nm) in a certain order
superposed on the violet line (a05 nm) of the next higher order. How many lines per cm
arc there in the grating if the angle of diffraction is 30"?
- 6.^ In^ Ramsden's eyepiece a^ coaxial^ lens^ system^ is^ used.^ There^ are^ two^ lenses^ in^ air^ and are of equd focal length of separated (^) by a distance 2fl3. Find positions (^) of the (^) cafdinal points.
- Discuss the physical significance of (^) numerical aperture (NA). How does it (^) depend on
refractive index of core and cladding?
- Calculate the thickness of doubly (^) refracting plate capable (^) of producing (^) a path (^) differences
of -l (^) between extraordinary (^) and ordinary rays (^) of wavelength (^) 5g90A. {use (^) Fo =^ 1.53; *d (^) Fr.: i.54) 9- What is (^) an electric dipole (^) and dipole moment? Show that electric (^) field for a short dipole drops inversely to cube (^) of the distance at (^) any point from the (^) dipole on an axial (^) line.
OR What (^) is an electric qudrupole? (^) Calculate potential (^) for points on the (^) axis of the qudrupole.
for
by
of
TRIBHUVAN LINIVERSITY INSTITUTE OF ENGINEERING
Examination Control Division
2073 Shrawan
ill:s.--- i__r_"_"_ul _:B_9*^ _^ *^ |I{llvtrrLj 90^ " l i P.og""--"^ I^ :ly?,3?t'ijl: pass^ ttrart<s^ i^32 i i' ::11:1:'"^ ;^ B_c.T,^ Br.EL_B:4_e4'j'.:"1j::':.^ ::^ i ilgslSryl (^) -'-ir-l - iltrt _ :, r!r.^ -i
1
Subject: - Engineering Physics (SH4A2)
Candidates are requir6d to give^ their answers in their own words as far as practicable. Attempt (^) 4ll q*estions.
AII questions carry equal marlc.
Assume suitable data if necessary.
Write the differences between mechanical oscillation and e.m. oscillation. Set up the
differential equation of damped harmonic mechanical oscillation. Obtain the relation for
frequency of such oscillation. Hence explain the conditions for different types of damped
oscillation OR
Define sharpness of resonance. Derive the relation for current amplitude of forced e-m
oscillation. What are the measures of good acoustic building? Show that the reverberation time
decrease with increase in absorbing factors in a hall.
Two thin lenses (^) of focal length (^) fl and f2 (^) separated by a distance having an equivalent
focal iength 50 cm" The combination satisfies the condition for no chromatic aberration
and (^) minimum spherical aberration. Find the separation between the two lenses if (^) both
lenses are of same materials.
Prove that the intensify of first maxima is 4.54Yo of the central maxima in Fraunhoffer's
single slit diffraction. OR
Write the physical meaning of dispersive power and resolving power of grating. Show
that resolving power is directly proportional to the total number of rulings (^) on the grating.
Newton's Rings arrangement is used with a source emitting two wavelength Lr and l.z. It
is found that the nth dark ring due to 1"1 coincides with (n+l)th dark ring to ?,2. Find the
diameter of nth dark ring. (11 :6x10-s^ cm,)"2= 5.9x10-s cm radius of curvature of the lens
R:90 cm). A quartz crystal has refractive indices (^) 1.553 and 1.544. Calculate the thickness (^) of a
quarter rvave plate for sodium light of wavelength 58904".
Explain the terms stimulated emission, population inversion, optical pumpling and
metastable. Explain working principle of He-Neiiaser.
A heavy circular ring ofradius R oscillates in a vertical plane about a horizontal axis at a
distance x from the cgnter. Show that the time period is minimum when (^) x = R
T.^ i
n
9. Derive the relation^ for^ potential^ at^ axty^ point^ due^ to^ an^ electric^ dipole^ and^ show^ that no
work is done in bringing^ a^ charge^ from^ infinity^ to dipole^ along the perpendicular bisector
of the dipole. OR
A plastic^ rod^ contains^ uniformly^ distributed^ Q^ charge.^ The^ rod^ has been^ bent^ in^ 120'
circular arc of radius 'rl^ as^ shown^ in^ figure below.^ Prove that the^ electric^ field^ intensity^ at
the center ofbent rod^
ls'^ o'83Q 'tr =^ -qne^f'
10. Derive the relation^ for^ rise^ and^ fall^ of^ current^ in^ charging and^ discharging^ of^ capacitor
through resistor. Plot^ graphs between^ current^ and^ tirne^ and^ explain the^ figures'
11. The^ space^ between^ two^ concentric conducting spherical^ shells^ of^ radii^ b^
: (^) 1.70 cm and a = l.?0 cm and a:^ I.2A cm^ is^ filled with^ a^ substance^ of^ dielectric^ constant^ k:23.5.^ A potential difference Y^ :^73 V^ is^ applied^ across^ the inner^ and^ outer^ shells. Determine^ (a) the capacitance of^ the^ device (b)^ the free charge q on^ the inner shell.
12. What is^ Hall-effect? Derive^ an^ expression^ for^ the^ Hall^ coefficient and^ established^ the
relation between mobility^ of^ charge^ carrier^ and^ conductivity^ of material^ of wire.
OR
Derive a relation resistivity^ of^ a^ conductor using microscopic^ *iew.^ From your resulf
explain why resistivity of a^ conductor increase^ with^ necessary^ with^ increasing temperature.
13. Explain the phenomenon^ of^ self induction.^ Calculate the value^ of^ inductance^ for^ (a) long
solenoid and (b)^ Toroid.
14. What is Ampere's law? Derive the^ expression^ for^ magnetic^ flux^ density outside^ and^ inside
a long straight conductor^ canying^ current^ I.
- Define^ poynting^ vector.^ Prove^ that3^ =fi"ilt*o,^ where^ the^ symbols^ have^ theii^ usual
meanings.
- Discuss the^ significance^ of^ the^ wave function and^ deduce^ the^ time^ independent Schrodinger's wave equation.
- over^ certain^ region^ of^ space^
the e|1cbic potential^ i,-'.:^
15x-3x2y+12yi'. Find^ the
i";#'-,Ji;i::",,:lr:;l-T$"#fJ:":ml'i:rfi ffiiegionT.*" ,r.ffiJff"":::, methods^ to carculate^ the^ capacitance^ of a^ capacitor_.and^ hence
determine the^ capacitanoe^ of^
a
"vfnaril.'r
J"p""i'it of^ inner^ and^ outer^
radii 'a' and^ 'b'
respectivelY. "ffil'L drift speed^ of^ electrons^ Yf:^30,:.:Y,"li-:-:"*tied
througlr a^ copper
12. Calculate^ the^ drift^ speed^
or elcuuurD 1 - wire of^ cross-,""uotuti*"u^ i^ **' and electron^ dersity^ t0'"^ m--'
.-^+^- rrannc nrove that the^ energy density^ in
- Determine the^ energv stored^
tl ,'-"i::l:j'-lflT;"lllJij|lt " 3#HT"il1'";::tJd;rtiona
to square of^ magnetic^ field'
OR
obtaicanexpressionforrnagneticfieldintensityduetoacircularcoilcarryingcurrentat
itsa'xialpoint ' ^ n^ ----^ masretic^ field i (^) '75T'lf a
14. A coppet^ strip 3'0^ cm^ wide^
and 2'0 mm^ thick^ is^ placed^ in^ a
current of^150 e^ i,^ *"p^ i"^ the^ strip,cal""r""^Al^
Hall voltage^ ano^ (ii)^ Hatl^ mobility^
if the
number of electrons^ peiunit^
volurne i,^ g'i"Ig'b';la^ resiJti"ity^ is 1'72x10-o^ ohm-m'
+ l/- *\
l5: Define poynting^ vector'^ Prove^
that t =;i.U" "J
16.Ab€amofelectronshavingenergYoof3eVisincidentonapotentialbarrierofheight
eV.Ifthewidthofthebarrieris20A,calculatethepercentagetransmissionofthebeam
tbroug! the^ barrier'^ *d<:F
a
Examination Control Division 2072[{afiik
r' (^) Candidaies ard required to give their (^) answers in their own words as far as (^) fracticable. { (^) Atternpt All questions. / (^) All (^) 4uestions cory equal moks. { (^) Assume suitable data if necessry.
- Dfferentiate between bar pendulum^ and torsional Usrng a torsional pendulum,
derive a relation for modulus of rigidity of the metallic wire.
OR
Compare the daraped and forced LCR oscillation. Derive the differential equation of
forcod ern-oscillation and compare it \D'i& driven mechanical oscillation
- Show that in a bar pe,ndul,,m, minimum time period is achieved if radius of gtrration (^) is
equal to the distance of point of suspension or point^ of oscillation from cent€r of gravity.
- Write some features of acoustically good^ auditorium. Derive Sabine's fomrula
- (^) Two thin (^) converging lenses of focal lengths 3 cm and 4 cm respectively are placed coa:rially in air se,parated by a distance of 2 cm. An (^) object isplaced at 4 cm (^) in front of first lens. Locate the positions^ ofthe principal points and final (^) 44*=
- What is polarization? Derive the relation for plane, elliptical ana circutar polarized (^) light. OR
What are the coherent souroes of light?.How such souroes develop in lab? Show that ttre
square of diarneters of the nt dark ring by the reflected light of Newton's ring. is (^) directly proportional (^) to the natural number.
- Define accelrtanoe angle and numerical aperture. In an optical fiber, show that Numerical Aperture (NA) (^) = (^) tI*{(24), q,mbols have their usual meanings
- In a Fraunhofer Single slit diffiraction, a convex lens of focal length 20 cmis placed^ just
after a slit of width 0.6 mm- If a plane wave of wavelength 6000Ao falls on slit normally,
calculate the separation between the second minima on either side of central rna,ximum.
- (^) Calculate the minimum no'of lines per cm in a 2.5 cm wide grating which wi[ just oo resolrrc the sodium lines 5890 A and 5896 A in sEcond order spectrum
24
.
. TRIBHWANIA{TVERSTTY
INSTITUTE OF ENGINEERING
A thin ring made of plastic of radius R is un]formly charged with linear charge density 1,.
Calculate the electric field intensity at any point at an o<ial distance y^ from the centeS. If electron is constrained^ to^ be in^ axial line^ of^ the^ same ring, strow^ that the^ rnotion:of electrohisSHM. (^) ).^ :..
Eram. (^) Nov llleli (2Li(r6 (^) ct. Later (^) Batch)
Ievel BE FulI,ltdarks
Programme
BEI..BE)q BCT, BIE
B*Aeri. Pass^ lllarks^32
Ycar/Part ut (^) Time 3 hrs.
OR
. (^). Discuss the behavior^ of^ dielectrics^ in^ a^ paraliel plate^ capacitor. Based^ on^ Gau$s^ law^ of
TRIBHWAN UNIVERSITY
. INSTITUIE OF ENGS{EERING Exaqination Control Division 2071 Shawan
r=lErffi-{ Qso
'oR
, (^). (^) -. : Calculate electric,field,at any point is .a,xial flstance
due Io a dipole and a quadrapole.
Whx conclusion you^ can draw from your results.
r' (^) Candidates are required to give (^) their answers in their own u,ords as (^) far as practicable. { (^) Attenpt&guestions. { (^) AII questiotrs (^) cury equl marks. { (^) Assutru suitable data (^) drucessry.
l. Derive a relation to find the moment of inertia of a rigid body about an axis passing thmugh its center^ of gravity^ using^ the^ torsional pendulum. OR What is resonance? Formulate the differential^ equation of forsed^ electromagnetic oscillation..Theu determine the expression for resonant frequency. 2- A sting bas a linear density of 625 gm/m^ and is stretched with a tension^ 50N. A rirave,
vfiose frequency and amplitude are 160[Iz and l0mm respectively, is travelling along the
string. At what average rate.is $e wave transporting en€rgy along the sting?
- (^) Why is it impofiant to study t}e (^) ieverberation timq (^) before the construction (^) of a Cinema
Hall?'Derive a relation for reverberation time based on absorption coefficient, volume
and surface area ofthe hall.
4, (^) What trappens (^) to tlre energy when waves perfectly cancel to each other in interference?
'Derive the relations forthin film interference by reflected light.
OR
. (^) Show ttlat the dianreters of the Newton's rings when two surfaces of radii Rl and R2 are
placed (^) in contact arc related by the relation (l/RlXl/R2) :^ (4nud2,), where (^) n is the
integer number ofthe fringes
- A grating with 250 grooveVmm is used with an incandescent light source. Assume (^) the visible (^) spectrum to range in wavelength fiom 400 to 700 nm. In how many orders ca:n (^) one. see the entire visible spectrum?
- Definc.the polarization of light Write.its importance in different optical instruments. Dcrive the relalion for the thickness of quarter^ wave plate aod half wave plate.
- Two thi4^ coayerging lenses of focal length 3cm (^) .and 4cm respectively are placed
coa:<ially in air and separated by distance of Zcm. An object is placed 4cm in front of the
first le, s. Find (^) the position of the naturc of the image and its lateral magnification.
8.. A glass-clad fibcr is made with a core glass of refractive inde:< L55 and the cladding is
dop"d to grve a fractiorial index difference of 5.5x104. Determine (i) Cladding index (ii)
the critical intemal reflection angle (iii) the exemal critical acceptance angle and (iv)
numerical ape{twe (NA).
- A particle^ of charge -q and m&s.m is placed m-idway between two equal positive charges
qs of separation d. If the negative charge -q is displaced in perpendicular.direction to the
line joining^ them and released. Show that the particle (^) describes a SHM with a period.
El!ro. ;lr}:..,:,''
Irevel BE^ FuIl^ ivlarks Programme BEL;^ BEX,^ BCT, BIE, B.Apri. .Pess (^) lVlarks Year / Part Ut^ Time 3 hrs.
.lI I I t.'-t.. I ,l^ I !
. :^ ...'^ :
I0. Charges^ ave'uniformly^ distributed through out^ the^ volume^ of,arr^ infinitely^ large^ cylinder
of radius ia'.^ Show that the elecbic field at a distance^ 'r'from the^ cylinda^ axis^ r^ <^ a^ is
given (^) by p^ = fL^ where p (^) is the volume charge density.
ll.Acytindrical capacitor has radii a^ and^ b.^ Show that^ half the^ stored eler:tric^ potential
energy lies within a cylinder whose radius is t = .6-b'
12. Explain Hall Effect. Derive a relation for hall resistance.^ From this relation explain^ the
meaning of quantization^ of hall resistaoce.
13. The current density in a cylindrical wire of^ radius R^ = 2 mm^ and^ uniform^ cross-sectional
area is given^ by^! =2 x^ I0s Am2. What is the current through the outer^ portion of^ the^ wire
between radial distances R./2 and R?
14. Explain the phenomenon^ of "self-induction". Find an expression^ for the self-induction of
.
a toroid having N numbers of tuqns, radius r and^ carrying current^ i. (^). OR
State Ampere's law. Find the exprerssions for magrretic field outside and inside the long
straight wire^ by using this law.
- Write dovm the Maxwell's equations fer non conducting Find the equation of propagation
of plane electromaguetic wave for E-field and B-field for such rnedium. Show that
elechomagnetic wave travels with velocity less than velocity of light in (^) such medium.
- Derive schodinger time independent wave equation. A particle (^) is moving (^) in one
dim. ensional potential^ well of infinite height urd width 'a'. Find the expression for e,nergy
of (^) the particle
I I II I I! i I!
I! ! I! II I I I I t i
- Prove that electric field due to^ a short dipole^ at^ axial point^ is^ twice^ that at^ equatorial^ point.
10. A capacitor of capacitance C is^ discharging^ through^ a^ resistor^ of^ resistance^ R.^ After.how
many time constants is the stored energy 1/8 of its initial value? (^) ,
11. Give a general method to calculate electric field and potential due to continuous charge
distibution. Usrng your^ method, calculate electric^ field^ at an^ equitorial distance^ y^ due^ to^ a
long charged rod having linear charge density 1".
12. Considqr a circular coil of radius R carrying cunent I. Find the magnetic field at any
point on'the axis of the loop at a distance z from the center of the loop. Show that the
circular current carrying coil behaves as a magnetic dipole for large distance.
13. In a Hall Effect experiment, a current of 3.2A lengthwise in a conductor 1.2 cm wide, 4.
cm long and 9.5pm thick produces^ a transverse Hall voltage (across the width) of 40pV
when a magnetic field of L4T is passed perpendicularly through the thin conductor. From
this date, find (a) the drift velocity of the charge carriers and (b)^ the number density of
charge carriers.
14. Derive an expression for growth and decay of current in LR circuit. Explain inductive
time (^) constant by sketching graph (^) between current and time for both cases.
OR
Derive expressions for inductance of a Solenoid and Teroid. Then show that inductance is
the property^ of the coil.
15. Write and explain Ampere's law in magnetism. How Maxwell modified it. Based on this
modified equation, explain the (^) term displacement current. Prove displacement current is
equal to conduction curerit.
16. Explain Schrodinger's wave equation. Derive time independent Schrodinger wave
equation. Use this equation to find energy for a particle in a box of infinite square well
potential.
j
'ii
24R TRIBHWANUNIVERSITY INSTITUTE OF^ ENGINEERING Examination Control Division
2069 Chaitra
Exem. Rt'gular
LeveI BE^ FullMarls 80
Prograrnme
BEL, BEX, BCT,
BIE. B.Acri. Pass^ Marks^ 32 Year / Part Ul^ Time 3 hrs.
Subject: Physics^ (5H402)
{ (^) Candidates are required to give (^) their answers in their own words as far as practicable. / (^) Attempt All questions. { (^) eA questions carry equal marks. / (^) Assame suitable data if necessary.
- Point out the similarities and dissimilarities between the oscillations of bar pendulum and
torsinal poendulum. Show that the radius of gyration is equal to distance from center of
,sulpension
to center of gravity of compound pendulum,.when tfne pgrio.d in minirqum.
- Derive a differential equation for LC Oscillation. Show that the maximum value of
electic and magnetic energies stored in LC circuit is equal.
OR
Prove that if a transverse wave^ is travelling^ along a^ string,^ then^ the slope at any^ point^ of
the string is numerically equal to the ratio of the particle speed to the wave speed at that
Point- r
- The time of reverberation of an empty hall is 1.5 sec with 500 audiences present inthe
hu$'th" reverberation time falls to 1.4sec. Find the no. of persons present^ in^ the^ hall^ if^ the
reyflFtration time falls down to 1.32 sec.
4',
- Show that the intensity of the first subsidiary maxima of Fraunhoffer's diffraction at (^) a single slit is 4.5o/o of that or principal maxima. OR What is double aifkctionf Explain how Nicol prism can be used as polarizer and analyzer?
- In^ a Nefion's^ ring experiment,^ the radius^ of curvature^ of the lens is 5cm and the lens
diameter is 20mm. (a)^ How many^ bright rings are produced?^ Assume that ?u:589nm
(b) How many bright rings would be produced if the arrangement were immersed in water
(p=1.33)?
- A diftaction gratting 3cm wide produces the (^) second order at 33' with light of wavelength 600nm. What is the total number of lines on the gratting.
- What is population^ inversion? Explain why laser action cannot occur without population inversion between atomic levels?
- What are cardinal points of an opticai system? Determine the equivalent (^) tbcal Iength of a combination (^) of two thin lenses separated by a finite distances.
- A ring has a charge q (^) uniform distributed (^) in it. Derive (^) an expression for the electric (^) field at any point^ on the axial line of the ring. Extend your^ result (^) to find the potential. OR
Write an expression for electric field at any point in the axial line of a charged ring.
Using this equation, calculate the electric field at any point in the axial line of a charged
disk.
: .
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!
24 TRIBHWA}.II.'N{VERSITY
INSTITUTE OF ENGINEERING
.Examination Control Divjsion. i,
2069 Ashad
Eram. \ur^ llacli^ (?0(16^ ct^ Lirtcr^ Balclr)
I-evel BE^ Full^ lllarks^80
Programme
BEL, BE)L
BCT, BIE
B.APri.
Pass Marla 32
Year/Part Ul Time 3 hrs.
Suhiect: Physics (SH^ 402)
,/ (^) Candidates are required to give (^) their answers (^) in their own words as far as practicable. { (^) Anempt (^) 4lquestions. { (^) All questions carry (^) equal mwks. y' (^) Assurne suitable data if necessary.
' (^) 1.'
Obtain'an'expreiiion for'the time period^ of a compormd pendulum and show that its time
period (^) is unaffected by the fixing (^) of a small additional mass (^) to it (^) at its centre of suspension. OR What (^) is electomagnetic oscillation? Derive alitrerential equation of darnped LCR oscillation and find its frequency.
- A particle is moving with simple harmonic motion in a straight line. If it has a speed v when the displacanent is x1 and (^) speed v2 (^) when the displacement is xz then show that the I
vz^22
Xr 2 x
v
amplitude of the motion is, a = 22
vz -Yt
- In the progressive wave, show that the potential energy and kinetic en€rgy of every particle will change witli. time but the average K.E. per unit volume and P.E. per unit volume remains constant.
4- Two coherent sources having constant phase 6 but different amplitudes Ar and Az superimpose, prove that the (^) intensity of superimposed beam is
I = Ar2 +^ Ar2^ +2Ar.A,^ cos6.
o; Explain the phenomenon of double refraction. Describe the (^) construction and action of
Nicol prism.
- White light is incident on a soap film at an angle - sin'[{]urra trre^ reflected^ light^ on \s/ examination by a^ spectrometer^ shows^ dark bands. The consecutive dark^ bands^ correspond
to wavelength 6.1x10-scm and 6.0x10-5cm.If p=I.33^ forthe film, calculate its ttrickness.
- Light of wavelenglh 600nm is incident normally on^ a^ slit of width 0.lmm.^ Calculate^ the intensity at^ H.2o.
- Two lenses of focal lengths 8cm^ and 4cm are placed^ at a certain distance apart.^ Calculate
the position ofprincipal points^ if they form an achromatic combination.
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- (^) An optical fiber has a NA of 0.2 and a cladding refractive index^ of^ 1.59.^ Deterrrine
acceptance angle for the fiber in^ water which^ has^ a^ refractive^ index^ of^ 1.33.
- A ring has a charge q^ miformly distributed in it.^ Find^ the expression^ for^ the electric^ field at any point on the axial line of the ring. Locate the point^ at.which the^ field^ is^ madmum. OR
Prove ttrat electric field due^ to a short dipole at a:rial point is twice that at equatorial poi"r.
- A particle^ of charge (^) -q and a mass m is placed^ midway^ between two^ equal positive charges qo of separation d. If the negative charge 1 is displaced in perpendicular
direction to the line joining^ them and released, show that the particle^ descries a^ SHM^ with
t
a peliod^ r (^) = (^) [e-",
mn3asJ;
. Lsgo I
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11. 11A cylindrical capacitor has radii a and b. Show that halfthe stored electric potential
energy lies within^ a cylinder of radius r = ..[6.
l2.Aflat silver strip of width 1.5cm and thickness l.5mm carries a current of 1504. a
magnetic field of^ 2.0 Tesla^ is applied perpendicular^ to the^ flat^ face^ of the sttip.^ The^ emf
developed a$oss the width of strip is measured to be l7.9pV. Estimate the number density of free electrons in the metal.
- A straight wire segment of length / carries current I. Show that the magnetic field B (^) ; produced (^) by that segment at a displace y from it along a perpendicular bisector is (^) ,
B=(Fo tzr':flttf4+qf)1.
14. Find the inductance of a toroid having N number ofturns and radius R.
- (^) OR
Show that the energy per unit volume in electic field and magnetic field are proportional
to the square of their fields.
- State and explain Maxwell's equations. Derive the continuity (^) equation: V.i (^) = g^. 'at
16. Determine the total energ"y of a particle using Schrodinger equation, when the potential
energy has value^ V=0 for 0<x<4 and V:efor x<0 and x)a.
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