physics paper-1 cse questions

8/10/2019 Physics Paper-1 CSE Questions

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CIVIL SERVICES EXAMINATION (MAINS)

PHYSICS PAPER - I: CLASSICAL MECHANICS

TUTORIAL SHEET: 1

(Conservaton !a"s)

1) What is the recoil energy in electron - volts of mass 10-23 gm after emission of a r ray of energy of1 Mev? (1990)

2) Define differential scattering cross-section. Write don the de!endence of "#therford scatteringcross-section ()$ on the scattering angle and s%etch this de!endence gra!hically. &n the !resentcase the total scattering cross section 'f() dt#rns o#t to e infinite. omment on this res#lt.

(1990)3) * ne#tron of energy 1 Me+ collides ith a stationery heli#m n#cle#s and is scattered. Ded#ce the

moment#m of the ne#tron and of the heli#m n#cle#s in their center of mass system.

(1990),) Define differential scattering cross section for a scattering !rocess. he differential scattering

cross-section for ne#trons scattered elastically from a solid is of the form

( )( )

2

i fB K K

e

= here * / are constants and

0fand0i are res!ectively the ave

vectors of the incident and scattered ne#tron Determine the total cattering cross - sections$ givenKi Kf

= . (1991)

) rove that if 4 and 41 are res!ectively the ne#tron energies in the laoratory system$ efore andafter collision ith a n#cle#s of mass n#mer *$ then

( )

E

E

A A Mc

A

1 2

2

1 2

1=

+ ++

Where Mc is the cosine of the scattering angle in the centre of mass system. (1991)

5) What do yo# mean y centre of mass of a system of !articles? Derive e6!ressions for theinstantaneo#s !osition vector and velocity of the centre of mass of s#ch a system of !articles

(1992)

7) 8sing "#therfords oservation that the n#mer of - !articles scattered at angle and falling on

#nit area of the screen varied as cosec 2

4

$ ded#ce an e6!ression for the !roaility of

scattering eteen angles : d .(1992)

;) * roc%et of mass 1000 %g. is ready for a vertical ta%e off. he e6ha#st velocity of its f#el is ,.%m#ired in ; seconds if the f#el e=ection rate is 2.0 %g


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10) @ind the fractional decrease of %inetic energy of a of mass m1hen a head on elastic collision ta%es!lace ith another !article of mass m2initially at rest. &n this conte6t sho hy hydrogen o#ld eest to e #sed for sloing don. *ct#ally D2A$ not B2A is #sed. Why?

(1993)11) What is centre of mass? ho that there e6ists only one centre of mass in a system of !articles.

Disc#ss the #sef#lness of centre of mass in st#dying motion of a system of !articles. (199,)12)he distance eteen the centres of A6ygen and aron atoms in a A molec#le is 1.2* 0.

Determine the !osition of the centre of mass of the molec#le relative to aron. (*ss#me atomicmasses of aron and A6ygen as 12 15 res!ectively).

(199)13) * !article of mass m$ moving ith an initial velocity +0is acted on y a central re!#lsive inverse

s>#are force$ F k

r=

2 . ho that the cattering angle de!ends on the im!act !arameter Cas

2

0cot2

mVb

k

=

(1990)

1,)* !article of mass m1moving ith a velocity +1#ndergoes an elastic collision ith a !article ofmass m2at rest$ in laoratory - frame. *fter the collision the first !article moves at a certain angle tothe direction of its initial velocity$ and this angle is in laoratory-frame and in centre of mass-

frame. &f the ratio of massesm

m

2

1

is *$ sho that are related as*

1cos

sintan

+

=

(1995)1)&n the B3molec#le$ the three hydrogen atoms forms an e>#ilateral triangle. he distance eteen

the centre of this triangle from each hydrogen atom is 0.939 *o. he nitrogen atom is at the a!e6 ofthe !yramid ith the three hydrogen atoms forming the ase. he distance eteen the hydrogen ndnitrogen atoms is 1.01, *o. @ind the !osition of the centre of mass relative to the nitrogen atom.

(1997)

15) he to atoms of a molec#le of a gas interact according to the !otential ( )125 r

/

r

*r += r eing the

se!aration distance eteen the to atoms. Determine * and / if the !otential energy (r) ' (r0) atthe e>#iliri#m se!aration r ' r0.

(199;)17) Bo do e infer the la of conservation of linear moment#m from etons las of motion?

* stationery om e6!lodes and on e6!losion$ it fragments into three !arts. o of these !arts$hich are of e>#al masses$ fly a!art !er!endic#lar to each other ith a velocity of 50m


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21) "am and hyam are to s%aters eighing ,0 %g and 50 %g res!ectively. "am traveling at , m


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TUTORIAL SHEET: %

(Rotatn& 'ra#es o Reerene)

1*What is #nderstood y the term Foriolis force? Atain e6!ressions for velocity acceleration of a!article in rotating coordinate system.

(19;;)%* Define oriolis force and rite an e6!ression for it$ thro#gh s#itale e6am!les$ e6!lain the ay this

force varies in different !arts of the earths s#rface and for different velocities of the concerned!article.

(19;9)+* Write short notes on (&) oriolis force (1991$ 1993$ 1997) (&&) &nertial forces in a rotating frame (1992)

,* 46!lain hat oriolis force means. Disc#ss the action of oriolis force on a ody falling freely onthe earth at latit#de FF

(199,)* &f the earth ere to rotate at Fn times its !resent s!eed of rotation ao#t its a6is$ the a!!arent eight

of a ody at the e>#ator o#ld ass#me Lero val#e. @ind an e6!ression for Fn. (199)

.* Define oriolis force. Atain an e6!ression for the oriolis force. Bo does it acco#nt for the

hirling of inds in o!!osite directions in orthern and so#thern Bemis!heres?

(1995)

/* Atain the e>#ation of motion of a !article moving relative to a rotating frame of reference 46!lainthe term re!resenting oriolis force in this e6!ression. (2001)

0* @or a freely falling ody from the height Fh on the s#rface of the earth in the northern hemis!here

ith a latit#de F$ sho that the deviation of the ody toards east at the final stage is given y 1


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T3tora! S4eet: +

(S5ste# o Part!es)

N 1) * system ith to inde!endent coordinates 61and 62has the folloing EagrangianO

E 'o

2 o1 2 2 2

2 2

2

1 (6 ) 16 (6 ) 6

2 ( 6 ) 2+

+

P$ Q$ R eing constants. Atain the Eagrangian e>#ation of motion. (2001)

N2) Determine e>#ation of tra=ectory for a !artic#lar #nder central force F @ $ the magnit#de of hich isgiven y @ ' -* < rS : / #ation of motion. 8se themto get the e>#ation for the orit . (2001)

N,) Write the Eagrangian e>#ation for a system of !articles hich is acted #!on y conservative forces.What is a cyclic coordinate? ho that the generaliLed moment#m con=#gate to a cyclic coordinateis conserved. (2003)

N) * !article moves in s!ace ith the EagrangianE'1#ations of motion ith its hel! for a conservativesystem. (2005)

N;) Write don the Eagrangian of a free !article in rectang#lar artesian coordinates. &dentify all cycliccoordinates. ho that the constants of motion otained for the considered form of the Eagrangian arenot e6actly the same as those hich follo from the conce!t of free !article. (2007)


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T3tora! S4eet: ,

R&6 7o65 85na#s

1. What are !recession and n#tation? ho that the ang#lar velocity of !recession is related toang#lar moment#m E and e6ternal tor>#e as O' E I . *ss#me XXY.

(199)

2. 46!lain !recessional motion of a to!. * solid s!here of radi#s 2 cm and mass 0gm has a thin nail oflength mm fi6ed !er!endic#lar to its s#rface. When this s!here s!ins li%e a to! ith a s!eed of 20rev#ivalent to a !#re rotation ith the same ang#lar s!eed ao#t ana6is thro#gh the !oint of contact of a rolling ody.

(2000)

7. Write the 4#lers e>#ations for the rotational motion of a right ody ith one !oint fi6ed$ #nder theaction of a tor>#e . *!!ly these e>#ations to disc#ss the rotational motion of a symmetrical to!on the asence of any force other than the reaction at the fi6ed !oint.

;. What do yo# mean y the moments and !rod#cts of inertia? ho that the ang#lar moment#mvector is related to the ang#lar velocity com!onents y linear transformation relations? (200,)

9. Derive 4#lers e>#ations of motion for a rigid ody rotating ao#t a fi6ed !oint #nder the action ofa tor>#e. When a rigid ody is not s#=ected to any net tor>#e$ rite don 4#lers e>#ations ofmotion of the ody ith one !oint fi6ed. (2005)

10. he ang#lar moment#m Mof a rigid ody com!rising of !articles and rotating ith ang#larvelocity Y is given yM ' [ m% r%6 (Y 6 r%) here the origin coincides ith the centre ofmass.46!ress the com!onents ofM in terms of com!onents of inertia tensor .Bence$ sho that themost general free rotation of a s!herical to! is a #niform rotation ao#t the a6is in fi6ed s!ace.

(2007)

5


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TUTORIAL SHEET: S;ea! Re!atvt5

1. ho from the EorenL transformation that to events (t1't2) at different !oints (61'62) in reference frame are not in general sim#ltaneo#s in reference frame 1hich is moving in the :6 direction ith theconstant velocity + ith res!ect to . (199;)

2. What is the moment#m of a !roton having %inetic energy 1 /e +? the energy e>#ivalent to !roton restmass is 0.93; Mev. (19;;)

3. Write don EorenL transformation relations and !rove that 62:y2:L2-c2t2is invariant #nder thistransformation. (1990)

,. *n event occ#rs at 61'50m$ at t1';610-; s in a reference frame 1hich is moving along the common \or \1 a6is ith a s!eed of 3c#ations. ho that for +#ationsred#ces to Halilean transformation e>#ations. 46!lain the !hysical significance of EorenLtransformations. (1993)

9. Write short notes on mass-energy e>#ivalence_. (1993)

10. tate and e6!lain variation of mass ith velocity$ hence find an e6!ression for the density of a ody inan aritrary inertial frame of reference. (199,)

11. he density of gold in its !ro!er frame of reference is 19.36103%g#ivalent to the restmass of an election is 0.1 me +. (199)

1,. he coordinates of an event in an inertial frame are (2m$o$ o$ 610-;). What ill e the coordinatesof this event in another inertial frame 1moving ith a velocity 0.5 0 in :6 direction ith rest 6 to s.he origin of to frames coincide at t't1'0. (1995)

1. Atain the relativistic transformation relation for density in inertial frames. What is the e>#ivalentenergy corres!onding to 1 am# of mass? (1997)

15. * ] meson travels toards the earths s#rface from high #! in the atmos!here ith a s!eed of 0.99. &tdecays after traveling a distance of 5%m. &n hat time does the ] meson decay as meas#red yoservers in reference frames (i) o#nd to the earth (ii) o#nd to the meson itself. (199;)

7


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17. Bo is an election volt connected to other #nits of energy li%e the =o#le or the erg?Determine the s!ace of an election of energy 1.3 Me + ass#ming its rest energy to e 0.l Me +.

(199;)1;. rove that the e6!ression 62:y2:L2-c2t2is invariant #nder EorenL transformation. (1999)19. Descrie the set-#! of Michelson-Morley e6!eriment. Why as a fringe shift e6!ected in it? Bo are its

negative res#lts #nderstood? (1999)20. What is FEorentL ontraction? * s!aceshi! of rest length 100m ta%es ,]s to !ass an oserver on 4arth.

What is its velocity relative to the 4arth? (2000)21. Derive an e6!ression for the mass-energy e>#ivalence #sing the !rinci!le of s!ecial relativity.

(2000)22. he mass of m#on at rest is 207 Me here Me is the election rest mass (0.11 Me + ). he mean life

time at rest for m#on is 2.2 ]s. he life time of m#on emerging from an accelerator is meas#red in thelaat 5.9 ]s. 4stimate the s!eed of these m#ons in the laoratory. (2001)

23. * !erson is a s!ace shi! is holding a rod of length of 0. m$ the s!ace shi! is cr#ising at a s!eed +!arallel to the earths s#rface. What does the !erson in the s!ace shi! notice as the rod is rotated from!arallel to !er!endic#lar to the s!ace shi!s motion? What does an oserver on earths s#rface notice?

(2001)2,. o s!aceshi!s are moving at a velocity of 0.9c relative to the 4arth in o!!osite directions. What is the

s!eed of one s!aceshi! relative to the other? (2002)

2. *n oserver * sees to events at the same s!ace !oint (6'y'L'0) and se!arated y t'10-5s. *notheroserver / sees them to e se!arated y t1'3610-5s. What is the se!aration in s!ace of the to events asoserved y /? What is the s!eed of / relative to *? (2002)

25. *n oserver 1sees to odies * and / having e>#al rest mass a!!roach each other ith e>#al #to!!osite velocity of the ody ,c#alitatively differ from its non-relativisticanalog#e? alc#late the Do!!ler shift in the fre>#ency of a !hoton traveling along y-a6is$ ith res!ectto an oserver moving along the 6-a6is ith a constant s!eed #. (2003)

2;. * meson of rest mass ` comes to rest and disintegrates to a m#on of rest mass ] and a ne#trino of Lerorest mass. hoe that the %inetic energy of motion of the m#on is

'(`-])2 c2< 2 ` (200,)

29. Write don the e6!ression for the relativistic mass of a !article moving ith a velocity in terms of itsrest mass. 4stalish from the aove e6!ression 4insteins mass energy relation 4'mc2. (200,)

30. ho that the length E of an o=ect moving ith a velocity is given in the direction of motion y2 2

0E E (1 < c )= 1#ivalent to another EorentL transformation.Bence rite don the 4insteins velocity addition relation. (2005)

32. he so#rce b moves along the 6-a6is at a s!eed v$ and emits light at an angle to the 6-a6is of its onframe. &n th -frame the emitting angle ith the 6-a6is is . Bence 6 and 6-a6is are coincident. ho thatthe e6act relativistic aerration form#la can e derived from the velocity transformation relations. (2005)

tan' sin1 V v2


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33. tate the ost#lates of the !ecial theory of relativity and ased on these otain EorentL as ell asinverse EorentL transformations. Bence$ otain an e6!ression to concl#de that a moving cloc% r#ns moresloly than a stationary cloc%. (2007$ 3 mar%s)

3,. *n #nstale !article has a lifetime of microseconds in its on frame of reference and is movingtoards the earth at a s!eed of 0.;.What ill e the lifetime of the !article to an oserver on the 4arth?

(2007$ 10 mar%s)

3. * ody of rest mass m0 ismoving in the !ositive y-direction at a velocity of 0.5 relative to thelaoratory frame. alc#late the com!onents of the fo#r dimensional moment#m vector in the laoratoryframe and in the frame of an oserver ho is travelling in the !ositive 6-direction at a s!eed of 0.; relativeto the laoratory frame. (2007$ 20mar%s)

9


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=AVES

TUTORIAL SHEET: .A

(S#;!e Har#on Moton)

1. ine %ilograms of merc#ry is !o#red into a glass 8 - t#e of #niform internal diameter of 1.2cm. &t

oscillates freely ao#t its e>#iliri#m !osition. alc#late the !eriod of oscillation. (1990)2. * !article of mass 10g lies in a !otential given y + (6) ' 362: 0.2$ here 6 is in meters and + (6) ino#les. Write don the e>#ation of motion and solve it. What is the fre>#ency of oscillation? (1991)

3. * !article e6ec#ting sim!le harmonic motion has an acceleration

3

2

cm


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TUTORIAL SHEET: .7

8a#;e6 Moton$'ore6 Os!!atons

1. alc#late the rate of energy dissi!ation y a dam!ed harmonic oscillator$ in the ea% dam!ing limitWith o1$ so that 0. ymols have their #s#al meanings.

(19;;)

2. Write don the differential e>#ation for a dam!ed sim!le harmonic oscillator. olve it and disc#ss thecharacteristics of dead - eat motion. (1990)

3. Hive a mathematical analysis of forced viration and hence e6!lain the !henomenon of am!lit#deresonance.

(1992),. ho that for forced oscillations am!lit#de resonance and energy resonance do not occ#r at the same

fre>#ency.(199)

. Write the e>#ation of motion for an oscillator driven y a sim!le harmonically varying force. Atain thecondition for ma6im#m energy transfer to the oscillator.

(1995)5. he am!lit#de of a dam!ed Ascillator of fre>#ency 300 BL red#ces to one - tenth of its initial am!lit#de

after 3000 Ascillations. alc#late the dam!ing constant and the time in hich its energy ill red#ce toone - tenth of its initial energy.

(1997)7. What are dam!ed oscillations? Atain the differential e>#ation for dam!ed oscillations and rite its

!ossile sol#tion. 46!lain$ ith corres!onding s%etches$ hen there can e very heavy dam!ing$ criticaldam!ing and ea% dam!ing.

(1999);. *n ideal massless s!ring of force constant % has a mass m attached to one of its ends$ the other end eing

fi6ed to a rigid s#!!ort. he s!ring is horiLontal and the mass moves on a horiLontal floor. +elocity vacts on the mass. *ss#ming the dam!ing to e light$ otain the fre>#ency of oscillation.When m' 0.1 %g and %'10 n#ency of oscillation is v1#encyin the asence of dam!ing. alc#late the val#e of constant .

(2003)9. Write don the e>#ation of motion for a dam!ed harmonic oscillator ass#ming the dam!ing force

!ro!ortional to the velocity of the !article. Atain the general sol#tion for its dis!lacement as a f#nction of time. Disc#ss the cases of over dam!ing$ #nder dam!ing and critical dam!ing. (200,)10. &n the steady state forced viration a !oint !article of mass Fm moves #nder

the infl#ence of an e6ternal force (@ sin !t) in addition to the restoring force V (%6) and dam!ing force V

(Q6 ) . ho that (i) the am!lit#de is ma6im#m hen ! ' Y2

V 22

$ here %


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TUTORIAL SHEET: .C 7eats< Statonar5 "aves< P4ase > ?ro3; ve!ot5< H35&en @s Prn;!e

1. @or a certain ave system the ang#lar velocity and the ave vector are related as follosO

=

< oka

f ora

ka

si n2

Determine and !lot the !hase velocity and the gro#! velocity for this system. (1990)

2. he !hase velocity of s#rface aves of ave length is V gp = + 2 2

12

here is the s#rface tension and

the density of the li>#id and g is acceleration d#e to gravity. @ind the gro#! velocity and e6!ress it in terms ofthe !hase velocity. @or hich avelength is the !hase velocity a minim#m? (1991)

3. 46!lain the las of refraction of light on the asis of B#ygens !rinci!le. (1991)

,. he refractive indices of a material of avelengths 090 *o$ 3,0 *o and ;90 *oare e>#al to 1.5,7$ 1.5,0 and1.530 res!ectively. 4stimate the !hase and gro#! velocities of light near ' 3,0 *0.

(1993). Disting#ish eteen !hase velocity and gro#! velocity. alling gro#! velocity g and !hase velocity 1 in a

medi#m of refractive inde6 n$ estalish the relation

Cg C n dnd= + 1 1 here refers to the avelength of the related light in vac##m. (199,)

5. ertain string has a linear mass density of 0.2 %g#ency BL and am!lit#de 0.01 metre. &f at t-0$ the end has Lero dis!lacementsand is moving along the !ositive y direction$ derive the ave s!eed$ the ave length and the ave e>#ation of theave in the string. (2001)

7. he !hase velocity in a material is g


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TUTORIAL SHEET: /

?eo#etra! O;ts

1. * ray of light starts from !oint * and after reflection from the inner s#rface of s!here reaches to diametricallyo!!osite !oint /. alc#late the length of a hy!othetical !ath */ and #sing @ermats !rinci!al$ find the act#al

!ath of length. &s the !ath minim#m? (*ns. 2 dia$ o)2. &n fig#re$ is a !oint so#rce of light. &f the distance of from the center A of the s!herical reflecting #rface

is 0.;r and if the light ray starting from and after eing reflected at reaches at !oint N$ ho y @ermats

!rinci!al os


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TUTORIAL SHEET: 0

Intererene

1. * soa!-film of refractive inde6 1.33 is ill#minated ith light of different ave lengths at an angle of ,o.here is com!lete destr#ctive interference for ' ;90 *o. @ind the thic%ness of the film. (1991)

2. *n interference !attern is otained y #sing to coherent so#rces of light$ and the intensity variation isoserved to e 10q of the average intensity. Determine the relative intensities of the interferingso#rces. (1993)

3. ho that the interference fringes in #ncoated thin films are distinct hen seen in reflection$ #t veryindistinct in transmission. (199,)

,. &n a i!rism e6!eriments the fringe-idth ith light of avelength ' 900 *o is 0.,3 mm. Anintrod#cing a mica sheet in the !ath of one of the interfering rays the central fringe shifts y 1.;9mm. &frefractive inde6 of mica is 1.9$ calc#late the thic%ness of the sheet. (199)

. ho that the interference otained in yo#ngs to-slit e6!eriment are hy!erolic in sha!e. 8nder hatconditions these are e6!ected to a!!ear straight? (1995)

5. Why does a oa! film a!!ear colo#red hen it is vieed y reflected hite light? * thin film isill#minated y sodi#m light of avelength 900 *o. &ts refractive inde6 is 1.,2. alc#late its minim#m

thic%ness so that it a!!ears dar% in reflected light. (1997)7. alc#late the minim#m !late se!aration in a @ary - erot interferometer to otain free s!ectral range of0.0 *oin the avelength region 000 *o. alc#late also the smallest resolvale avelength differencefor reflectivity of 0.9. (199;)

;. What are the essential conditions for oserving the interference of light? o oherent so#rces ithintensity ratio ,O1 interfere. @ind &ma6


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TUTORIAL SHEET:

8raton

1. he diameter of the central Lone of a Lone-!late is 2.3 mm. &f a !oint so#rce of light ( ' ;9.3manometer) is !laced at a distance of 5 metres from it$ calc#late the !osition of the first image. (19;;)

2. &n do#le - slit @ra#nhofer diffraction calc#late the fringe s!acing on a screen 0 cm aay from the slits.&f they are ill#minated ith l#e light ' ,;00 *o$ slits se!aration d ' 0.10 mm$ andslit - idth a ' 0.020mm. What is the linear distance from the central ma6im#m of the first minim#m ofthe fringe - envelo!e? (19;9)

3. * single slit of idth 0.1,mm is ill#minated normally y monochromatic light and diffraction ands areoserved on a screen 2m aay. &f the centre of the second dar% and is 1.5cm from the middle of thecentral right and$ ded#ce the avelength of light. (1990)

,. ho schematically the intensity distri#tion for a 2-slit @ra#nhofer diffraction-interference$ if slit-idths are 2each and centres of slits have se!aration 5. *ss#me incident light falling normally$ andlimit the disc#ssion to the central diffraction and range. (1990)

. Disting#ish eteen @resnel and @ra#nhofer classes of diffraction of light. Disc#ss the theory of !lanegrating and hence find an e6!ression for the ang#lar dis!ersion of a !lane-grating. (1992)

5. What is @ra#nhofer diffraction? 8nder hat conditions may it e oserved? @ind an e6!ression for theintensity distri#tion in do#le slit @ra#nhofer diffraction$ ta%ing the res#lt for diffraction at a single slitas given. (1993)

7. Atain the intensity !attern d#e to @ra#nhofer diffraction at to !arallel slits. 4ach slit has a idth Faand the se!aration eteen the slits is Fd. Bo many interference fringes ill a!!ear in the centraldiffraction ma6im#m$ if d ' ,a? (199)

;. * fine slit is ill#minated y monochromatic light of avelength 5000 *o. * thin ere is !laced !arallelto the slit and the diffraction !attern is oserved on a screen at a distance of 1m from the ire. &n theshado of the ire e>#idistant fringes of thic%ness 1.mm are oserved . Bo do yo# e6!lain this

oservation? alc#late the diameter of the ire also. (1995)9. Hive the conce!t of @resnels half !eriod Lones. Descrie the salient feat#res of @resnels diffraction

!attern d#e to a straight edge$ shoing the intensity distri#tion. Bo are these feat#res e6!lained?(1997)

10. Differentiate eteen @resnel and @a#nhoffer diffractions. Bo can one e6!lain the @resnel diffraction!attern d#e to a straight edge? (1999)

11. Monochromatic light from a distance so#rce of avelength falls on a do#le slit. * glass !late ofthic%ness t is inserted eteen one slit and the screen. alc#late the intensity at a central !oint as thef#nction of thic%ness t. (2001)

12. Disc#ss the @resnel diffraction !attern formed y a straight edge #sing the corn#s s!iral. (2002)13. Atain an e6!ression for the intensity of light in the fra#nhofer diffraction !attern d#e to a circ#lar

a!ert#re. What is *iry !attern? 46!lain ith a neat diagram. (2003)1,. * narro slit ill#minated y monochromatic light of'5,00 is !laced at a distance of 3 meters from a

straight edge and the screen is 5 meters$ alc#late the distance eteen the first and the fo#rth dar%ands. (200,)

1. What is the essential difference eteen interference and different of light? Bo can yo# achieve@ra#nhofer diffraction in the laoratory? 8sing the conce!t of @ra#nhofer diffraction at a single slit$ findo#t the intensity distri#tion !rod#ced y to slits of e>#al idth. (200)

15. he \ and co-ordinates of orn#s s!iral can e e6!ressed >#antitatively y to integrals. Derive thee6!ressions for these integrals. (2005)

17. he radi#s of the first Lone in a Lone !late is 2.00 mm.What ill the !osition of the first image of a !oint

so#rce of light of avelength ' 00 nm !laced at a distance of m from the Lone !late. (2007)

1


16/41

TUTORIAL SHEET :12

(Reso!vn& Po"er o Instr3#ents)

1. tate "ayleigh criterian for limit of resol#tion. ho that 2ma6

middle ;

&

&

=

(1992)2. * diffraction grating ith 3 10,lines is #sed in the second order in the range of avelength 5000 .

@ind the smallest () it can resolve.(1992)

3. Disc#ss the theory of diffraction grating and find conditions for the asent s!ectra. Disting#isheteen resolving !oer and dis!ersive !oer of a grating.

(199,),. he ang#lar se!aration eteen to distant stars is 1 arc - second. &f the effective avelength of light

is 00 $ hat sho#ld e the diameter of the o=ective of a telesco!e so that the stars are =#stresolved?

(1995). * !lane transmission grating has 5000 lines !er cm. Determine the ang#lar se!aration eteen theto lines of sodi#m of avelengths ;95 and ;90 in the second order s!ectr#m. &f the idth ofthe grating is 2$ cm. $ ill these lines e resolved?

(1997)5. Define dis!ersive and resolving !oers of a !lane transmission grating and otain e6!ressions for the

to. ho that the first and second order s!ectra !rod#ced y s#ch a grating ill never overla! henthe incident light contains avelengths in the range of ,000 to 7000 .

(199;)7. 46!lain the terms resolving !oer and magnifying !oer of an o!tical instr#ment. An hat !arameter

do these !hysical >#antities de!end in case of a telesco!e? @or a given resolving !oer hat is the

o!tim#m magnifying !oer in this case?(199;)

;. odi#m light is incident normally #!on a !lane transmission grating having 000 lines


17/41

TUTORIAL SHEET: 11

Po!araton

1. * eam of linearly !olariLed light is changed into circ#larly !olariLed light y !assing it thro#gh a sliceof crystal 0.003 cm. thic%. alc#late the difference in refractive inde6 of to rays in crystal ass#ming

this to e minim#m thic%ness that ill !rod#ce the effect and that the avelength of light is 5 10-7m.(19;;$ 19;9)

2. 46!lain mathematically ho left and right circ#larly !olariLed light is !rod#ced y comining tolinearly !olariLed eams. Hiven a eam of light$ ho can one e6!erimentally test hether it is#n!olariLed or circ#larly !olariLed? (1990)

3. Ded#ce the !ossile thic%ness of a >#arter ave !late of >#artL hich is to e #sed for odi#m light ofavelength ;90 *o. (o' 1.5;$ e' 1.,;5) (1991)

,. Hive an o#tline of @resnels e6!lanation of o!tical rotation. Bo does o!tical rotation d#e to materialvary ith ?@or an o!tically active material the difference eteen the refractive indices for right - handed and left -

handed virations ("- E) for ' ,00 *o

is 12 10-

. 4stimate the o!tical rotation ca#sed y 1mmthic% !late in light of ' ,00 *o. *ss#me ("- E) to e inde!endent of .(1992)

. Hive an acco#nt of the origin of o!tical activity in >#artL crystal. * afer of crystalline >#artL ofthic%ness 2.9, 10-m is #sed to change a eam of linearly !olariLed light ( ' ;9 nm) intocirc#larly !olariLed light. @ind the difference in refractive inde6 for the to aves in the crystal$ass#ming this to e minim#m thic%ness that ill !rod#ce the effect?

(1993)5. Descrie ho @resnel has acco#nted for the rotation of the !lane of !olarisation of light. 46!lain the

action of a half - shade device. (199,)7. * left circ#larly !olariLed eam of light (' 5000 *o) is incident on a >#artL crystal (o!tic a6is !arallel

to the s#rface). @ind the state of !olarisation of the emergent eam. (hic%ness of >#artL crystal ' 2.3 10-m$ e' 1.3; 0' 1.,,,). (199)

;. What is a >#arter ave !late? 46!lain its #se in the !rod#ction and detection of circ#larly !olariLedlight. @or calcite ' , 72 0*$ 0 '1.59 and 4' 1.,;;. &f the minim#m thic%ness of a !late that can

e c#t from calcite is 30 m$ hat sho#ld e the minim#m thic%ness for !re!aring a >#arter ave !late? (1995)

9. What is a >#arter !late? * !hase retardation !late of >#artL has a thic%ness 0.1,35 mm. alc#late theavelength in the visile region for hich this !late ill act as a >#arter ave !late. he refractiveindices of >#artL for ordinary and e6tra ordinary rays are 1.,,3 and 1.33 res!ectively.

(1999)

10. @o#r !erfect !olariLing !lates are stac%ed so that the a6is of each is t#rned 30ocloc%ise ith res!ect tothe !receding !late the last !late is crossed ith the first. Bo m#ch of the intensity of an incident#n!olariLed light is transmitted y the stac%? (2000)

11. Why does one get !olariLed light from icols !rism? Bo sho#ld one ad=#st the !olariser and andyser$so that an intensity of the incident light is red#ced y a factor of 0.2.

12. Bo do yo# %no that the light is a transverse ave? What is a >#arter ave !late? Bo is itconstr#cted? (2002)

13. * >#artL >#arter ave !late is to e #sed ith the sodi#m light (';59 ). What sho#ld e itsthic%ness. (200,)

1,. Why does one see to image !oints for a single o=ect !oint hile vieed thro#gh a calcite crystal?What is this !ro!erty of the crystal %non as? What is an o!tic a6is of a crystal? 46!lain the meaningof !ositive and negative crystals ith one e6am!le for each %ind. (200)


18/41

1. What is o!tical activity? Hiven reasons for the concl#sion that o!tical rotation in li>#ids has amolec#lar origin. What do yo# mean y ordinary and e6traordinary rays? What are !ositive andnegative crystals? Hive an e6am!le of each. om!#te the minim#m thic%ness of a >#arter-ave !latemade from >#artL for incident avelength of ;9.3 nanometer. Hiven ]0'1.,, and ]4' 1.3. (2005)

15. Bo o#ld yo# !rod#ce !lane !olariLed light y reflection ? What is /resters la? alc#late theang#lar !osition of the s#n aove the horiLon so that light reflected from a clam la%e is com!letely

!olariLed. he refractive inde6 of ater is 1.33. irc#larly !olariLed and #n!olariLed light are !assedin t#rn thro#gh a icol !rism. he icol is rotated ao#t the direction of light as a6is. What o#ldyo# oserve in each case? Bo o#ld yo# disting#ish eteen them? (2005$ 20 mar%s)

17. onsider s#!er!osition of to !lane !olariLed electromagnetic avesO 4y' a cos (%6-t) and 4L' cos (%6-t:k) . Disc#ss the conditions for the res#ltant ave to e

left circ#larly and right circ#larly !olariLed ado!ting the convention as seen y an oserver travellingith the ave. (2007$ 20 mar%s)


19/41

TUTORIAL SHEET: 1%

LASERS

1. 46!lain laser action inO(i) Beli#m - eon Easer (19;9$1991$ 1997)(ii) "#y laser (1990)

2 * r#y laser !rod#ces a eam of light of avelength 59,3 *oith a circ#lar cross - section of 1cm indiameter. alc#late the diametre of this eam at a distance of 1000 %ilometers.

(1992)3. 46!lain the general !rinci!le of laser action. What do yo# mean y !o!#lation inversion? Disc#ss the

involved in the r#y laser. * !#lsed laser is rated at 10 m W. &t generates 3 ns ide !#lses at fre>#ency00 BG. om!#te the instantaneo#s !oer in the !#lse.

(1993),. he light (' 5000 *o) from a laser of sectional diameter 1.0cm and !oer 0.20 att is foc#sed y a

lens of focal length 10cm.Determine the area of the image and intensity in it in att#ency of the emitted !hotons and the order of 4insteins coefficient /21 (1997)

9. * 3 MW laser eam hich has a diameter of 1cm is foc#sed y a lens of focal length cm. heavelength of laser is 10$000 *o. alc#late the intensity at the focal !lane of the lens.

(1997)10. What is !o!#lation inversion? Mention the methods of achieving !o!#lation inversion. 46!lain the

conce!t of negative tem!erat#re.(1997)

11. * short - foc#s lens is #sed to foc#s a laser eam of avelength 532; *o. &f the eam idth iscom!arale to the focal length of the lens$ calc#late the area of cross-section of the region of foc#s.

(1999)12. 46!lain hy a to - level system is not ade>#ate for laser o!eration. Dra the essential !arts of a r#y

laser and e6!lain the or%ing !rinci!le.(1999)

13. 46!lain the !henomenon of self foc#ssing of laser eams. (2003)

1,. 46!lain ho 4insteins * and / coefficients are related to the !henomena of s!ontaneo#s and stim#latedemission of radiation$ res!ectively. Derive the relation eteen * and /. 4stalish that at very highfre>#ency aro#nd \-ray avelength regime$ lasers cannot e made as easily as at lo fre>#encies$ e.g.$far infra-red regime.

(200)


20/41

TUTORIAL SHEET: 1+

(S;ea! To;s)

1. Write a short note on

(i) Bologra!hy (1995$ 1999$ 2000)

(ii) !atial tem!oral coherence (19;9)(iii) #rity of s!ectral lines and coherence length (1991)

2. What is a hologram? 46!lain ho the image of the o=ect is formed hen one loo%s thro#gh it.

(1990)

3. Define coherent length. * heli#m - neon laser emits radiation at avelength ' 523.; nm ith

' 2!m. alc#late the coherent avelength.

(1993)

,. What is meant y tem!oral and s!atial coherence ? ho that the coherence length E ' N here is

the mean ave length and N re!resents the !#rity of a s!ectral line. (1995)

. What is s!atial coherence? onsidering yo#ngs to slit e6!eriment$ !rove that the distance eteen

the slits m#st e s#fficiently less than

for otaining fringes of good contrast is the avelength

of light #sed and is the angle s#tended y the so#rce slits.

(1997)

5. 46!lain the !henomenon of !#lse dis!ersion in ste! inde6 fire.(2003)

7. What is hologra!hy? Descrie the e6!erimental set #! for Haors on-line hologra!hic recording. What

are the limitations of Haors e6!eriment. Bo ere these overcome y Eeith and 8!athei%s?

(2003)

;. Draing a neat diagram$ disc#ss ho light travels thro#gh on o!tical fire. ho that the n#merical

a!ert#re of a commercially availale o!tical fire is aro#nd 02. 46!lain its !hysical significance.


21/41

ELECTRICITY > MA?NETISM

TUTORIAL SHEET: 1,

(E!etrostats)

1. o !oint charges each of magnit#de :2 mill co#lom are !laced at * and / in front of an infinite

cond#cting !lane$ hich is gro#nded. he line A*/ is !er!endic#lar to the !lane ith the !oint A on the!lane. &f A* ' 1m and */ ' 2m$ calc#late the force on the charge at *.(19;9)

2. he com!onents of an electrostatic field in vac##m are give as

2

3r

(6

r

a46 +=

r

f6L4L= $ here a$ $ c and f are constants 6$ y$ L the rectang#lar artesian

coordinates and r2' 62: y2: L2. 8sing the asic e>#ations oeyed y the electrostatic field in +ac##m$find the relations eteen a$ $ c$ and f and determine the charge density at a general !oint in s!ace.

Wo#ld that e6!lain the oserved field?(1990)

3. ho that the electric field intensity d#e to any distri#tion of charges at rest can e e6!ressed as thegradient of a !otential. What is the relation eteen !otential and !otential energy?* thin disc of radi#s " is #niformly charged$ eing the charge !er #nit area. @ind the !otential and theelectric intensity at !oints on the a6is of the disc. Bo do these change as one crosses the disc? 46!lainthe changes !hysically. (1991)

,. o charges are !laced at a distance 1 meter. he magnit#de of one charge is do#le that of the secondcharge. @ind the ne#tral !oints in the to cases (i) the charges are of the same sign (ii) the charges are ofo!!osite sign. What ha!!ens to the ne#tral !oint if the to charges are of e>#al magnit#de and o!!ositesign?

(1992). tate o#loms la and sho that the electric field can e derived from a !otential f#nction. &f the

charge distri#tion is contin#o#s$ find the integral form#la for determining its field.(1992)

5. 8sing Ea!laces e>#ation otains an e6!ression for the !otential eteen to coa6ial cylinders. (199,)7. *n electric di!ole is !laced in an e6ternal electric field. @ind the interaction energy eteen the electric

di!ole and the field. *nd hence find the force and the tor>#e acting on the di!ole(199)

;. *n electric di!ole moment

2! is !laced at (r$ ) in the electric field of another di!ole moment

1! $

!laced at the origin. *ss#ming that the electric !otential$ +$ at (r$) d#e to 1is ( ) $r,

)os!Mr$+

2

0

1

= find

the di!ole V di!ole interaction energy.(1995)

9. 8sing Ha#ss la find the electric field inside a cylindrical ca!acitor and hence derive the e6!ression forits ca!acitance. @ind the dielectric constant of the material inside a 0mm long ca!acitor of ca!acitance,0 @ having inner cond#ctor of radi#s 1mm$ o#ter cond#ctor of radi#s 10mm. Which of the materialshas s#ch a val#e of the dielectric constant? (1997)

10. Determine the energy of attraction an electric di!ole and a !lane ond#cing #rface at Lero !otential. (199;)

c6y4y

r=


22/41

11. * !otential field is given y ' (62: y2: L2) volt

@ind the electric field at a !oint (6$y$L) and the charge density in the region. (1999)

12. alc#late the electric field as a f#nction of !osition d#e to a di!ole hose !otential is cos,Z rS herer'6S:yS. he di!ole is at the origin of 6$y system. (2001)

13. * ond#cting s!here of radi#s a is !laced in #niform 4o. 8sing the method of images sho that

!otential is given y3

2

a4o r cos

r

(2001)

1,. alc#late the electric field for a !oint on the a6is of a #niform ring of charge F> and radi#s Fa. hothat the ma6im#m val#e occ#rs at 6 ' ua is held at a distance d in the front of an infinite gro#nded cond#cting !lane. What is theelectric !otential in front of the !lane? (200,)

21. Derive a!!ro6imate e6!ressions for the !otential and the radial as ell as the aLim#thal com!onents ofthe field d#e to an electric di!ole at !oints far aay from it. *lso derive e6!ression and hence descrie

the effect of a #niform electric field on a di!ole hich can rotate freely. (200)22. What is molec#lar !olariLaility? Derive la#si#s - Mosotti e>#ation relating the molec#lar!olariLaility ith the dielectric constant of a dielectric material. (2005)

23. tarting from Ma6ells e>#ation$ D ' j$ here D is the electric dis!lacement density and j is thecharge density$ derive oissons e>#ation. Ded#ce Ea!laces e>#ation for charge-free region fromoissons e>#ation. (2005)

2,. * !otential in cylindrical coordinates is a f#nction of r and w #t not of L. Atain the se!arateddifferential e>#ations for " and x$ here +' "(r) x (w) and solve them. (2005)

2. Derive !oisson e>#ation starting from the o#loms la for a set of !oint charges. (2007$ 20 mar%s)25. Atain the sol#tion of the Ea!lace e>#ation in cylindrical coordinates. (2007$ 20 mar%s)


23/41

TUTORIAL SHEET: 1

(7ot-SavartBs !a" > a;;!atons)

1. * ire of length 1 is ent into the form of a rectangle of sides a and and carries a c#rrent &. alc#late

the magnetic field intensity at the centre of the rectangle. ho f#rther that the intensity is minim#m fora ' (19;9)

2. tarting from /iot-avarts la$ calc#late the magnetic field at the centre of a solenoid of length 1 metre$radi#s 2 cm and having 2 t#rns !er cm.$ the c#rrent thro#gh the solenoid eing 1 *m!ere.

(1990)3. * charged !article moving horiLontally toards the east ith a velocity of 10m


24/41

TUTORIAL SHEET: 1. (EMI > A*C*)

1. * 220 volt 0 cycle * s#!!ly is connected to a circ#it containing a resistance of 20 ohms$ in seriesith a 100@ a!acitor. Determine the c#rrent and the !hase.

(19;;)2. *n electromotive force 40in !t : 41in 2!t is im!ressed on a circ#it containing an ind#ctor and aresistor. et #! the differential e>#ation oeyed y the c#rrent and sho that in the steady state thec#rrent com!rises to sin#soidal terms. alc#late the average !oer dissi!ated in the circ#it. Whatis the difference$ if any$ eteen a varying c#rrent and an alternating c#rrent?

(19;9)3. * circ#lar coil of ire having 100 t#rns and radi#s 10cm is rotating ao#t a +ertical a6is in its on

!lane #niformly at the rate of ,;0 revol#tions !er min#te. here is a horiLontal Magnetic field ofintensity 0.01 #ation for the discharge of a ca!acitor connected in series ith a resistor " and an

ind#ctor E. &f "0 stands for $)

E2 disc#ss three cases (&) "X"0. What ill yo# oserve if the

discharge ta%es !lace at a lo tem!erat#re hen the material of resistor has ecome s#!ercond#cting?

(1991)

. he total energy 8 in an oscillating E- circ#it is given y 8 ' 8 / : 84' $)

>E&

2

1 22 + hen the

resistance of the circ#it is Lero. @rom this sho that it is an oscillatory circ#it and find the time

!eriod. (1992)5. &f steady voltage is a!!lied to an E-" circ#it$ sho ho voltage across the ind#ctance and the c#rrent

in the circ#it changes ith time. 46!lain the term ind#ctive time constant.(1992)

7. * harmonic e.m.f is a!!lied to a series circ#it$ containing resistance$ ind#ctance and ca!acitance.Derive the e6!ression for the c#rrent and condition for resonance.

(1993);. * series circ#it consisting of ,.10 ohms of resistance$ ;10 B of ind#ctance and 22 @ of

ca!acitance is e6cited y a constant voltage am!lit#de generator of variale fre>#ency. *t hatfre>#ency is the ma6im#m !oer delivered?

(1993)9. * harmonic e.m.f is a!!lied to a !arallel resonant circ#it$ containing resistance "$ ind#ctance E and

a!acitance . Derive e6!ressions for resonance$ ang#lar fre>#ency 0and the andidth .(199)

10. alc#late 0$ and >#ality factor N for E" !arallel resonant circ#it given the val#esO ' 0.,@$ E ' , mB$ and " ' 1

(199,)

11. ho that the energy stored in a a!acitor is)2

> 2hile the energy stored in the ind#ctor is $E&

2

1 2

here the symols have their #s#al meanings. (199,)


25/41

12. *n alternating voltage is a!!lied to " circ#it connected in series. 8nder hat conditions it acts asan (i) integrator and (ii) a differentiator?

(199)13. *n alternating voltage of varying fre>#ency is a!!lied across a to-ranch !arallel circ#it of "1and

E in series and "2and in series as shon in @ig. /eloO@ind its resonant fre>#ency. &f "1 and "2 are not Lero$ state the conditions hen the resonant

fre>#ency is given yE)2

1f0

=

(199)1,. elf-ind#ctance of to coils$ * and /$ connected in series is 2 m B or 10mB de!ending on the

relative c#rrent directions in the coils. elf &nd#ctance of * is 10mB calc#late m#t#al ind#ctance Mof the !air of coils$ co#!ling factor and lea%age factor. &f the c#rrent in coils is changing at the rate of1000 *#encies f!and fginter-related as

r11fsf! += here a(

)

)r= (1995)

15. * relay has a coil resistance of 10and ind#ctance of 1B. &t is energiLed y a single voltage !#lse of10+$ hich remains constant for 20 ms and then falls to 0+. "elay contact closes hen theincreasing c#rrent reaches 200 m* and o!ens hen the decreasing c#rrent is at 100 m*. alc#late

the time for hich the relay contact is closed.(1995)

17. he elf-ind#ctance of !rimary and secondary coils of a ".@ transformer is 10mB each. When thecoils are connected in series$ self-resonating fre>#encies are 132.5 BG and 10;.3 BG. alc#latethe m#t#al ind#ctance eteen the coils the inding ca!acitance.

(1997)1;. Define >#ality factor for an *.. circ#it and disc#ss the meaning of electrical resonance in a series

E" circ#it. 46!lain the term shar!ness of resonance(199;)

19. o coils are connected in series and their total self-ind#ctance is ,.,0 mB. When c#rrent isreversed then total self-ind#ctance is 1.50 mB. *ll the fl#6 d#e to the first coil lin%s the second coil$

#t only ,0q of the fl#6 d#e to the second coil lin%s the first coil. @ind the self-ind#ctance of each ofthe coils and their m#t#al ind#ctance.

(199;)20. * !otential difference ith a fre>#ency of 0 cycles !er second is a!!lied to a coil of resistance 1

ohms and ind#ctance 2B. alc#late the !oer factor of the circ#it.(199;)

21. *n E V V " circ#it has a resistance of 100 ohms$ a ca!acitance of 0.2 @ and an ind#ctance of B.*n a.c. so#rce 4 ' 0 in 1000t +olt is connected in the circ#it. alc#late the average !oerdissi!ated.

(1999)


26/41

22. &n a series E V V " circ#it connected to an alternating constant voltage so#rce the c#rrent

am!lit#de is

n

1times the am!lit#de at resonance at fre>#ency 1and 2. Atain an e6!ression for

its >#ality factor at resonant fre>#ency. (1999)

23. o ind#ctance coils having ind#ctances E1 and E2 and negligile resistances are connected in!arallel. he coils have a m#t#al ind#ctance M. Atain an e6!ression for the effective ind#ctance ofthe comination.

(1999)2,. @or anR-L-Cseries resonant circ#it$ sho that 210 fff = $ heref0is the resonance fre>#ency andf1

andf2are the half-!oer fre>#encies. &s this relation tr#e for a !arallel resonance circ#it in hich R,Land Care connected in !arallel to each other? 46!lain.

(2000)2. * seriesR-Lcirc#it has a constant d.c voltageVa!!lied at the time t ' 0 y closing a sitch

(a) Derive an e6!ression for the c#rrent in the circ#it

() alc#late the voltage dro!s acrossRand acrossL.(c) *t hat time are these voltage dro!s e>#al?(d) @ind the !oer dissi!ated yR and !oer stored inL.(e) ho that the steady-state energy is stored in the magnetic field.

25. What val#e of ind#ctance has to e #sed so that a lam! ith rating of 200 volt 10 am!eres lightsthe same ay ith 20 + so#rce at 0BL.

(2001)27. *n ind#ctance is connected to a 5volt attery thro#gh a resistance ". What is the steady state c#rrent

in the circ#it? *fter hat time the attery o#ld e delivering one half its steady state c#rrent?(2001)

2;. 46!lain the #se of a !arallel resonance circ#itO 1) as a re=ecter circ#it 2) for c#rrent am!lification.(2001)

29. * series E" circ#it ith E'2B$ '2 ]@ and "'20 is !oered y a so#rce of 100 volts and varialefre>#ency. @ind the resonance fre>#ency fo he val#e of N

i. he idth of resonance andii. he ma6im#m c#rrent at resonance.

(2002)

29. * ridge netor% ith resistance ca!acitance and ind#ctance is given in the aove fig#re. ho thatthe condition for alancing the ridge is inde!endent of the fre>#ency of a!!lied voltage.

(2003)

30. &n an a.c. circ#it a resistance (R' 100) and a ca!acitance (C' 1 ] @) in series are connected to ana.c. so#rce V' 200 sin (100 t). alc#late the c#rrent thro#gh the circ#it and voltages acrossR and

C. Dra a vector diagram re!resenting the magnit#des and !hases of the voltages. (2007)


27/41

TUTORIAL SHEET: 1/(r4oBs !a"s > a;;!atons)

1. tate irchoffs las of the distri#tion of c#rrents (a) in the #s#al form for steady c#rrents and () in aform a!!licale to alternating c#rrent netor%s. Disc#ss the method for com!aring ind#ctances y #singMa6ells ridge. tate the disadvantages of the method. (199;)

2. *n ind#ctance in connected to 5 volt attery thro#gh a resistance ". What is the steady state c#rrent inthe circ#it? *fter hat time the attery o#ld e delivering one half its stead state c#rrent? (2001)3. 8sing irchoff las find c#rrents in each ranch of the circ#it shon in the folloing diagram.

(2002),. * netor% N" is connected as shon in the fig#re elo. *!!ly irchoffs la and sho that thec#rrent floing thro#gh the 20 resistor " is 0.029 *.

(200,)


28/41

TUTORIAL SHEET: 10(E!etro#a&net =aves)

1. Derive an e6!ression for the oyntings +ector and e6!lain its significance. * light so#rce (1 iloatt)is radiating energy #niformly. Determine the intensity of the electric field at a distance of one meter

from the so#rce. (19;;)2. Write don Ma6ells e>#ations in vac##m. ho that in the so#rce-free case$ oth the electric and

magnetic vectors oey ave e>#ations of identical form and considering a !lane ave sol#tion$ !rovethat the electric and magnetic vectors and the direction of !ro!agation are m#t#ally !er!endic#lar. hof#rther that there is a !ro!agation of energy given y the !oynting +ector

(19;9)3. &n a certain region of s!ace in vac##m$ the com!onents of the magnetic ind#ction are (in #ations$ otain$ differential e>#ations for scalar and vector !otentials. olve

the e>#ation for scalar !otential in a dielectric medi#m having so#rce of charge density .(199)

12. ho that atten#ation constant and !hase fact for an electromagnetic ave$ !ro!agating in a

!erfectly cond#cting medi#m are e>#al. *t hat fre>#ency the s%in de!th in silver is 1 m$ hen thecond#ctivity of silver is 30 105siemens


29/41

(1995)13. Write don Ma6ells e>#ations in free s!ace and hence sho that the !hase velocity of the

electromagnetic ave is e>#al to the velocity of light in free s!ace.(1997)

1,. Atain the characteristic im!edance of the vac##m. Derive the e6!ression #sed.(1997)

1. Derive the ave e>#ations for

4 and

/ and solve one of these for !lane ave !ro!agation in an#no#nded$ homogeneo#s dielectric medi#m. @#rther sho that in a !lane ave

0$/$4 form a

m#t#ally orthogonal right handed system.(199;)

15. * traveling electromagnetic ave is descried y the e>#ation 46(G$ t) ' 0. cos. (20tV2G). Determine(i) s!eed of the ave$ + (ii) ave length$ (iii) ime !eriod$ (iv) Direction of !ro!ogation.

(199;)17. he electric field vector of a !lane electromagnetic ave is given y

6zt%Lcos44 0

+=

Write the magnetic field vector. alc#late the average energy !er #nit vol#me stored in electromagneticfield and the average energy fl#6 density.

(1999)1;. alc#late the !ea% val#es of 4 and

/ for a laser eam of !oer 210

10att and radi#s 0.1mm.(1999)

19. Fhe introd#ction of the dis!lacement c#rrent is one of the ma=or contri#tions of Ma6ell. Disc#ss.(2000)

20. 8sing Ma6ells e>#ations$ derive the electromagnetic ave e>#ations for a cond#cting medi#m andsolve it.

(2000)21. What is the limiting case of a metallic cond#ctor in the aove case? 46!lain.

(2000)22. What is ga#ge transformation? Define co#lom ga#ge. Derive the e>#ation for vector otential #nder

co#lom ga#ge. (2001)

23. Define scalar and vector !otentials. "ecast Ma6ells e>#ations in terms of these !otentials.(2001)

2,. Derives the energy contin#ity e>#ation for electromagnets aves #sing the !o#ting vector.(2001)

2. Why did Ma6ell have to introd#ce the idea of dis!lacement c#rrent? Derive the ave e>#ation fromMa6ells e>#ations. Atain @resnels form#la for reflection and transmission coefficients of the electricfield vector here it is !er!endic#lar to the !lane of incidence.

(2002)25. What are vector and scalar !otentials for the electro magnetic field? *re they #ni>#e? 46!lain hat are

co#loms EorentL ga#ges. Derive the electromagnetic ave e>#ation in EorentL ga#ge and sho that itis e>#ivalent to Ma6ells e>#ation.

(2002)

27. fine !ointing vector and e6!lain its significance. he electric field vector for an electromagnetic fieldtravelling in vac##m is given y 4 '40cos(%L- t) zEalc#late the !oynting vector for the ave and sho that its magnit#de is e>#al to the energy density ofthe ave time the velocity of light.

(2003)


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2;. * !lane ave of fre>#ency Y travels into to linear dielectric media. &t has a normal incidence at theinterface of the media. Hiving a!!ro!riate o#ndary conditions$ otain e6!ressions for the intensities ofreflected and transmitted rays. (2003)

30. What are the +ector and scalar !otentials? Derive Ma6ells e>#ation in terms of these !otentials.

(200,)

31. ho that the !ointing +ector 9

4 B re!resents the energy flo !er #nit time oth in magnit#de anddirection in case of a !lane electromagnetic ave. (200,)

32. ho that the electric and magnetic field vectors$ 4 and / $ !lane electromagnetic aves are m#t#ally!er!endic#lar in a !lane normal to the direction of !ro!agation. Bo are !hases of 4 and / related toeach other?(200)

33. Write don the macrosco!ic from of the Ma6ells e>#ation in any isotro!ic (#t inhomogeneo#s)medi#m and define the symols a!!earing therein. onvert these e>#ations in the integral forms tohighlight the las re!resented y these e>#ations. (200)

3,. Descrie !hysical significance of the dis!lacement c#rrent considering the e6am!le of c#rrent flothro#gh a ca!acitor. (200)

3. What do yo# mean y a ga#ge transformation? What is its im!ortance? ho that the EorentL ga#gecondition .*: 1. {k ' 0 is EorentL invariant. Bere * and k are the vector and scalar !otentials. (2005)

c2 {t

35. tarting from Ma6ells e>#ations of electromagnetic field in vac##m otain the classical ave

e>#ations for the fo#r field vectors 4$ D$ / and B. ho that the field vectors can e !ro!agated asaves in free s!ace ith the velocity of !ro!agation e>#al to 3 6 10;m


31/41

TUTORIAL SHEET: 1

7!aD 7o65 Ra6aton

1. Write don the e6!ression for energy distri#tion of a lac% - ody radiation at tem!erat#re andded#ce Wiens dis!lacement la. (19;;)

2. Define solar constant and say hich of the val#es 1.3, W#ency s!ectr#m and the Wiens distri#tion at the other end.

(199;)10. alc#late the ma6im#m amo#nt of heat hich may e lost !er sec. y radiation from a s!here of 10

cms. diameter at a tem!erat#re of 227o hen !laced in and enclos#re at a tem!erat#re of 27o. Hiventhat ' .7 10-2att


32/41

1. tate "ayleigh-eans la. ho that the intensity of emissions at a !artic#lar avelength is !ro!ortionalto the tem!erat#re T. Disc#ss the limitations of this la in descriing the intensity distri#tion ofemission s!ectr#m of a lac%ody. (2007$ 2 mar%s)

TUTORIAL SHEET: %2THERMAL PHYSICS :7as Cone;ts

1. alc#late the or% done in com!ressing adiaatically 10-3%g of air initially at to one -half itsoriginal vol#me. (Hiven density of air at ' 1.293 %g.


33/41

TUTORIAL SHEET: %1CarnotBs C5!e an6 Entro;5

1. * arnots engine is made to or% eteen 0o and -200o. alc#late its efficiency. Derive the e6!ression yo##se for calc#lation.

(19;;)2. * vol#me of one gm. mole of an ideal gas e6!ands isothermally to fo#r times its initial vol#me. alc#late the

change in its entro!y in terms of gas constant. (19;;)3. 1%g of ice at 0o is melted and converted to ater at 0o . om!#te the change in entro!y.

(19;9),. * and / are to h#ge loc%s of same metal. he loc%s are connected y a h#ge rod of the same material. he

tem!erat#res of * and / are 100 and 00 res!ectively. he rate of heat cond#ction is 10,


34/41

!ecific heat of ater ' ,.2 % %g-1-1and latent heat of f#sion of ice ' 335 % %g-1p (2005)

1;. rove the la of increase of entro!y. ho that for a system at fi6ed tem!erat#re and !ress#re to e ine>#iliri#m$ its His free energy sho#ld e minim#m. (2007)

19. * system at tem!erat#re 1is ro#ght in contact ith a reservoir at tem!erat#re 2 1. When the system and thereservoir reach the thermal e>#iliri#m$ calc#late the change in the entro!y of the #niverse ass#ming the heatca!acity of the system to e constant. Disc#ss hether the considered change is !ositive or not. (2007)


35/41

TUTORIAL SHEET : %%T4er#o65na# re!atons4;s

1. Atain the cla#si#s cla!eyron e>#ation

( )

d!

d-

E

- v v=

2 1here the symols have their #s#al meanings. (19;9$ 199,)

2. 4stalish the relation )! )v - !-+-v !

= (1991)

3. Write don the general e6!ression for the o#le - elvin effect and define o#le - elvin coefficient$ .ho that for an ideal gas ' 0 (1991)

,. he density of steam at 100o is nearly 0.50 10-3%g


36/41

~' 1 {+ - + ! { !alc#late the val#e of ] for an ideal gas and inter!ret yo#r res#lt !hysically. (2005)

13. 4stalish the relation

8se it to find o#t an e6!ression for ! on one mole of a gas hose internal energy is given y8' c V (a#ation of state ( : a


37/41

(net t4eor5 o &ases)

1. * gas !ossess a Ma6ellian velocity distri#tion f#nction sho that the fraction of molec#les in a givenvol#me that !ossesses a velocity (:+6) in one direction only and hose magnit#de is greater than someselected val#e +ois

( )

=

0+

2120

2

166

-

mverf1

2

1d+vf

symols have their #s#al meanings.(19;;)

2. @ind the tem!erat#re at hich r.m.s. velocity of nitrogen molec#les in earths atmos!here e>#als the

velocity of esca!e from the earths gravitational field. Mass of 2atom ' 23. 2, 10-2,gm. Meanradi#s of earth ' 5370 %m.

(19;;)

3. alc#late the mean free !ath of heli#m atoms at $ the co-efficient of viscosity eing 190 10-7%gm-1g-1. *tmos!heric !ress#re ' 0.075 13.5 1039.;1 #iliri#m attem!erat#re 300.

(1990);. Write don Ma6ell - /oltLmann distri#tion for the energy of molec#les of a gas at tem!erat#re .

@ind the energy at hich this distri#tion !ea%s. om!#te in e+ the mean energy of molec#les of a gas

at 27o.(1991)

9. alc#late the tem!erat#re at hich the average s!eed of B2molec#les e>#als that of A2molec#les at30.

(1992)10. * shoer of 5 103molec#les$ each travelling initially ith same velocity$ traverses a gas. 4stimate the

n#mer of molec#les hich ill travel #naffected even after traversing a distance e>#al to tice themean free !ath. (1992)

11. Derive an e6!ression for the !ress#re e6erted y an ideal gas on the alls of the chamer in terms ofconcentration of molec#les Fn$ gas tem!erat#re and a #niversal constant. !ecifically disc#ss ho comes into the !ict#re?

(1993)


38/41

12. Derive e6!ressions for the Ma6ellian distri#tion of (i) one com!onent of velocities (ii) onecom!onent of momenta$ in the molec#les of an ideal gas.

(199,)

13. alc#late the most !roale s!eed +!$ the average s!eed V and the root - mean s>#are s!eed V212

for hydrogen molec#les at 273 . (199)1,. What is /ronian motion? Ded#ce 4insteins form#la for translatory /ronian motion of !articless#s!ended in a li>#id and hence determine the *vogadros n#mer.

(1995)1. tate the !rinci!le of e>#i!artition of energy. What are its limitations? ho that it is a!!licale only

hen the energy is a >#adratic f#nction of the associated variale.(1995)

15. ho the distri#tion of velocities for tem!erat#res 1 $ 2 and 3 (1 2 3) of gas molec#les

according to the Ma6ell - /oltLman la. 8sing this la !rove that the most !roale velocity is3

2

times the root mean s>#are velocity. (1997)17. Atain an e6!ression for the mean free !ath. Mention the correction introd#ced y Ma6ell. alc#late

the val#e of *vogadros n#mer$ if the mean free !ath of nitrogen molec#les at is 5.; 10-;m. hemolec#lar diameter is 3. *o.

(1997)1;. *t the the mass of one litre of B2 is 0.09 gm. alc#late the (i) "M (ii) Mean (iii) Most

!roale s!eed at 27o. (1999)

19. he "M s!eed of A6ygen molec#les at A0 is ,50 m


39/41

TUTORIAL SHEET: %,S;e 4eat o so!6s

1. hermal energy of a solid is given y the relation( )

E % g d

e

%

KBT

m=

1

"

here

m =KB &

% Deing the Deye tem!erat#re.

2. Hiven g () ' 5h2


40/41

TUTORIAL SHEET: %

S;ea! to;s

1. Write short notes onO(i) egative tem!erat#re (19;;)(ii) rod#ction of lo tem!erat#re #sing adiaatic demagnetisation (19;;$ 1991)

2. Write an e6!lanatory o#tline of thermal ioniLation of atoms and the s!ectra of starss!ecifying hat information e get from the latter.

(19;9)3. Disc#ss ho stars are classified on the asis of their s!ectra. /riefly mention hat

different information ao#t stars can e otained from the st#dy of their s!ectra.(1990)

,. Define thermodynamic tem!erat#re of a magnetic system. Ma%ing #se of His e>#ation$derive an e6!ression for cooling !rod#ced d#e to adiaatic demagnetisation !rocess. Whyis the method #sed only after !re - cooling to a lo tem!erat#re?

(1993). What is an adiaatic demagnetisation cycle? Disc#ss the cycle in terms of M-B indicator

diagram?(199,)

5. Descrie riefly ho it is !ossile to determine the elements !resent at the s#rface of agiven star.

(199,)7. Define thermodynamic tem!erat#re of a magnetic system. Disc#ss ho cooling ta%es !lace

d#e to adiaatic demagnetisation. 46!lain$ hy cooling d#e to adiaatic demagnetisationis im!ortant at lo tem!erat#res.(199)

;. 46!lain ho very lo tem!erat#re can e !rod#ced y adiaatic demagnetisation.(1999)

9. Bo one can otain the vario#s ty!es of informations ao#t the !hysical conditions on thestellar #rface #sing thermal ioniLation e>#ation to inter!ret the stellar s!ectra.

(2000)10. Bo can one otain a tem!erat#re and identify the elements in the stellar odies

8sing ahas thermal ionisatron e>#ation?(2001)

11. Atain +ander Waals e>#ation of state for real gases. What is the val#e of criticaloefficient for an ideal gas?ho that the +al#e of the critical coefficient for +ander Waals gas is inde!endent ofthe ty!e of the gas.

(2001)12. ho that the chemical !otential of a system is an intensive >#antity and is a f#nction of

tem!erat#re and !ress#re only(200)

13. tate D#long and etits la. Bo does it agree ith e6!eriment ? Disc#ss the limitationsof the classical theory and s#ccess of the >#ant#m theory in e6!laining the s!ecific heat ofsolids. (2005)


41/41

TUTORIAL SHEET: %.

Statsta! Me4ans

1. Derive the /ose- 4listeins distri#tion for an ideal gas. (2002)

2. Dis#ses the !henomenon of /ose V4insteins condensation. Atain the e6!ression forthe condensation tem!erat#re. /riefly comment on oservation of /ose V4insteinscondensate. (2002)

3. 100 !articles at a tem!erat#re are distri#ted among three energy levels$ 04 '0$

14 = and 24 2= . What is total energy of the system? (2003),. Define @ermi energy. @or an ideal @ermi gas of !articles at asol#te Lero tem!erat#re$

sho that the total energy is 3

here%n< > is the average n#mer of !articles in the %

th

>#ant#m state$derive an e6!ression for the average n#mer of !articles in the gro#nd state of an ideal/ose gas. (200)

5.() 8tiliLe the aove e6!ression to elaorate the conce!t of the /ose V4insteincondensation and disc#ss that the !henomenon e6!lains >#alitatively the !ro!erties inthe lo Vtem!erat#re !hase of li>#id ,Be. (200)

7. Derive the e6!ression for the @ermi V Dirac distri#tion f#nction. "e!resent it gra!hicallyfor ' 0 and 0. (2005)

;. Derive a relation eteen the total n#mer of fermions in terms of @ermi moment#m andhence otain the e6!ression for the total energy 4 of the system at asol#te Lero.

omine this e6!ression ith the e>#ation of state +' (2

physics paper-1 cse questions

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