IAS Mains Physics 2014

8/17/2019 IAS Mains Physics 2014

1/17

C

Q

.

I

u

1

V

iam

;

tx

am

20

.14

I

~ D

R N -

N -

R I Z

A I

mR

ic

ii l/

P

HY

SIC

S

~

~

I I

a

pe

r

.

Tim e a llow ed:

Three

H ours

~

J i

< f i

: 2

5

Maximum Marks:

250

rr·f.W

rsc

rrr f

Wn

1

J/f$

/{gil

TfT£

Zl1l

< > 31f

rtftm P

I

fi ti

fl TfT £

Zl1l 1/

fff i i

~ :

Trf .

r

rr

mr


2/17

WJS

SECTION

~ s w

e r ll of th

e

follo

wing :

. 1 X

lJ=5

(a) ·

a

it;

1

im

1ffiOI it> 'iR rC p =

Po a it>

t Po ~

'1

\

r

'iR rC ~ 3

fu

r

~

t ~ ~ I ~

1ffiOt it>

CORUT - ~ ~

t 2

a eft ~ '1\,

~ l f C I I C f l ~ U ~

"ffiQ ch)f';w:

I

The

density

inside a so

lid sphere o

f radius a is

g iven by p

=Po a wher

e ·.

r

p

0

is

th

e

d

ensity at

the

sur fa

ce and

r

denotes

the

dista

nce f rom

the

cen t r

e . Find

the·

gravi

tational

field d

ue to th is sphere

at a distance

2a

f

rom

its

ce

ntre.

(b) ~ I

3fu

I Sfllm: 1%

(311f.f?

t1)

1

@ it

i t ~ ~ 1

3li J i t > ~ - ~ ,

3fu

~ ~

~

lffil)

it

t

~

1

3li J

it>

~ - ~

1

m

.

.

.

it;

m • fcF

r' = M

R

2

+ I, R

1@ if; ~ I J

~ ~

0 0 1 ~ ·

~ 3fu

MmOOT S ;04GH ~

f I

a

nd

I be

the

M o men ts

o f Ine

rtia

of

a body about

an xis

passing

thro

ugh an

arbitrary

origin

and

ab

out a parallel

axis

through

the

ce

ntre

o f mas

s

r

espectively ,

show th

at I

=

MR

2

+

I

, where

R is

the

posit i

on

v

ector of

the

cen

tre of ma

ss

wi

th res

pect to t

he arbitr

ary

ori

g in

and

M is

the mass

o

f

the

body.

C

DRN N RiZ

A

1

1

www.examrace.co


3/17

0

(c)

R

l

i T ~ T

ffi:n

~

~ ~ t f t

~ 1 1 ,

i H d l

( ' : 1 ' f :

: r - f < l f < f l

· ~

(ff i1 ~

~

ri

~

m ~

TJfu qm

n

t I ~ ~

~ · ~

· ~ ·G

JO ~

fcld

(OI lRitQ>

I ~

f

cRrn

~

C f l l l ( C f l

TJfu

~ ~

~

~ ~

l < l ~ ' 1

l d l

~ ?

A sphere of

radiu s

R m oves with veloc ity

ri

m

an

incom pressible,-·

non-v i

scous i

deal

flu id .

C a lc

ulate .

the p

ressur

e d

istrib

ution ove

r th

e

sur fa

ce of

the

sphere

.

D

o you

th

ink t

hat

a forc e

is n

ecess

ary to

keep

.the

s

phere in

u

niform

mot

ion

?

d) .

i i F R I ~

~

A - ~


4/17

Q2

a)

~ " " l

\ l > ~

Q:

m ~

'T <

tiloA;

q

rt i

ii m

~ ,

q · ~

f.r<

ra

q t

:

rr@

~

31P

.1 i

fi ~ -

~

C

R "

® m

3

1P.1

if; ~

cBr c

n l

~

ff fi:m

) q

~

)

CiiT{


5/17

A

mi

rror

is movi

ng through vacuu

m with

a

relati

vistic

speed v in the

x-directio

n. A beam of light

with

f r equenc

y roi is normally

i

ncident

(from x = oo)

on

t

he

mi

rror

.

(i) What

is the f req

uency of the

ref lec ted lig

ht

expre

ssed

in

te

rms o f

roi,

c and

v?

(ii) What i

s

the

energy

of each ref lec ted photon ?

(b) m

3(a) -q, ~

3l1Gfd

i1

f<

t;{olg ' Cfil 3f

u:m ~ ~ P

i CITVm

2

) m (1)

G{l< l

ffii1 f


6/17

(b) '

3 1 1 ~ ~

q;ur

\% (

~ ; m : r ) %

Sf'lW

l:%

31'tfH

1 J ffi

~ wr ~

1

•

f

n q;ur

c

fit C > ~ ~ )

\%

I

1 J

ffi 31cffQ_Cf

i JB

~

fl: ) q; ') Wa 4il

Nl QO I

A

c

harged

particle

is m

oving under

the influ

ence of a

point nuc leus .

S h o w

that

the

orbit of

the

par t ic le i s

an

ellipse.

Find out the

t ime. pe r iod

of

the mot ion.

(c)

\% ~ 4 1 1 ( 1 4

R I4 1 fclctd'l itW

T ( S ( i ~ f ? l l l l

W>'loftll

Cfllf-fcfliltrur

dO

C >T qf):Ofi( ''l

lN QO

I

dt

..

C

onsidering a plane

t

ransmission

diffrac

tion grating w

here d is

the

distance between

two consec

utive ruled l

ines , m. as

the order numb

er

and

0 as the

angle of diffra

ction for norm

al incide

nce, c

alculate the

5

a

ngular

dispers

ion dO for an

in

cident light of wav

elength

A.

1

d/..

C DRN

N RIZA

6

www.examrace.co


7/17

·

SEC

TIO

N

A

nsw

er

l

l o

f th

e fo l

low i

ng:

..

10X

5=5

0

(a)

~ W I · ~ - ~

wifrr

.q,

~ < f u r ~

y = 2

e m ~ ~ ~

3ilt:i

Cfli14

B

mm

~

~

~

~

o f

F

. ~

~

B

fiHB

~ ~

:

'0

·1 i

: n

m ~

1

m m

m

r PI

; I

·

In

a Y

oun

g d

oub

le

sl it

e

xpe

rime

nt . the.

fi r

st b

righ

t · m

axi

mum

i

s

· dis

plac

ed

by

y

=

2

em f

rom

t

he

ce

ntra

l m

axim

um

, f he

spac

h1g.

l:>ctw

cci1

sl

i ts

and

dis

tanc

e f rom

th

e sc

reen

a

rc

0·1 m

m

a

nd.1

m

res

pect

ively

, f in

d

the

wa

vele

ngth

o

fligh

t.

1

(b

)

~

~

f.fi

~

~

q j

mfil l ·

( ~ d f

.-5fimr)

q

3 i

4 1 \

< : j R

k ~

~

I .

.

.

.

D ef

ine

En

thal

py an

d

show

tha

t it re

mai

ns c

onst

ant

in

a

thro

tt lin

g

p

roce

ss.

1

(c)

~ ~ ' n

w f i ' l

f.fiB

>

ICflR 4

1(4fl:C

fl

q,lcJ

Aicfi

l B i

lm

~

?

~

·fcR

T.R ~

<

j f.f ~

~

~

q m

H

ow

docs

hol

ogra

phy

diff

er fr

om

conv

en t

iona

l

pho

togr

aphy

? W

hat

arc

the

req

uire

men

ts fo

r th

e fo r

m ati

on an

d

rea

ding

of a h

olog

ram

?

10

.

d) fclf

i+;(UI

f

.r;q-q

l q;

) S N

~ c:n

B

.q, ~

l l '

l l < l ~ q

~

B

1il: ~

v

~

t

r.fl( F

l

~ 1 ;

I

In de

rivin

g

radi

ation

l aws

, we

con

side

r a

cubi

cal

co

ntai

ner o

f volu

m e V

co

nta i

n in g

a

pho

ton

gas in

equ

ilib

r ium

.

Ca

lcul

ate the

d i

f fer

ent ia

l

n

um

ber o

f all

ow e

d n

orm

al m o

des

o f f r

eque

ncy

ro.

c)

~

wfl<

fl(UI

~

~

~

~

:Jm

3lT


8/17

Q6. a

)

fcn

~

(1

'1 fcll:

'ft Ml) q;ur ~

~

. ~

~

~ I

~ ~

~

1 f

t ~

c

hlMt >

fcn g,'Jd·i'i

C

fiT

~ c,

rrn

r ~

~ .

~ .

~

~ 1

.

Show

tha

t the

grou

p velo

city i s

equ

al to pa

rticle v

elocit y

. A lso

pro ve

that

the grou

p veloc

ity ofth

e p o

tons

is equal

to c, t

he ve

locity

oflig

ht.

5

(b)

( ~

) ~

m I = I

~ t = O

R

= 0

~ ~ .

~ f

c n

fc

nBT L

C R

t q ~

St>ikl<

h

'lll1

ffi -q

3

1Tmftf

~ ) f

.l1001R1f

un, ~

·wu

~ :

1=1

0

1

+ ~ ) e

- Y

R

2 1

R ~

. i l

- .

- y

y= -

ro

=-

ro=

t a n

6 =

.

·

L

0

LC

2ro

For

initial

current

conditions I = 1

0

and

d l

= 0

at

t = 0 , show

that

the

dt

tim

e depe

ndent

curr

ent i

n the

cri t i

cal .da

m ping

c as e f

or an

LCR

c

i rcu it i

s

g iven

by

1=1

0

1+ ~ )

e - y t /

- y

and

t a n

o=

.

2ro

c) Qpi

l


9/17

(b)

20°C.l:R

1:fFft ~ fct>c:.·il ll'i ( k ~ r q ; ) f 1(1'1

c f l ~ Q ;

I

One

kg

of

water

at

20°C is converted

into

ice

at

-10°C

at

constant

pressure.

Heat

capacity

of water

is 4,200

J/kg.K and that

of ice is

2,100 Jlkg.K.

Heat of fusion of

ice

at

ooc is

335

x10

3

J/kg. Calculate

the

total

change ih

entropy of

the system.

(c) ~

q

~ .

f r - ~

q

< >\·

. ~ . m 'll:

~

'1ft ' ) _ l 1 1 ~

q

z - ~ ~

m2l 1:

WI.

~ ' 1 ( 1 ( 1

~ S i i l < f l < l

cRrr

~

'Cf>RUT

>l'Cffi? f . P " " ' 1 ~ f u ( 1

~

>1Gn

:

A

k 2 2

z .

E

0

cos

kz-

rot),

roJl

. k

afu:

ro tfcRur

afu:

Cfll

0

fi


10/17

Q

S.

a

)

. fCI

ll

FN

'("q d

I C I

<

€T f

CfiT

R:

q

i

:fi

i f

ro

q:;uj1

'fiT ~

1

m

I

C

DR

N N

R

IZA

1

www.examrace.co


11/17

T;

·::•

Explain the four thermodynaiJ1ic relations of Maxwell. Using the sa:me,

_

..

obtain the

l a u s i u s ~ l a p e y r o n e q u a t i o n

·

·•

. . ·

·

· .

·

· 5

dP L

=

(d)

~ c f f i ~ t : ' t - • i l ~ ( ' : l l ' l H .

fc«RuJ

f i Wi

(f fq

m

~

.1·

Using Maxwell-Boltzmann distribution law prove that

there

cannot be

any negative absolute temperature.

10

C:DRN N RIZA

www.examrace.co


12/17

f.

m

f

ft

r

f

'f l

T

: ff

f.r

r

f

t

T

im

e

A

ll o

w

e

d

:

T

hr

ee

H

ou

r

s

+

l

iR

ic

tf

l

~

-

n

f

-

1

1

P

H

Y

S

I

C

S

a

p

er

I

I


13/17

~ - - - 3 1

SECT

ION A

Q. l(a)

500 eV l ft1ur

~ of W21

i) -c;q;

~ ~ T '

3Th: ii)

-c;q; ~ ~ < t ; ; _ 1 1

of

t

~

• l ~ t 4 '

oFt

lf

fi'Pi

1 1 eV = 1.6

02 x 10 -19

J)

ind

the de Broglie

wave length o

f i) a neutron

and ii) an elec

tron moving w

ith a kinetic

energy

of

500

eV.

I

eV

= 1.602

x

10 19

J) 10

Q. (b)

/)


14/17

Us

ing

the

co m

m

uta t

io n

re la

tion

s

[x

, Px

]

[y, P

yl

[z

, P

2

]

=

iii,

ded

uce

the

com

mu

tatio

n re

lati

on b

etw

een

the

com

pon

ent

s of

ang

ular

m o

men

tum

o p

er at

or L

.

[

L

L

x

y

z

[L

,L

]=il iL

and

y

Z

X

~

, L

]

= ~

L

2

0

X

y

Q.

2(b

) 1J,'

ifi'

'f>UT

*

fu\;

'f

m'[-3

W.

;rcr

M

iifi

(OI

9iT ~

~

I

rrff

'

P f

f i -

~

(

11flif

i(OI

FT

~

Ob

ta in

th e

t im

e-d

epe

nde

nt

Sch

ro di

nge

r eq

uat

ion

for

a p

ar tic

le .

Hen

ce

ded

uce

th e

ti m

e

in

dep

en d

ent

Sch

ro d

in ge

r e

qua

tion

.

20

Q.

2(

c)

t(

' f iffi tf

ff< f

0.3

hfm

*

1J

,'ifi'

if

w

q

F

T 1

J,'ifi'

~

f f nciT

iiiTc

iT

450

0 A

*

·'tm

'l

iT

R I>

3l(1I

T ~

7

(e/m

1

.76

x 10

11

c/k

g,

c

3

.0 x

10

8

m

s-

1

)

A

sa m

ple

of

a c

er ta

in e

lem

ent

is p

lace

d in

a m

ag

neti

c fi

el

of fl

ux

de n

sity

0.3

tesl

a. H

ow

far

a p

ar t

is th

e Z

eem

an

co m

po

nen

t of

a

spec

tral

li n

e of

wa

vel

eng

th 450

0

A ?

G

ive

n :

e/

m 1

.76

x

10

11

c/kg

, c

3

.0

x 10

8

m

s-

1

.

10

Q.

3(a)

m

*

1J.'fi' 'f>

UT *

1m(

<

:i41<

ti


15/17

Q.

4(

a)

AIA

H

I ;;

fil:r

r;,

~

;;

ftl:

rr;,

fm

c)

o

f;

fW

; · ~

~

1

3

UJ

of

; ~

f

i

't<

m3

IT

91

1

fc r

:r rc

l

(

~

E

4lf

i1R

:'lf

) 3

ft\

=

1 q

-

=

2

3

'fE2

113

IT

of;

f

W;

3f'

l1c

l'

' it

of;

ff

itl

I

O

bt

ain

a

n

ex

pre

ss

ion

f

or

th

e

no

rm

al

Z

ee

ma

n

sh

ift.

I

llu

str

ate

th

e

Ze

em

a

n

sp l

itt

ing

o

f

spe

ct

ral

li

nes

o

f

H

ato

m

an

d

th

e a

llo

w

ed

tr

ans

iti

on

s f

or

th

e

l =

1

an

d

= 2

s

tat

es

.

20

Q.

4

b)

if>

>

RT

WJT

I

3

UJ

3IT

tfr

tr@lT

A

3\h:

'Rl1J1l]

Z

R

f'Rr

'\l'


16/17

Q. 5(e) ~

'E ;fn:r

'lf66l

(«\' ) if I l l )

3ih: (121)


17/17

What are the magic numbers in nuclei ? List the experimental evidences indicating their

existence. 20

Q.

8(

c) 100 V

m

fiT II r

n-

"S ' iR F 3Ti- F ' 1 1 R

('flTJ1: T

;;mn filrn< >r ~

-0.0125 m

3

/coulomb

I

llx

=

0.36 m

2

v

1

s

1

fiT l1T'f ~ ~ ~

~

m\1-o/R

Documents

IAS Mains Physics 2014