Post on 06-Jul-2018
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
8/17/2019 IAS Mains Physics 2014
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
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8/17/2019 IAS Mains Physics 2014
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 - ~
8/17/2019 IAS Mains Physics 2014
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{
8/17/2019 IAS Mains Physics 2014
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
8/17/2019 IAS Mains Physics 2014
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
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8/17/2019 IAS Mains Physics 2014
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
8/17/2019 IAS Mains Physics 2014
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
8/17/2019 IAS Mains Physics 2014
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
8/17/2019 IAS Mains Physics 2014
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
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8/17/2019 IAS Mains Physics 2014
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
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8/17/2019 IAS Mains Physics 2014
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
8/17/2019 IAS Mains Physics 2014
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)
/)
8/17/2019 IAS Mains Physics 2014
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
8/17/2019 IAS Mains Physics 2014
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'
8/17/2019 IAS Mains Physics 2014
16/17
Q. 5(e) ~
'E ;fn:r
'lf66l
(«\' ) if I l l )
3ih: (121)
8/17/2019 IAS Mains Physics 2014
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