CSIR Physical Sciences June 2012
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Transcript of CSIR Physical Sciences June 2012
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8/17/2019 CSIR Physical Sciences June 2012
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1.
(
'#fTir A
)
3 i ' ~ T f i r i i i f l lt'r
?J f if
Vii
if
rn i l l ~ r r
'l f
r;rrm
mrr..r,;r it 1
2.
rr :?fr it 1
3. "
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: 1.
' ~ n : l -
l l o : s wi-nch
;C\):U
lm i
br
n '
l : ~ : e n
hei.;;h
:s. The
r:11io
o
f t
he
m,1;se
;; of
Kl
:J
; :nm p
rism g
t v;n fD J
lO O:l l
) hose
n
o le
;; lV II
I
t
he
e
m 10
f•f 1
;;:
L
he•r.h
rs.
N
' rhc p
ile
h
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l
.
<
rl l'l
'
tlr-
lt
MW
fit
Wr
$
i
t .
2
.
12
P w
r li
."irt
t
;
t
ri
'
"' '
/i
3.
H
p
i i
r Re
'n
lJ S
;
;l {
{ fN
o
rtff
;
ftm;
rn
<
;Jm
U
lt
' r
I r
tr
l1fR
:
f
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1
4.
p
2
p
2d
=
d
'
2
.
d >
2d
J
.
d
=2
d
4.
d
•:.
2
d
w
iJiT
R
o·:
ifh
ll f
i I
iif
ilfl'i:
1 d
lk
B
f m
mr
'
r
/
iii T
{ ' f{
'
, i
(
)( )"
<
; 3 R
i1 '
f f
f
l
l .
JIE .
f?:r
nif '
;
;t iJiT
R.
w
I
f A
:'if?
¢
: f t
B
if ll
' i;
r
lh
*
I
f f f l
1/'cl
on
3
f
ulcr
um
a
s
sho
wn
Ill
the
d and
d a
rc
rel
ate
d b
y
1
2d
d'
3. d
= 2
d'
4
d
and
IJ
O•E
, an
d
tW
l o
the
r p
oin
ts B
:rn
rl
B
on the same
longitudes, respectively, hut
at
L
ati
tude
6
0°
S. T
he
the
lati
tud
t"$)
tl
tt· po
int
l
a
nd
B,
B
' ar
e
by
I.
,{A
'
B
/1
2.
A
A'=
2
8B
'
3.
A
A
'=
(
B
B
' 4
.
A
A'=
B
B
1
4.
l i < J ~
l . · . r
S
n
(lw
ing
th r
ou g
h a
tub
e a
s
shO
I\1 1
.
T
he
c
ro:s
s-s
ecti
ona
i a
rea
s
a t
A and
C
ar
e
eq
ual
.
an
d
gre
ate
r rh
.ul
t1
1e
a.n
:a at
B.
If
the
t
1ow
i
s st
ead
y,
then
th
.: p
r.: '
*un
: o
n
tht
wa
lls
at
8
.
les
s m
an
ha
t ac
:\
and
th
at a
t
C
.
2
.
m
or e
tha
n th
at
A
a
nd
tha
t
II
C.
3<
?.a
me
&
,at
at
A
and
th
at
a
t C.
4.
m
or
e
t
han
tha
t
a
t
A
bu
t
k
ss
l
hal
l
tha
t
a
t C
IS . Matc h the tw o
lms
A
B
c
D
L
a
b
c
d
2
d
c
b
a
1
a
c
i
b
4.
d
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25. '7
f"f
f i t ; ~ ~ iff
::
=x+ J'
"'T:f7li
MR
/ : ) W f f f ~
/ f. I
f(:J11lr
2·
J ~ f f
'i/l'T
t
y+xy
2.
xy
3.
)
'
:_xl
9
be t l ~ < : real part
of an
aru
tl)1tc
f
unction
f
z
of lhe complex vari
able
. The mugUla
tJ part of
f z)
is
y+xy
2
.
y
3.
4.
'
y·
26.
L
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3.
2
9. ,..r,rm i 9
10
9
;, /
v
1
{ 1 w
. ~ t
G7 rrz
:::mi
f[ ili r : ; ;
: , r i f i I ~ J
~ ' f ;i
I f[il
i
P\
O.l
l c
i
7l t
r
rflr rt
vfl<
c
3 "
1 x
>fro
r
di f .to iifl'
f. 1 l im
rfrt
'' '
'
t.. t
~
?.T- 7
' f l ' i ? ' 11<
;Jr
q
1
6Q l?o
3.
20 l l:Q
2
r(x)
l
i 1
r(
x)
,
2
2
. 40
""
4 o
iro
2.
.>:
+V(x)
2x
4
,
V
(x)
2x
31 .
tfft
;;l
f 1'{:
ft.·r?
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I.
mffN
N2v0 1
2.
\
Mitt
1ITtl1 JJR
2
3.
\M
itt
t:r f
J
ik l.O
I
4.
l1
mtff
1IT
tl1 NN t.
O I
I
F
2.
-F
3.
F
o _
-
r
r•
4.
i'
30_
r
r
•
33 r[11f
~ f l 1 1 i'ft1
T
~ w:f -(:ICntia
J
1
2
wh
ere F s ll co
nstmt vec
tor, is
I
ft
2.
3.
.•
30
F
- r
4.
-t
.. 30_
F r
r'
JJ
A
n ele
erromag.nc
tic a ~ - e i
s
iru:idem
on
a
wall::
r-air
lntcr ce
. The p
hase of l
he perpe
ndicular
cc
mponi Tlt of
he ele
ctric field, o
f he
rd leeted
w:we into lhe
water is
found to remalt
l tbll sam
e for
a
il
angles o
f incidenc
e. The
of he rnagnec
ic
fr
cld
l
do cs ot
c hM
ge
2.
changes
by 3JT
/2
3.
ch
anges
by
;r
2
4.
changes
by
;:
3
4 fk t •
um 1
il1fr 1fR
fm f f pr r#
f i'f.?.}
34 T
ne magneti
c field at a
distar.ce
R
f
rom a long
ftrt'
Jft
Iff
mt qw
.JFj'11f1 if ~ t i f T
straight
wir
e c:uzying a
t c a d y
urrent 1 is
proportio
nal to
2.
i
/R
1
4.
I
I R
Js.
~
t
m
~
ilfVT
;t
J1iTil iVf
w
'iR 'i1i
'f111
Js.
#11
11 rn
r ii,
ff;m
, , n r , n J
it
TT lTV1
1m i
t
~ t
I
0
2.
1l
2
3
.
ll
±2(11
, +n
1
+
n,
4.
± :
2
2.
1/
R
2
4.
1
1
R
The
m p o n e m
along
an
ar bitrary
direction
;;
•
wi
th direction c
osmes
n,.ns,n,), of h
e spm ofa
. I.
. rc
dTh
·
spm
- 2 p:lttlC:
e IS mcasu
. e
I'< Sillt w
I
)
2.
±-·n
2
:
3.
h
..-n,
+n
,
4.
11
2
2
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40 .
N
;f
rrlfrr r r
iEiiff
t
L }V
+ l
2.
lv'( N
I
)
/2
3.
N(N +I)/2
4.
N
4 L lV ifiTJt
t 'l l i / f[il
i
ftrr fi:n M11 J.WIT'T J
l
Tl
ff lr rtfR
t ; p r r
F
lnfd
V(k
1
L
u 8
~ r d q ; i/
k
11
liiK«It;r
R'tlmq;
iJil
t'?fi e.:: lf . f
irr 1 >tvv iit1 J ~ ~ a f
OF iJlf
tt
2.
3.
4
.
2
3
Nk
,T
.) 2
42.
fir 'i
t:7ihl
ft1 uiili Jif i
llt
'iNil'fJi
~ f { r { ~
17 f.r#J
11 ri vr
V,
11);.;:
1
i Pttfl1
V
0
iJl1
1[('11
K
v - - - ~
3
.
0.33 v
IJIO V
43. ~ r q
J
'i$'('8
> 4)¢
i l l1m it I. 5
V ,'+1)/2
4
N
41 .
1'hc lh.-e
c n e r
of
a
gas of N
p
rtie
les m
a
volume
V
a
nd at a
lem
pe ilture T 1s
F = N k . T
n [ l i : . V
~ T l •
where
a,, lS
a
co
nstant and k , dc
nolc:s th
e:
l.k>l
lmumn
Wlll i t l nL
l l te
inter
nal energy o
f
he
g;.ll>
is
L
2.
5
2
3
N k . ~ n
u$V(k.r
)' )NJ-%
;vk"T
.vk
1
l ln
[
.,V
j
(k ,rf
42. In the op-amp
cm:mr show1
1 inlhe ~ ; u r c
below.
the mpui
v o h ~ g
V,
is
1
V.
The
valut
of1hc
ou tput
V:.
L
-0.33
V
3.
- 1.00
v
11(
2.
4.
Vo
i
::
11(
0.50V
0.25
v
43-.
31
U
V an d
5 rnA m
forwa:d
i:
'oiZt;:;.
an 80 externa
l efficiency
of he
LEP . ho
w
many
photo
ns arc emi
tted per sec
ond?
].
5. )
X
3.
0.8 )(
2
.
u
x
10
1
4.
2.5
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44
.
4
3.
OOO
Q
t
l1R
tf t l
/?ml
.
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1
5
(
~
c
J
f)
-
n
,
'
n
,
0
·
I
1
1
wr
ti
n
1
,
:
:r
n;
~ ~ I f
flC
-
t't ..
..
«
t l
l
..
.
~ J I P ~
48
.
rr
q;
'M
ill
r
t
#
I
. i Y
rrq
; ;/;
19
m
r;
v
J
J{J
; fflf
? m
"I
n
J
tq
;
fl
ff'a
t iJ
iill-
< r
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4 1.
4'
1.
49,
50.
5{),
16
2N · l
l
,\ '
3
N. -1
+])
'-·
4.
3
2 2
•ont..nns lll::lllj'
ball;,, e a ~ h With a ntunber p.:tm
lt:tlun i 111c:re
an:
h :nc
t h < e : ~ l )
numbl:r
''
(n:lmc y one ball wl
th l t·.vo balls v
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17
1,
the
particle will execute ttmple hannonic motion in the right well with
an
an ,,'Uiar frequtmcy
(j)=fi
2 tl1e particle will
exe}'
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I
\•
r
.
8
4
fl
4
ii rsin
S/07
RD/12 5AH 28
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1
9
56.
Whi
ch
o
f th e
fol
low
ing
is
a
sc:
I-ad
join
t ope
Tllt
or
in t
he
sph
er ic
al
po
w co
ord
ina
te s
yst
em
r,
J. fl')
1
l
ih
2.
ll
si
n
3
6
f)
}
8
3.
57.
F
-tr;r tj
'1fl;r
f.m
lv
E x
B j
2.
IE
l -IB
il
l.
5
7.
W
hich
ll f
he
fol
low
ing
q
uan t
ll1e
s
is
Lo
ren
tz m
vil
ri:m
t?
L
IEx
B
2
.
2.
i
3.
o
J
4.
4
.
.. .
.
0
0
- I
S i
l l
8
4,
5
8. \
ha r
gc s
Q
.
Q :U
l\1 -
Q
a
re pl:
1cc<
l 0
111
tbe
v
crt1
oes
o
f l n
eq
ui l
ate r
al U H
l.llgle
AB
C
of
s1d
cs o
f
a
a
s s h
ow n
in
the
ftgu
re
20
2
uQ
i
2
.
J
4.
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2
1
L
l M
2
(0)
2.
I
M
2
(0)
T
-T,(
l
M.
z(O)
)
T
r
3.
I -M
1
4
.
1-
l> f
1
T
fc;
T
6
1 T
he
mag
:neti
T.ati
on
M
o
fa
ferr
om a
gnet,
as a
fun
ction
of
the
k:mp
ermu
re T
an
d the
ma
gnt:l
lc
fie
ld f l i
s
desc
ribed
by th
e equ
a tio n
M =
tan
h(
1
; . v
i
I
n th es
e un
it s t
he
zer
o·fic
:lu
m
agn
etic
SU
SiR
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3
66
Jm117f I V
;f; fliP
1f tt
T qr:
fit<
1R
ft• - >
Trtl"'
7iftfrfi ' f
YfdJ: ' t
f
Vf11 r #
I Wt
f {tfff
: Jfl'-' '
~
F
trrr t m
I.
7
2.
3, 011
A
V
4
,
v
66
. Co n
sid er a
sinusoi
da l w av
efo rm
or amp l
itude
V and
f
rl iucnc
y
Stl>rting
lro
m an
> ~ l < l r y
m
ll alti
me, the
w a\'efo
nn
is
s
am pled
ut
intc
n• ah
of
J )
.
If
the corn
::spond
u1g Fuu
ri
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2
(311
/ he
"'2 X I
o·
t
o>fm ?
,
J l
fi
3
4
1/
2
6
9. l11c
sp c;;t
r' .llhnc
l'Om::sp
unding
10
:m ~ t o m i c
tr
tli1Sitio
n from J
=
1
t
o J = 0
stmes
splits
ltl a
m< Jb T
chc fiel
d of
I
kG
ul
lO thn:e
comp<
>ncms
~ m t «
y l. 6;.;
l 0
.,
A
If the
1
,;;ro
tlcld
sp
ectral
me cm
rcspo11
ds
to l849
A w
ha.tts m
e
h
-
;, :zx
CIIL)
Pn
2
2.
}
2
2.
cx p(
-15)
co:n:s
pondm
g
10 t
he =
1 s
1otc' {Yo)
ll
m
ay
l/2
3. exp(1
5 )
exp(
30)
7
0. ll
1c ~ r ~
to cleat.
: a
lallJcc v:u:a:
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25
J;f
f l({f f i tqq
t ) = t ~
s g . n -
J F l l l vrmr
f
g
eit>r t
iJi ilf
w
iFI11
i
l
2.
3.
4.
7
2. Co
nsider
n ele
ctron i
n
a
o
ox ofh
mg tlt L
With
pe nod 1
c bm.md
ary co
ndition
v; x
=VI
(x
+
L
73
.
If " l .
tl )
I
i
.
L
h2h2
h .
•"'
. .
ne e
ectron
1s m
1e
rp,
x
=
·
e ·
wnn energy
~ > ·
::--
w
at
IS
,,e
correcuon
£O
ns
JL
2m
ene
rgy, 0 se
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