Elasticity - प्रत्यास्थता @irfanullah_mehar.pdf

Elasticity - प्रत्यास्थता @irfanullah_mehar.pdf

1. Physics
<br>
Notes
<br>
IrfanullahMehar/
<br>
[email protected]
<br>
irfanullah_mehar
<br>
WorldofWisdom
<br>

2. Most
<br>
(Elasicit
<br>
Dtrouction
<br>
9JYa)
2013(ERastiai
<br>
(Hooke'glaw)
<br>
Llasticbehauiousofmattens
<br>
shape,
<br>
called
<br>
,Jhat
extenal
foree8hichtmestoohange
<br>
sizefam,
Length
<br>
oeormation
foree.
<br>
F
<br>

3. Elastieity
the
propetyofmatte
<br>
bytheintue
e
<br>
mattes
eppos
<br>
tochangenshape,yolume
<br>
foree.ates
biestoglitt
<br>
Shapr
cgaize,
<br>
o
<br>
e2e
<br>
teel
isonoeelasticthaunubbe
<br>
bcee
<br>
Gteelopposses
<br>
rathesthen
ebber change
of
<br>
dsohapebyappying
<br>
Sare
<br>
inetal
<br>

4. Those
<br>
viginal
<br>
chjects
<br>
emhs
<br>
pefactly
<br>
shape
cempletcly
<br>
conpleteltaftes
<br>
objects.
<br>
ohiah
can
g
tueir
<br>
deformaticnforee,
<br>
clastfeobjeots,
<br>
Quatz.
<br>
iutiadahape
<br>
Thoseobjeatshiohqete
complekelg
<br>
Graineeod
not
<br>
to
<br>
pongetly
<br>
Wax
WedsoiI
<br>
acalled
<br>
inblaste
<br>

5. That
<br>
adwhfohobfeete
<br>
oriinal
akape
after
memavng
<br>
calledclasticiit.
<br>
elastiety
<br>
sLjeat.
<br>
cbieot
<br>
elaatic
er
<br>
triesto
<br>
Elatie
Limitis
propetyd
objeatohile
<br>
iuthepropetg
<br>
cCunt
be
<br>
AUthe
obiect
<br>
b
<br>
thern.
<br>
it,
<br>
matter
<br>
ptaetly
inelashie
<br>
teir
<br>
petecty
<br>
object.
<br>
nnate
<br>

6. PlasticbeharioRhwill
ancneaueik
<br>
behaicaecrese.
<br>
elaatic
<br>
LOhenadeormatienkoreeaets
eY
<br>
Dntena
<br>
cbjecte
<br>
tuen
<br>
a
<br>
oil
occw
<br>
frcef
mattes,á
calted
<br>
eeaction
foree.
<br>
eaistan
ce
<br>
olwetointemoleaules
<br>
Teactionforceoil
<br>
callecintenal
<br>
Mamtue
detornatieniteàsho
<br>
31924
<br>
beegal
in
<br>
tueconditiem equilr!
<br>
Cbnun.
<br>

7. Stess
<br>
externa
<br>
HferaoShess)
<br>
pafet
papendfoulasdafomatie,
<br>
wnil
<br>
Stress=
<br>
Fext.
<br>
A
<br>
Fextfaste
<br>
-
Tm'T
<br>

8. 11
<br>
Theraio
changeinahapeaze
o
<br>
cbjeatcuetodeformatiemerce
,
called
<br>
Ghain.
<br>
Togsfe(baim)
<br>
Stain
<br>
Ohamgesi,shape
<br>
Griginalahape
<br>

9. ClongilucdlhalShres
4longthsiral
Ghain.)
<br>
(Tenaile)
<br>
-it
(Compmrscim)
<br>
A
<br>
uen
<br>
o15)
Q.
<br>
Ceugth
ahange
<br>

10. (3)
<br>
11
<br>
VolumetcshressRVblumebicShrain
<br>
(Tensile)
<br>
Sheaning
<br>
F
<br>
A
<br>
A
<br>
ti)
<br>
=
<br>
Graln
<br>
tan
<br>

11. Note -
<br>
Logthcinal
<br>
Vumetric
<br>
Gras
<br>
Volumetc
<br>
lao)-
<br>

12. Rsbet
hooke6
<br>
7Robet
<br>
Robert
<br>
huekegives
afundameutal
coy
<br>
Lmit.
<br>
inl618.
<br>
Aecosting
<br>
totlet
<br>
prepesthiomaltoein
ncle
tleeelatay
<br>
shessitdicety
<br>
Elasticity
coctfefend
s
tleretef
otressto
<br>
srain.
<br>
Elastieitycoforeent
istaesundometal
<br>
prepexty ttesnohioh
represeuts
<br>
hacfuief
natte.
<br>
Elastieitycrfelevdlrsnt
olepeno
<br>
stran.t
lydepenc
<br>
ntere
maltes
<br>

13. (1)
<br>
NOOnatters.
<br>
Elasteity
<br>
Dimension
-
<br>
(Yng's
90dtubutoElaattety)
-
<br>
AAL
<br>

14. Fo
<br>
cwiYe
<br>
k,
<br>
A()Iy
<br>
F=kAt
<br>
F
<br>
Forcecnstantoesire
<br>
Ald
F
<br>
ADU
<br>
1
<br>
A
<br>
Y
<br>
Y
<br>
AD4
<br>
FQ
<br>
Fl
<br>
(
<br>
KI
<br>
A
<br>
YA
<br>

15. CanbinationofYoug's
<br>
A
<br>
Lnet
<br>
)o) (Seriescowbination]
<br>
Anet
<br>
net
<br>
22
<br>
Modaluse
elasticity/
<br>
A
<br>
Combineticonoives.
<br>
frmendtoeud)
<br>

16. L
<br>
FL
<br>
AD
<br>
AY
<br>
EnetLet
<br>
L
<br>
Awet
Y
net
<br>
A,X, A,Y.
<br>
AYnet
<br>
2
<br>
2
<br>
Ymet
<br>
(2)iR}) (PasllelConbinatien)
<br>
(fromswcetocuface)
<br>
Lnet
L
<br>
e-fmulaYaadRolehe
<br>
A
het
<br>
A
<br>
2A
<br>
*F=YAe
<br>

17. Q.1
<br>
Fnact
<br>
YuetAetAlet
<br>
Lhet
<br>
2YhetYh
Ys
<br>
Fe
<br>
oireetformulo
<br>
YaaclKaho
<br>

18. Q.2
<br>
Ans
<br>
cc)
<br>
(d)
nFSK
<br>
A
<br>
Al=
<br>
(a)
<br>
(iv)Aeor
<br>
(b)
co
<br>
(c)2XL
<br>
(Ans-C
<br>
(d)2xL
<br>
Ae
b
<br>

19. Ans
<br>
-C9)
<br>
(6)Tsy
2c
<br>
16DCm.,cIG
1mm
<br>
(d)oa
T
50
com,
<br>
)AQ
<br>
ol2
<br>
3X163
3x163
<br>
3i)e50162
<br>
O5X10xoo5Xô
<br>
And
<br>
d2
<br>

20. (2)
as3991)2oris
<br>
(
VeleemetrneElattletyGoeficfed)
:
<br>
forsolid
,
Liqulo
Rgses.
<br>
K
<br>
F/A
<br>
Tsobasic
<br>
k
<br>
Dso
choc
<br>
Kansg
<br>
Tcohemnat
<br>
Adabatc
<br>
(BaTK)
<br>

21. Basfc
<br>
kirKaK
<br>
C=0
<br>
Knusledg
<br>
1
<br>
1
<br>
k=
<br>

22. (
<br>
Y
<br>
(3)34yias
(moculusobigilrby)
)
<br>
FL
<br>
m)
<br>
F/A E
<br>

23. Factos
<br>
(8yHrtting)
<br>
Ex.
<br>
T1
<br>
olastieit
<br>
(D)Aut
k
Y
<br>
Y
<br>

24. (Potssicrnratio)
<br>
longtugnal
<br>
(o)
<br>
Tuesahio
o
hransvers
<br>
ratio.
<br>
AL
<br>
Shain
to
<br>
called
penitso
<br>
rin
<br>
d
<br>

25. 7heoriticaly
<br>
Ans
<br>
Expeimedlly
<br>
gnaGrade2023/Susi2)
<br>
2X10
N
<br>
F2105
<br>
(9)I-6X10SB)
3o2X)0
3(c)le6X]
6
<br>
Y=oxo'"
N
<br>
Strain
<br>
-1
<br>
-2
<br>
O.2
<br>
Y
<br>
AY
<br>
Y
<br>

26. 2nolGoades02g(Bana<ort)
<br>
Stres
<br>
Ane
<br>
A
<br>
A,
B
<br>
Strain
<br>
X-)
<br>
°T=tne
=
<br>
gl
<br>
1
teuneSlepe
1->Y^
<br>
X162
<br>
)309
X)0
<br>
Ane-B
<br>
(c)Yo>s>Ye
<br>
Ane-c|
<br>

27. 2ndGhrade2o18
<br>
(D)
<br>
gndGade9o5
<br>
(A)
<br>
(8)
s
<br>
Ans
<br>

28. Pns
<br>
9ndGrodeoO|
<br>
HeCd)
<br>
(A)
2x166N/m2(B)
8X1o5
N/m(06xI0
N/m
<br>
P=4x)0Nm2
<br>
nndGyrode9015(sPc1)
<br>
(9)210
<br>
X)D
<br>
)
<br>
k=?
<br>
A1:
(B)2:1(c)y:J(D)184
<br>
1:9.
<br>

29. 2nol
Gzde
oo
<br>
A)2
<br>
Al
<br>
FA
<br>
AY
<br>
A
<br>
FQ
<br>
A
1
<br>
B
aR
<br>

30. ()
ICm()Dem(c)3em
D)yCm
<br>
.11
<br>
Fixed
<br>
1stGradepold
<br>
L,
=L
<br>
(c)
<br>
Oe06Cm3
<br>
"y=
F:
L
<br>
712.A0
<br>
(A)12.0X10 N/m (o)
120X16b
N/2
<br>
Aus-A
<br>
26X)6N/m (o)26X10'°N/2
<br>

31. Q.12
<br>
Ans
<br>
P=
<br>
K=
<br>
K=
<br>
PU
<br>

32. (A)yY
<br>
4StGade2o5
<br>
()
<br>
(A)
<br>
(B)
<br>
(c)2Y
<br>
doesnt
<br>
(O)
<br>
dependc
F,A,d,
v
,
20,Av,r
<br>
(8)Ga
K
cc)
<br>

33. Ans
<br>
ce)
m
<br>
FL
<br>
AQ
F
<br>
D)
<br>
(B)
A
<br>
As
<br>
'Some
<br>
(1X163)
<br>
Secorlingto
<br>
(2x163)2
<br>
(2x10)2
<br>
(6y
<br>
1
<br>
d2
<br>

34. QI5
<br>
Ans
<br>
(9)
Y Ys
<br>
(8)
,
<br>
(0)P
<br>
38
<br>
Ar
<br>
Vr3
<br>
AV
<br>
Serie
<br>
3AY
<br>
(Pasallel)
<br>
3Ar
<br>
3B
<br>
AnsD
<br>

35. (A)
Vs
<br>
A
<br>
A
<br>
Ane-
YFQ
<br>
AAO
<br>
AY
<br>
V-Cogt.
<br>
Ane-B
<br>

36. (A)4F
<br>
(0)6F(c)3FCD)E
<br>
Y-const.(7oey
)
<br>
Axl=cont.
<br>
A
<br>
1
<br>
Al
-
Con
<br>
Y
FL
<br>
AAQ
<br>
F=YaA
<br>
F
A
<br>
FH
<br>
FoA2
<br>
A,A
<br>
A3A
<br>
9
<br>
Fa-9F)
<br>
An-c
<br>

37. Note
<br>
182.
<br>
A
<br>
FAQAY
<br>
Fa
<br>
F
<br>
Y-FL
<br>
)0=
<br>
(8)18
y(C)1:
<br>
A
<br>
fL
<br>
AY
<br>
Fo
<br>
(D)Bt
<br>

38. 20
<br>
Y-
conste(
Boe1h)
<br>
d
<br>
2.
<br>
F-
contut.
<br>
Y
<br>
Fl
<br>
AA0
<br>
FQ
<br>
(A)
0o
04mm
<br>
161X10
<br>
d?
<br>
d,2
<br>
(B)0
o
05mm
<br>
(o)
0
15
mm
<br>

39. Y
<br>
AY
<br>
AA
<br>
N/
<br>
1X166xLkIO!"
<br>
Ans-9
<br>

40. R
<br>
alosk
dometohetch.ay
<br>
Stastfe
Potectialeues
<br>
sprng
<br>
Ax
<br>
U=FAQv
<br>
2
<br>
U
<br>
usire
<br>
stoned
<br>
F
<br>
Loara
<br>
2
<br>

41. Shress
-
Shrain
<br>
|sress)
<br>
fH
A
<br>
Cuve
<br>
(Shai)
<br>

42. J
gaDuctile
attes)
<br>
sg (Britle
maffer)
<br>
A
<br>
Lay(Elastomers)
<br>
Ex.
-
ubbe,
Aorta
<br>
a,
<br>
a.
<br>

43. (Ohen
fce
acts othe,tlen
ess
<br>
+
sun
asepyupertiomaltocaoh
<br>
othe,
<br>
A
<br>
Poinl
n
callod
<br>
B
<br>
fherponl
<br>
dssnlHal
<br>
wie,
<br>
Tlusacoicallod
<br>
porpertenalitypoite
<br>
Ceecctregs
<br>
matlecell
ges
<br>
batmatle
<br>
Ghteofteremn
<br>
porntOto
<br>
elasti'ose,
<br>
fscalleapet
<br>
B
<br>
pot
ofelastis
<br>
Cize&
<br>

44. wllbe
dnone
<br>
Shalnwilbe
<br>
becaus
e
<br>
ne
<br>
its
initialsfale.
<br>
Point
cs
calledpot
<br>
LinanEpentimcoef
<br>
due
to
<br>
Bbut
mette
cesilaot
<br>
atthlspont
<br>
AT
<br>
=
dAT
<br>
(a)
<br>
AAQ
<br>
F
YAAQ
<br>
fogzfa
<br>
plastieaiea,
<br>
peit
<br>
broleeaalewn.
<br>
FYAoAT
<br>
A
<br>
E
gAT
<br>
Thermelshest
<br>

45. -
<br>
Y=8K(1-2~)
<br>
Y=2n(14)
<br>
K
<br>
3K-2n
<br>
6K42n
<br>
ta)w)ac
<br>
eo
<br>

46. Q.22
<br>
Cc)8ittle
<br>
cd)Plasticg
<br>
(n)Ey(Ducle)2iR
(Brittle)
<br>
3nguides
<br>
7
<br>
Y
<br>
Lonleas
<br>
Y
<br>
X
<br>
ptastic
<br>
Puctle
<br>
Aus
<br>
B
<br>

47. U
<br>
Vo
<br>
Cb)5V
<br>
12
<br>
C)v/5()25V
<br>
(As-D
<br>

48. Q25
<br>
Ans
<br>
F-m
<br>
(a)1:2(6)134(c)2:1
<br>
Y-H
<br>
Tcomst.
<br>
A-cst.
<br>
(Const.),
<br>
(d)1:1
<br>
Y
<br>
Ansc
<br>
XV
<br>
L
81r23dy
<br>

49. Q.27
<br>
(a)
K
<br>
(b)Ke
<br>

50. Q.
29/
<br>
Ane
<br>
Ans
<br>
(a)332
<br>
ol
<br>
cd)
3uR
<br>
UxT
<br>
Cb)223
<br>
us)-Cen.
<br>
Ans-c
<br>
Cc)384()488
<br>
32
<br>

51. (afeTfRiy
<br>
(A)
<br>
Ca)
<br>
FQ
<br>
(8)
<br>
2K
<br>
(b)
<br>
T
<br>
9K
<br>
lolg k
<br>
EA
<br>
(c)
<br>
T
<br>
FL
<br>
(d)
<br>
(0)
<br>
k
<br>

52. Qo33
<br>
Ans
<br>
(a)G250T(b)O13J
()0.0
75
<br>
A
<br>
U=YX
<br>
XV
<br>
XAX0
<br>
U-yx
x
4/*XA
<br>
(U O.
075T)
<br>
4
<br>
(Ans-
C/
<br>

53. Q84
<br>
Ans
<br>
8
<br>
(4)
<br>
(c)
<br>
(a)Yx
<br>
2
<br>
Cc)Yx?A
<br>
(b)x2A
<br>
UYx()°xv
<br>
9L
<br>
Cd)2Yx²A
<br>
An-c
<br>

54. Ane
<br>
Ans
<br>
50Cm
<br>
(Y=2X16eN/m)
<br>
CA)SXx
1DJ
<br>
50
X10m
<br>
A
1
m2
<br>
Y
2
x
10°
N
<br>
(B)4X10
T(C)2X16J
<br>
4X10
<br>
1
<br>
2X50
X10
<br>
m
<br>

55. Ans
<br>
(a)293
<br>
F-Cemt
<br>
2.A
<br>
A
<br>
(b)3;4
<br>
|Ane-b
<br>

56. Qo38
<br>
Ane
<br>
Q40
<br>
Ans
<br>
(a)s
<br>
Cc)
<br>
Cd)
<br>
21
<br>
Y
<br>
ca)
\<
(6)Y=n
<br>
Ans
-
b
<br>
(3)
16 1
(c)8$1(d)1:1
<br>
(c)
<br>

57. Ans
<br>
(a)3Y=K(1-r)
<br>
2n
<br>
Ce)os(6K+h)r
<br>
2
<br>
(a)0100
<br>
-1
<br>
(b)K=
<br>
--2n
<br>
2n
<br>
Y+h
<br>
o.5Y-n
<br>
n
<br>
2n
<br>
Angd
<br>
d
<br>
O.5Y
<br>

58. Ans
<br>
(4)3x10'àN/m(b)2X162N/2
<br>
Y=GX10'2Nan2
<br>
()
<br>
2
<br>
6x18s
<br>
(0y
<br>
9n8-)
<br>

59. (9)24
<br>
Y 24m
<br>
fsore
<br>
(b)1.2(oo4)(d)O•2
<br>
(9)31290r
<br>
l.2
<br>
t).2-1
<br>
An-)
<br>

60. Ans
<br>
(a)O.00
2.
<br>
Note
<br>
Tle
m
)
X
)02
<br>
(0)
<br>
Ye
L
<br>
cc)shape
<br>
(c)o-008
<br>
(b)Brcadt,
<br>
Cl)
Velume
<br>
Ans-b
<br>

61. .49
<br>
Ans
<br>
Ans-cJ
<br>
Qo52)
<br>
(c)
<br>
(b)Ss
<br>
KT
=
(P)
<br>
An-c
<br>
(6)
xS7219
<br>
Ans
<br>

62. Q.59
<br>
o53
<br>
(a)
O.
4cc
<br>
(c)ocO25
cc
<br>
C=
4Xl0
5
<br>
Av=?
<br>
cb
<br>
V
<br>
(
<br>
(B)4X
1O cc
<br>
1X103
<br>
(D)o.O04cc
<br>
(*2)
<br>
AV
=PXVXC
<br>
yX0X100
X)SO
<br>
Ansg
<br>

63. Ane
<br>
(A))08
<br>
100
<br>
K2
<br>
1161
<br>
Brealšng
kosce
<br>
IK
2X1o
N
<br>
ercakinghessor
<br>
CD)2X1G
<br>
owire
bvolee
dore)
n
<br>
105X)0X200
<br>
that
torcebytheiree
<br>
atemar.strain,
<br>
PA
<br>
FaPA
<br>
Fd
A
dr2
<br>

64. Qo59
<br>
Ans
<br>
Q55
<br>
(a)
<br>
(A)Fa(8)
2FCc)4F(d)
F/4
<br>
Y
=
<br>
F,F
<br>
R
<br>
F
<br>
Pcr
<br>
F9
<br>
(3)rk
<br>
foy
<br>
Y+3K
<br>
Ans-c
<br>

65. Q56
<br>
Ans
<br>
Y
<br>
(Y=102Sc)
<br>
(A))"0xIN
<br>
(d)os5X10*Oge.
<br>
A.
5
<br>
Y-j0"
N
<br>
1+3K
<br>
(b)
J4oX10N
)0e5X1d
N
<br>
F
1d'XD5
X
<br>
-
05XI62
<br>

66. Q.57/
<br>
Qo5
<br>
(A)
<br>
(B)
<br>
Cc)
<br>
l-
10
5
/c)
<br>
1CO)2
<br>
(A)103N(8)
10"N
<br>
A1
C)2|X10
<br>
Y=
10"N/m2
<br>
(Y:l0'N/)
<br>
Cc)
<br>
)05N(D)109N
<br>

67. Q.59
<br>
Arns
<br>
Q.60
<br>
(9)o.49
X
I0"N/
<br>
K
<br>
=y-5X10
m
<br>
(A)1Xl0
<br>
(3)1-96X10"N/m
<br>
(D)6196X16N/m
<br>
1.96X10N
<br>
(b)|.
X
163
m2
<br>
-
<br>

68. Qo61
<br>
Ang
<br>
O2
<br>
F14
N
<br>
eg
<br>
S.6
X10N/
<br>
4e210"
<br>
(19)l2x1o"l
b)4o2
<br>
3X16)6
<br>
K
<br>
)A)
<br>
+X109YO0D2
<br>
nx18°.2X/0"
<br>
(Ana-c
<br>

69. 14]1/2y
<br>
Notr:
<br>
Q.G2
<br>
Basic
<br>
Knnolege
<br>
(<)
<br>
(b)3,33X)L2
N
<br>

70. .63
<br>
(A)2X106
N
<br>
A
lCN
0
<br>
Y
<br>
F=?
<br>
2X|0"
<br>
F
<br>
2X10xo.5
<br>
A
<br>
0.3X1o
<br>
(3)2)0
N
lc)
2X10
N
<br>
3X0
<br>
X01
<br>
2X10°
N
<br>

71. Ane
<br>
Cr/C
<br>
(9)
P(b)p(c)
<br>
Cp
<br>
EnyYny
for
<br>
En
Y-
E
<br>
E
<br>
fos.6
ci)T
<br>
)H1QP
<br>
P
<br>
Y
<br>
Xp
<br>

72. RPSC&RSSMBEXAMCALENDAR
<br>
ZITTAtciHyierfaf-
13a14fHdR2025
<br>
>1stGradeyérerfafg-31H
162026
<br>
>2ndGradeyitarfata-12193S
2026
<br>
>RH
SIYteTfafa
-
0531ÀT2026
<br>
VDOHdyitrfafe-094daR2025
<br>
LlçTHHSYteTff-
22¬dar2025
<br>
>aqeiguftfartterffa-
19
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21
fAda2025
<br>
>ytaleYâeTfafa-
22
7dr
2025
<br>
>alEATlccsHafqiterfafe-
23HdaR2025
<br>
>AfEIqfdercsyatam
fafa-
26faiaR2025
<br>
>pfqfaesyâaTfafa
-
8
HTÍ2026
<br>
>LABASSISTANTftarfafe-Hat
&
5rat
2026
<br>
>LDCYtemfafa-5els
2026
<br>
>CETds
yiteTfafa
-
2022
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2026
<br>
>CET12thLevelyerfafa
-
810H
2026
<br>
REETMAINSYÍteTfat-17
21
Hat
2026
<br>

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