উচ্চ মাধ্যমিক (HSC) ও বিশ্ববিদ্যালয় ভর্তি পরীক্ষায় পদার্থবিজ্ঞানের প্রয়োজনীয় সকল সূত্রাবলি একত্রে।

1. 01725-176911
SHADATH'S
SPECIAL PHYSICS CARE
GBP.Gm.wmGKv‡WwgK,BwÄwbqvwisIfvwm©wUGWwgkbc`v_©weÁv‡bi†mive¨vP
c`v_©weÁvb'im~Îvewj
BUET&VARSITYMISSION'iwmwbqiwk¶KbvRgymmv`vZfvBqv'i
Lyjbv'i e¨vPt wcwUAvB †gvo,Lyjbv
wet`ªt evmvq MÖ“c K‡i covi mxwgZ my‡hvM Av‡Q|

2. †fŠZRMr I cwigvc

হলে
শতকরা ত্রুটি
এখালে, যেল াে পূর্ণসংখযা বা ভগ্াংশ
যেল াে পূর্ণসংখযা বা ভগ্াংশ
 Q
P
R



+
=
†f±‡ii †hvM, we‡qvM Ges gvb wbY©q
• ( ) ( ) ( )k̂
z
B
z
A
j
ˆ
y
B
y
A
î
x
B
x
A
B
A 
+

+

=
→

→
• k̂
A
ĵ
A
î
A
R Z
y
x +
+
=

GKwU †f±i ivwk n‡j,
Gi gvb, 2
z
2
y
2
x A
A
A
R +
+
=

GKK †f±i wbY©q
• R

Gi w`‡K GKK †f±i,
|
R
|
R
r̂ 

=
•
→
A I B
→
Gi j¤^w`‡K GKK †f±i,  =  A B
A B
→ →
→ →


†f±i ¸Yb
• B
.
A


= AB cos  = AxBx + AyBy + AzBz
• B
A


 = AB sin  =
z
y
x
z
y
x
B
B
B
A
A
A
k̂
ĵ
î
 1
k̂
.
k̂
ĵ
.
ĵ
î
.
î =
=
= Ges 0
k̂
k̂
ĵ
ĵ
î
î =

=

=

 k̂
ĵ
î =
 , ĵ
î
k̂ =
 , î
k̂
ĵ =
 , k̂
î
ĵ −
=

†f±i ¸b‡bi cÖ‡qvM
• A

I B

†f±iØq j¤^ n‡j
AxBx + AyBy + AzBz = 0
• A

I B

‡f±iØq mgvšÍivj n‡j
z
z
y
y
x
x
B
A
B
A
B
A
=
=
†f±‡ii ga¨eZ©x †KvY wbY©q
• cos  =
AB
B
.
A


• cos =
AB
B
A
B
A
B
A z
z
y
y
x
x +
+
A‡¶i mv‡_ Drcbœ †Kv‡Yi †¶Î,
x = cos–1










+
+ 2
Z
2
y
2
x A
A
A
Ges
y = cos–1










+
+ 2
Z
2
y
2
x A
A
A
z = cos–1










+
+ 2
z
2
y
2
x A
A
A
Awf‡¶cwbY©q
• A

eivei B

Gi Awf‡¶c =
A
B
.
A


mvgvšÍwi‡Ki m~Î
• jwä, R = 
+
+ cos
PQ
2
Q
P 2
2
jwäi †KvY,  = tan–1

+

cos
Q
P
sin
Q
•
→
A I
→
B †Kvb mvgvšÍwiK A_ev i¤^‡mi mwbœwnZ evû n‡j Z‡e
mvgvšÍwiK ev i¤^‡mi †¶Îdj =
→
→
 B
A
•
→
A I
→
B †Kvb mvgvšÍwiK A_ev i¤^‡mi KY© n‡j Z‡e
mvgvšÍwiK ev i¤^‡mi †¶Îdj =
→
→
 B
A
2
1
 Need To Know:
1.  = 0n‡j, R = P + Q, hv jwäi m‡e©v”P gvb|
2.  = 180n‡j, R = P  Q hv jwäi ¶z`ªZg gvb|
3.  = 90n‡j, R = 2
2
Q
P +
4. R2
max + R2
min = 2R2
90
5. wZbwU ej †Kv‡bv we›`y‡Z fvimvg¨ m„wó Ki‡j G‡`i †h‡Kvb `yBwUi
jwä AciwU n‡e|
6. P = Q n‡j Ges ej؇qi jwä †h †Kvb e‡ji mgvb n‡j  = 120
7. P = Q n‡j Ges ej؇qi jwä †h †Kvb e‡ji wظY n‡j  = 0
8. P = Q n‡j Ges ej؇qi jwä †h †Kvb e‡ji A‡a©K n‡j  = 151
9. P = Q n‡j R = 2Pcos
2

Dcvs‡k wefvRb
• j¤^fv‡e wefvR‡bi †¶‡Î,
• Avbyf~wgK Dcvsk, X

= R cos 
• Dj¤^ Dcvsk, Y

= R sin 
MwZwe`¨v(DYNAMICS)
s = ut v2 = u2 + 2 a s v = u  at
s =






V0 + V
2 t a =
t
u
~
v
V =
2
v
u +
t Zg †m‡K‡Û AwZµvšÍ `~iZ¡, Sth = u + ( )
1
2
2
1
−
t
a
a =
t
t
m
n
m
n
S
S t
t
−
−
, S(t+1)Zg = StZg + a
 †eM, v =
dt
ds
Z¡iY, a =
dt
dv
= 2
2
dt
s
d
 x `~iZ¡ †f` Kivi ci Gi †eM
n
1
Ask nviv‡j, ¸wjwU AviI s
`~iZ¡ †f` Ki‡j s =
x
n2
– 1
 x `~iZ¡ cÖ‡e‡k‡i ci †eM A‡a©K n‡j, `~iZ¡ hv‡e, s =
3
x
 x `~iZ¡ cÖ‡e‡k‡i ci †eM GK-Z…Zxqvsk n‡j, `~iZ¡ hv‡e, s =
8
x
 GKwU ivB‡d‡ji ¸wj GKwU Z³v‡K †f` Ki‡Z cv‡i| ¸wji
†eM v ¸Y Kiv n‡j Z³vi msL¨v n‡e, n = v2
Ges ¸wjwU n
msL¨K Z³v †f` Ki‡j †eM n‡e v = n ¸Y|
P

A
Q

B
C
Q
P
R



+
=
O A
B
X

Y
 R


C

î -Gi mnM
ŷ -Gi mnM
ẑ -Gi mnM
AwZµvšÍ `~iZ¡
mgxKiY msµvšÍ mgm¨v
Z³vi mgm¨v
cošÍ e¯‘i MwZi mgxKiY
MwZi mgxKiY msµvšÍ mgm¨v

3. 2
gt
2
1
ut
h 
= 2
gt
2
1
h = [Avbyf~wgK w`‡K gvi‡j]
2
gt
2
1
ut
h +
−
= [h D”PZv n‡Z Dj¤^ eivei gvi‡j]
hth =
2
1
g(2t-1)
h D”PZv †_‡K GKwU e¯‘‡K wb‡P †d‡j w`‡j Ges GKB mg‡q
GKwU e¯‘‡K u †e‡M Dc‡i wb‡¶c Ki‡j, wgwjZ nevi mgq,
t =
u
h
Ges wgwjZ nevi ¯’vb, h 2
)
u
h
(
g
2
1
h −
=
v2
= u2
 2gh hth= u 
2
1
g(2t-1)
H = ut 
2
1
gt2
V = u  gt
m‡e©v”P D”PZv †_‡K bvg‡Z mgq
g
u
t =
m‡ev©”P D”PZvq DV‡Z mgq
g
u
t =
wePiYKvj
g
u
2
T = m‡e©v”P D”PZv
g
2
u
H
2
=
f~wgi mv‡_  †Kv‡b Ges Dj¤^ eivei gvi‡j
(i) cvjøv, R =
g
2
sin
v o
2
o 
(ii) MwZ c‡_i mgxt y = bx-cx2
(iii) m‡e©v”Pcvjøv Rmax =
g
v2
o
(iv) m‡e©v”P D”PZv, H =
g
2
sin
V o
2
2
o 
(v) wePiY Kvj, T =
g
sin
v
2 o
o 
 g‡b ivL‡Z n‡e:
= 45°n‡j R = Rmax =
g
u2
= 90°n‡j H = Hmax =
g
2
u2
= 76°n‡j R = H n‡e|
 GKwU wbw¶ß e¯‘i †h †Kvb mg‡q Zvr¶wbK †e‡Mi AwfgyL
¯úk©K eivei|
 H max =
2
Rmax
 = 45°n‡j H =
4
R
 cÖ‡¶c‡KvY  n‡j tan =
R
T
9
.
4 2
 GKB Avw`‡e‡M `yywU e¯‘i Avbyf~wgK cvjøv mgvb n‡e hw` wb‡¶c
†KvY  Ges AciwU (90°- ) nq|
 f~wg n‡Z wbw¶ß cÖv‡mi †¶‡Î Avbyf~wgK eivei Z¡i‡Yi gvb k~Y¨|
h D”PZv n‡Z Avbyf~wgK eivei gviv n‡j,
Avbyf‚wgK fv‡e wbw¶ß e¯‘i MwZi mgxKi‡Yi †¶‡Î
2
y
2
x v
v
v +
=
x
y
v
v
tan =

2
gt
2
1
h = s = ut
cÖw¶ß e¯‘i MwZi mgxKi‡Yi †¶‡Î
†e‡Mi Dj¤^ AskK, vy = v0sin0 – gt.
†e‡Mi Avbyf‚wgK AskK, vx = v0cos0
h= – usinot + 1
2
gt2
Vy = – u sin 0+ gt.
†K›`ªgyLx Z¡i‡Yi †¶‡Î a = r
r
v 2
2

= =






2
T
2
 =






2N
t
2

†K›`ªgyLx ej, F = m2
r
wbDUwbqvb ejwe`¨v
NEWTONIAN MECHANICS
❑ ˆiwLK I †KŠwYK MwZi g‡a¨ mv`„k¨:
ˆiwLK †KŠwYK
S  = 2πN
V =
t
s
/ v = r  =
t

=
t
N

2
a = r 
m I
F = ma  = I
ˆiwLK †KŠwYK
S = vt  = t →mg‡KŠwYK
S = vt
2
1  =
2
1 t →GKwU †eM k~Y¨ n‡j
S = 2
2
1
at  = 2
2
1
t

P = Fv P = 
Ek = 2
2
1
mv Ek =
2
1
I2
fi‡e‡Mi wbZ¨Zvi m~Î, 2
2
1
1 v
m
v
m =
e›`y‡Ki cðvr †eM V, e›`y‡Ki fi M, ¸wji †eM v, ¸wji fi
m n‡j, MV + mv = 0
wbw¶ß e¯‘i MwZi mgxKiY
D”PZvi mgxKiY

u
h
s
u
h= 2
gt
2
1
s=ut
u1
u sin 

cÖvm RwbZ mgm¨v
wbw¶ß e¯‘i MwZi mgxKiY
cÖw¶ß e¯‘i MwZi mgxKiY
†K›`ªgyLx Z¡iY RwbZ mgm¨v
fi‡e‡Mi wbZ¨Zvi m~Î

4. SHADATH’S PHYSICS CARE Academic and Admission Physics Solution
Contact: 01725176911
cðvr †eM V, †bŠKvi fi M, Av‡ivnxi †bŠKvi †eM v Ges
Av‡ivnxi fi m n‡j, MV + mv = 0
fi‡eM P= Ft = m (v-u) = mv
ej F = ma = m
( )
t
u
v −
( ) ( )
u
v
m
t
t
F 1
2 −
=
−
e‡ji NvZ
  
J Ft mv mu
= = −
m1u1 + m2u2 = m1v1 + m2v2
(G‡Ki AwaK e¯‘i g‡a¨ msNl© nq Zvn‡jI G m~Î cÖ‡hvR¨)
wgwjZ e¯‘i †eM, v =
2
1
2
2
1
1
m
m
u
m
u
m
+

[GKB w`K †_‡K G‡m
av°v †L‡j (+), wecixZ w`K n‡j (-)]
(i) DaŸ©Mvgx wjd‡Ui †¶‡Î: R = m (g + f)
(ii) wbgœMvgx wjd‡Ui †¶‡Î: R = m (g – f)
 MwZkw³ Ek =
m
2
p
mv
2
1 2
2
=
→ MwZkw³ n ¸b Ki‡Z n‡j eZ©gvb †eM v2 = v1 n
 w¯’Z Nl©Y ¸YvsK, s
Fs
R
= s
tan
= k = tan-1
(k)
i‡K‡Ui †¶‡Î, DaŸ©gyLx av°v ev ej, F = Vr .
dt
dm
wb‡¶‡ci mgq i‡K‡Ui Dci cÖhy³ jwä ej = Vr g
m
dt
dm
0
−
GLv‡b mo = i‡K‡Ui †gvU fi|
i‡K‡Ui Dci wµqvkxj jwäZ¡iY, g
dt
dm
m
v
a r
−






=
i‡K‡Ui Zvr¶wYK Z¡iY, g
t
m
M
r
V
a −

= 





→ AvbZ Zj eivei gv‡e©j ev †MvjK AvK…wZi e¯‘ Mwo‡q co‡j
†gvU kw³ Ek = 2
10
7
mv
n e¨vmv‡a©i myZvi mvnv‡h¨ m f‡ii cv_i‡K e„ËvKvi c‡_ Nyiv‡j
myZvi Dci Uvb ev †K›`ª wegyLx ej, F =
r
mv2
= m2
r
r ˆ`‡N©¨i myZvi mvnv‡h¨ evjwZ‡Z cvwb wb‡q KZ †e‡M Nyiv‡j evjwZ
n‡Z cvwb co‡e bv, †m‡ÿ‡Î v = rg n‡e|
†KŠwbK †eM,  =

t =
2N
t
‰iwLK †eM, v = r
 m f‡ii cv_i‡K r ˆ`‡N©¨i myZvi mvnv‡h¨ Nyiv‡j, I = mr2
(evwl©K)
 m f‡ii I r e¨vmv‡a©i GKwU †MvjK‡K wbR A‡¶i mv‡c‡¶
Nyiv‡j I = 2
5
2
mr (AvwüK)
 c„w_exi AvwüK MwZi Rb¨ c„w_exi RoZvi åvgK I = 2
5
2
MR
(R = c„w_exi e¨vmva©)
 evwl©K MwZi Rb¨ c„w_exi RoZvi åvgK, I = 2
Mr ( r = m~h©
n‡Z c„w_exi `~iZ¡)
 r e¨vmv‡a©i wis‡K wbR A‡¶i mv‡c‡¶ Nyiv‡j, I = mr2
 PvKwZ wbR A‡¶i mv‡c‡¶ Nyiv‡j, I = 2
2
1
mr
 wb‡iU wmwjÛvi‡K wbR A‡¶i mv‡c‡¶ Nyiv‡j, I = 2
2
1
mr
 m fi I l ˆ`‡N©¨i `Û‡K gvS eivei Dj¤^ A‡¶i mv‡c‡¶
Nyiv‡j = 2
12
1
ml Ges GKcÖv‡šÍi mv‡c‡¶ Nyiv‡j, I =
3
2
ml
 iv¯Ívi evuK,
rg
v
tan
2
=

KvR, kw³ I ÿgZv
WORK, ENERGY & POWER
 MwZkw³, Ek =
1
2 mv2
 w¯’wZkw³, Ep = mgh
 f‚wg n‡Z x D”PZvq MwZkw³, w¯’wZkw³i n ¸Y n‡j D”PZv,
x =
h
n + 1
 KvR W F S FS cos
= =
 
.  = Pt
mgh
mv
2
1 2
=
=
 ¶gZv,
t
W
P = =
t
mgh
=
t
mv
2
1 2
 ¶gZv, Fv
t
S
.
F
t
W
P =
=
=
 GKwU ivB‡d‡ji ¸wj wbw`©ó cyiæ‡Z¡i GKwU Z³v †f` Ki‡Z cv‡i|
Giæc n wU Z³v †f` Ki‡Z n‡j ¸wji †eM n‡e n ¸Y|
 n msL¨K BU‡K hv‡`i cÖ‡Z¨‡Ki D”PZv h GKwUi Dci
Av‡iKwU †i‡L ¯Í¤¢ ˆZwi Ki‡Z K…ZKvR, W = mgh
n(n – 1)
2
 nvZzwo Dj¤^fv‡e †c‡iK‡K AvNvZ Ki‡j, W=mg (h +x)
NvZ ej RwbZ mgm¨v
wgwjZ e¯‘i MwZ RwbZ mgm¨v
wjd&U RwbZ mgm¨v
MwZkw³ wbY©q
Nl©Y ¸YvsK RwbZ mgm¨v
i‡K‡Ui MwZ RwbZ mgm¨v
†Mvj‡Ki †gvU MwZkw³ wbY©q
†K›`ªgyLx ej msµvšÍ mgm¨v
†KŠwYK †eM msµvšÍ
ˆiwLK I †KŠwYK †e‡Mi m¤úK©
RoZvi åvgK
hvbevnb I iv¯Ívi evuK msµvšÍ mgm¨v
MwZkw³ I w¯’wZkw³ wbY©q
KvR I ¶gZv wbY©q
K…ZKvR RwbZ mgm¨v

5. SHADATH’S PHYSICS CARE Academic and Admission Physics Solution
Contact: 01725176911
 nvZzwo Avbyf‚wgKfv‡e †c‡iK‡K AvNvZ Ki‡j, W=
1
2
mv2
 cvwb c~Y© Kzqv Lvwj Ki‡Z W = mgh [Mo D”PZv
2
h
]
 Dc‡ii A‡a©K cvwb †Zvjv n‡j,
4
h
h =

 A‡a©K c~Y© Kzqvi m¤ú~Y© cvwb †Zvjv n‡j,
4
h
3
h =

 `¶Zv  me©`v p Gi mv‡_ ¸b nq|
 e›`y‡Ki ¸wji †¶‡Î, S
.
F
mv
2
1 2
=
 MwZ kw³, EK =
m
2
P2
 KvR kw³ Dccv`¨, 





−
= 2
2
mu
2
1
mv
2
1
W
 cvwb †g‡N cwiYZ n‡Z K…ZKvR, gh
A
gh
v
mgh
W 
=

=
= l
 Dj¤^ eivei f~wg n‡Z x D”PZvq EpI Ek
 MwZkw³ wefe kw³i A‡a©K n‡j, x =
3
h
2
 MwZ kw³ wefe kw³i wظb¸Y n‡j, x =
3
h
gnvKl© I AwfKl©
GRAVIATION & GRAVITY
gnvKl© ej, F = 2
2
1
d
m
Gm
AwfKl©ej, 2
R
GMm
mg
F =
=
f‚-c„‡ô AwfKl©R Z¡iY, 2
R
GM
g = = G
R

3
4
c„w_exi fi, M =
gR
G
2
c„w_exi NbZ¡, 

=
3
4
g
GR
h D”PZvq Z¡iY,
2
h
h
R
R
g
g






+
=
D”PZv, h = R
1
w
w
R
1
g
g
1
1








−
=








−
h MfxiZvq Z¡iY 




 −
=
R
h
R
g
gd
mylg Nb‡Z¡ `ywU MÖ‡ni Rb¨ → g  R A_©vr ,
2
1
2
1
R
R
g
g
=
`ywU MÖ‡ni fi mgvb n‡j → g  2
R
1
A_©vr ,
2
1
2
2
1
R
R
g
g








=
p
e
2
e
p
p
e
p
e
W
W
R
R
M
M
g
g
=









=
K…wÎg DcMÖ‡ni ˆiwLK †eM v =
GM
R + h
= R =
g
R + h
K…wÎg DcMÖ‡ni †eM I AveZ©b Kv‡ji g‡a¨ m¤úK©
v =
2
T (R + h)
f‚w¯’i DcMÖ‡ni AveZ©b Kvj, T =
2 r3/2
R g
gyw³‡eM, v= gR
2 =
R
GM
2
gnvKl©xq wefe, V =
R
GM
−
gnvKl©xq cÖvej¨, 2
r
GM
E =
†Kcjv‡ii Z…Zxq m~Î t 3
2
R
2
2
T
3
1
R
2
1
T
=
c`v‡_©i MvVwbK ag©
STRUCTURAL PROPERTIES MATTER
w¯’wZ¯’vcK ¸YvsK wbY©q
 ˆ`N©¨ weK…wZ =
l
L  AvqZb weK…wZ =
V
v
 Amn cxob =
Amn ej
†¶Îdj =
F
A
 Bqs Gi w¯’wZ¯’vcK ¸YvsK,
l
l 2
r
mgL
A
FL
Y

=
=
 AvqZb ¸YvsK, K
FV
Av
= =
v
PV
[P = Pvc =
A
F
]
w¯’wZkw³ MwZkw³
x h-x
mgq
h–x
h
x
Ep =
mgx
Ek= mg (h-
x)
K‚c RwbZ mgm¨v
MwZkw³ I K…ZKv‡Ri m¤úK©
Dj¤^ eivei w¯’wZkw³ I MwZkw³
gnvKl© I AwfKl© ej wbY©q
AwfKl©R Z¡iY, c„w_exi fi
I NbZ¡ wbY©q
c„w_exi wewfbœ ¯’v‡b AwfKl©R Z¡iY
`ywU MÖ‡ni fi I NbZ¡ RwbZ mgm¨v
K…wÎg DcMÖ‡ni †eM I AveZ©b Kvj
gyw³‡eM, gnvKl©xq wefe
I cªvej¨ wbY©q

6. SHADATH’S PHYSICS CARE Academic and Admission Physics Solution
Contact: 01725176911
 AvqZb ¸YvsK, K =

PV
 cqm‡bi AbycvZ,  =
Ld
D
l
 Y
Y
i
r
r
i
=
l
l
Y = 2n (1+)
 Y = 3k (1-2) û‡Ki m~Î:
cxob
weK…wZ = aªæe
 w¯’wZ¯’vcK w¯’wZkw³ ev †gvU kw³, W
YA
L
= 
1
2
2
l
 GKK AvqZ‡b w¯’wZkw³ E =
1
2
 cxob  weK…wZ =
AL
F
2
1 l

 cvwbi c„ôUvb,
L
F
T =
 e¯‘i IRb, W= cøeZv (F1) + mv›`ªej (F2)
 c„ôUv‡bi Dci ZvcgvÎvq cÖfve, T = To (1– t)
 Zi‡ji c„ôUvb,
( )

+

=
cos
2
3
r
h
g
r
T =


cos
2
g
rh
=
2
g
rh
 cvwbi †j‡f‡ji cv_©K¨, 







−

=

2
1 r
1
r
1
g
T
2
h
 mv›`ªej: F A
dv
dx
=  [cÖ‡kœ †Zj D‡jø¨L _vK‡j]
 mv›`ªZvsK:  =






F
A 





dx
dv
 †÷vK‡mi m~Î: F = 6r
 M¨v‡mi †¶‡Î ZvcgvÎvi mv‡_ mv›`ªZvsK
2
1
2
1
T
T
=


 †Mvj‡Ki cÖvšÍ †eM,
( )


−

=
9
g
2
r
2
V
 AwZwi³ Pvc,
r
T
4
P =
 †gvU w¯’wZkw³ t E = TA
 c„ôkw³ e„w×, E = AT = 4 (Nr2
-R2
)  T
 mvev‡bi ey`ey‡`i †¶‡Î, E = 24(Nr2
-R2
)T
ch©ve„wËK MwZ
PERIODIC MOTION
 T =
g
L
2 = 2
m
k = 2
e
g

1
2
2
1
g
g
T
T
= [hw` L AcwiewZ©Z _v‡K]

2
1
2
1
L
L
T
T
= [hw` g AcwiewZ©Z _v‡K]
 cwiewZ©Z †`vjbKvj wbY©q,
86400
86400
T
T
1
2 

=
 †eM V =  2
2
x
A −
 Z¡iY a = –2
x
 m‡e©v”P †eM Vmax = A
 m‡e©v”P Z¡iY amax = 2
A
 miY; x = A sin(t + )
 †`vjbKvj T =


2
 †KŠwYK †eM  =
k
m

d2
x
dt2 + 2
x = 0
 w¯cÖs Gi mgm¨v:
ej F = mg = kx → k wbY©q
K…ZKvR W = ( )
2
1
2
2
2
x
x
k
2
1
kx
2
1
−
=
†`vjbKvj 
= 2
T
K
M
=
g
x
2
 w¯cÖs Gi ej aªæeK
x
mg
K =
 †gvU kw³ =
1
2
m2
A2
 cvnv‡oi D”PZv wbY©q:
R
h
R
T
T
1
2 +
=
†`vjK GKw`‡b †¯øv/dv÷ n‡j,
R
h
R
86400
86400 +
=


Zi½
WAVE
 †hgb : cvwb‡Z m„ó †XD, Zvwor †PŠ¤^K ˆ`N©¨ → wØgvwÎK
 Zi½P~ov n‡Z Zi½P~ovi `~iZ¡ → 
 mg`kv m¤úbœ `ywU KYvi ga¨eZ©x `~iZ¡ → 
GKw`‡b slow ev fast mgq|
†`vjbKvj m¤úK©xZ mgm¨v
cwiewZ©Z †`vjbKvj wbY©q
m‡e©v”P †eM I Z¡iY
w¯cÖs RwbZ mgm¨v
cvnv‡oi D”PZv wbY©q
AbycÖ¯’ Zi½
w¯’wZ¯’vcK ¸YvsK I cqm‡bi
Abycv‡Zi g‡a¨ m¤úK©
w¯’wZkw³ wbY©q
cvwbi c„ôUvb wbY©q
†KŠwkK b‡j cvwbi Av‡ivnb wbY©q
mv›`ªZvsK wbY©q
cÖvšÍ‡eM I c„ôkw³ e„w× wbY©q

7. SHADATH’S PHYSICS CARE Academic and Admission Physics Solution
Contact: 01725176911
 wecixZ `kv m¤úbœ `ywU KYvi ga¨eZ©x `~iZ¡ →
2

 AMÖMvgx Zi‡½i Zi½ mÂvjb Ges KYv¸‡jvi ¯ú›`‡bi ga¨eZ©x
†KvY → 90
 AMÖMvgx Zi‡½i `kv cv_©K¨,  = x
2



 `kv cv_©K¨ 2 Gi †ewk n‡Z cv‡i bv| 2 Gi †ewk n‡j 2
we‡qvM Ki‡Z n‡e|
 `kv cv_©K¨ 2 Gi ¸wYZK n‡j `kv cv_©K¨ k~Y¨ n‡e|
 y = A sin


2
(vt – x) D‡jÐL¨, x Gi mnM me mgq 1 Ki‡Z
n‡e|
 k‡ãi †eM, v = f
 AwZµvšÍ `~iZ¡ , s = N
GKB Zi½‰`N©¨ I K¤úvsK wewkó `ywU Zi‡½i wecixZ w`K n‡Z
DcwicvZ‡bi m„wó nq|
 `ywU wb®ú›` we›`yi ga¨eZ©x `~iZ¡ =
2

 GKwU wb¯ú›` I GKwU my¯ú›` we›`yi ga¨eZ©x `~iZ¡ =
4

 wZbwU wb®ú›` we›`yi `~iZ¡ = 
  `~i‡Z¡ `ywU m¯ú›` I `ywU wb¯ú›` we›`y nq|
 †Kvb gva¨‡g AwZµvšÍ `~iZ¡, s = N
 †hLv‡b, N = K¤úb msL¨v.  = Zi½‰`N©¨
 PvKwZ‡Z m„ó k‡ãi K¤úvsK f = N  m
 f =
1
2l
T
m
GLv‡b, T = Uvb A_ev ej  = kg/m
 cÖ_g Dcmy‡ii †gŠwjK K¤úvsK, f =
1
l
T
m
 `ywU Uvbv Zvi HKZv‡b _vK‡j f1 = f2 nq|
 k‡ãi ZxeªZv †j‡fj,  = 10 log
0
I
I
dB
 k‡ãi ZxeªZv †j‡f‡ji cv_©K¨  = 10 log
1
2
I
I
dB
 kã Drm n‡Z `~i‡Z¡i mv‡_ kÖæZ k‡ãi ZxeªZvi m¤úK© e‡M©i
e¨v¯ÍvbycvwZK|
 Zi½‰`‡N©¨i cv_©K¨ †`Iqv _vK‡j, V2 – V1 = f  
 K¤úvs‡Ki cv_©K¨ A_©vr weU msL¨v †`Iqv _vK‡j,
f2 – f1 = N = V 








−
 1
2
1
1
 `ywU kã Zi‡½i DcwicvZ‡b cÖvq mgvb K¤úvs‡Ki `ywU Zi‡½i
DcwicvZ‡b k‡ã ZxeªZvi n«vm e„wׇK exU e‡j| A_©vr GK
†m‡K‡Û m„ó exU‡K exU msL¨v e‡j|
 exU msL¨v 10 Gi Dc‡i n‡Z cv‡i bv|
 f2 = f1  N
GKB n‡j (–), wecixZ n‡j (+)
Av`k© M¨vm I M¨v‡mi MwZZË¡
IDEAL GAS & KINETIC THEORY OF GASES
 P1V1 = P2V2 
2
2
2
1
1
1
T
V
P
T
V
P
= 
2
2
1
1
T
P
T
P
=

2
2
1
1
T
V
T
V
= 
2
2
2
1
1
1
T
P
T
P

=

 PV =
1
3
mnc2
.
 PV = nRT = RT
M
g
 E =
2
3
nRT =
2
3
M
g
RT (†gvU MwZkw³)
 E =
2
3
KT (Mo MwZkw³i †¶‡Î)
 c =
M
RT
3
 c =
M
KT
3
 c =

P
3

2
1
1
2
1
2
2
1
T
T
M
M
C
C
=
=


=
 MfxiZv h = (n – 1)  10.2 (n = AvqZ‡bi ¸Y)
 MfxiZv h = (n3
– 1)  10.2 (n = e¨vm ev e¨vmv‡a©i ¸Y)
 Mo gy³ c_,  =
n
d
2
1
2

. d = AYyi e¨vm , n = GKK AvqZ‡b AYyi msL¨v
 Av‡cw¶K Av`ª©Zv %
100
F
f
R 
=
c_ cv_©K¨
wb¯ú›` we›`y
my¯ú›` we›`y
AMÖMvgx Zi‡½i miY
Zi‡½i †eM
w¯’i Zi½
wQ`ª
N~Y©b
k‡ãi AwZµvšÍ `~iZ¡
k‡ãi m„wó
Uvbv Zv‡i m„ó k‡ãi K¤úvsK
k‡ãi ZxeªZv †j‡fj
k‡ãi Zi½‰`N©¨
exU
ARvbv kjvKvi K¤úvsK
M¨v‡mi †gvU MwZkw³
eM©g~j Mo eM©‡eM wbY©q
n«‡`i MfxiZv wbY©q
Mogy³ c_ wbY©q
Av‡cw¶K Av`ª©Zv wbY©q

8. SHADATH’S PHYSICS CARE Academic and Admission Physics Solution
Contact: 01725176911
ZvcMwZwe`¨v
THERMODYNAMICS
1.
9
492
R
5
273
K
9
32
F
5
C −
=
−
=
−
= 2.1C = F
5
9 
3. 5C = 9F = 5K = 9R
T = K
X
X
16
.
273
r







 Formula:  =
ice
stream
ice
x
x
x
x
−
−

 100 (C)
cÖK…Z cvV  ; x = µwUc~Y© _v‡g©vwgUv‡ii cvV
 Zvcxq ZworPvjK kw³, E = a + b2
→ Drµg ZvcgvÎv, C = –
b
a
→ kxZj ms‡hvM¯’‡ji ZvcgvÎv, 0 = OC
→ wbi‡c¶ ZvcgvÎv, n =
0 + c
2
 D”PZv h †`Iqv _vK‡j,  =
428
h
 e¯‘i †eM v †`Iqv _vK‡j  =
s
2
v 2
P1 V1 = P2V2 → m‡gvò cÖwµqvi †¶‡Î
P1V1

= P2V2

T1V1
–1
= T2V2
–1
(i) CP – CV = R (ii)  =
V
P
C
C
(iii) CP > CV
GK cigvYyK
CV
3
2
R
CP
5
2
R
wØ- cigvYyK
CV
5
2 R
CP
7
2 R
eûcigvYyK
CV 3R
CP 4R
1.  = 





−
1
2
T
T
1  100% 2.  = 





−
1
2
Q
Q
1  100%

1
2
1
2
T
T
Q
Q
=
 KvR W = Q1
Ae¯’vi cwieZ©b n‡j, ds =
T
ml
ZvcgvÎvi cwieZ©b n‡j, ds = ms ln
1
2
T
T
w¯’i Zwor
STATIC ELECTRICITY
 Zwor d¬v· t  = Z‡ji †ÿÎdj (S)  Zwor‡ÿÎ (E)
 MvD‡mi m~Î t |
 =

s
q
s
d
E


.
0 hw` 0
=
q nq, Z‡e Zwor d¬v·,
0
. =
= s
s
d
E



Zwor w؇giæ (Electric Dipole) t Zwor w؇giæi åvgK,
l
q
P 2

= Pv‡R©i cwigvY  `~iZ¡
Zwor w؇giæi Rb¨ Zwor †ÿÎ cÖvej¨, 3
0
4
1
r
P
E 
=

Zwor w؇giæi Rb¨ Zwor wefe, 2
0
cos
4
1
r
P
Vp



=
 Pv‡R©i †Kvqv›Uvqb t cÖK…wZi †Kv‡bv e¯‘i †gvU Pv‡R©i cwigvY n‡e
B‡jKUªb ev †cÖvU‡bi Pv‡R©i c~Y© msL¨K ¸wYZK, G‡K Pv‡R©i
†Kqv›Uvqb e‡j|
 †Kv‡bv e¯‘i PvR©, ne
q 
=
F =
0
4
1

 2
2
1
r
Q
Q







=


2
2
9
0
c
/
Nm
10
9
4
1
V =
r
Q
.
4
1
0


(†Mvj‡Ki Af¨šÍ‡i I c„‡ô wefe mgvb)
V = 9  109
 





+
+
+
r
q
r
q
r
q
r
q 4
3
2
1
V = 9  109

r
q
4
[me¸‡jv PvR© mgvb n‡j]
e¨vmva© , r =
evû
2
=
2
a
†K‡›`ª wefe k~b¨ n‡j, 0
q
q
q
q 4
3
2
1 =
+
+
+
2
9
2
r
Q
.
10
9
r
Q
.
4
1
E 
=

=

 ms‡hvM †iLvi ga¨we›`y‡Z jwä wefe: V = 9109
2
/
r
q
q 2
1 +
 ms‡hvM †iLvi ga¨we›`y‡Z jwä cÖvej¨: E = 9109
( )2
2
1
2
/
r
q
q −
q1 PvR© n‡Z x `~i‡Z¡ jwä cÖvej¨ k~Y¨ n‡j,
x =
1
2
q
q
1
r
+
[hvi ¯^v‡c‡¶ †m wb‡P n‡e]
 F = qE F= mg  qE
mg =
 E = –
dr
dV
 KvR = PvR©  wefe cv_©K¨
ZvcgvÎvi wewfbœ †¯‹j msµvšÍ
ˆÎa we›`y msµvšÍ
µwUc~Y© _v‡g©vwgUvi msµvšÍ
_v‡g©vKvcj/ ZvchyMj
iæ×Zvcxq cÖwµqvi
†¶‡Î
ey‡jU I SiYv msµvšÍ mgm¨v
m‡gvò I iƒ×Zvcxq cÖwµqv msµvšÍ
w¯’i AvqZb I w¯’i Pvc m¤•wK©Z
Kv‡Y©v BwÄb m¤úwK©Z
m¤úvw`Z Kv‡Ri cwigvY
GbƪwcRwbZ mgm¨v
Kzj‡¤^i m~Î
†Mvj‡Ki wefe
eM©‡¶‡Îi †K‡›`ª wefe
Zwor‡¶‡Îi cÖvej¨
ga¨we›`y‡Z jwä Ges wefe cÖvej¨
jwä cÖvej¨ wbY©q
Zwor ej I cÖve‡j¨i m¤úK©
Zwor cÖvej¨ I wef‡ei m¤úK©

9. SHADATH’S PHYSICS CARE Academic and Admission Physics Solution
Contact: 01725176911
 ˆe`y¨wZK †¶‡Î (E) I wefe cv_©K¨ (V) g‡a¨ m¤úK©: E =
d
V
 †kªYx mgev‡q Zzj¨ aviKZ¡: CS = (C1
–1
+ C2
–1
+ C3
–1
.... )–1
 mgvšÍivj mgev‡q Zzj¨ aviKZ¡: CP = C1 + C2 + C3 + ....
 cwievnxi aviKZ¡: C =
V
Q
 †MvjvKvi cwievnxi aviKZ¡: C= 40 .k r
 mgvšÍivj cvZ avi‡Ki aviKZ¡: C =
d
A
K 0

 =
A
Q
= 2
r
Q

= 2
r
4
Q

(†MvjK n‡j)
PvwR©Z avi‡K w¯’wZ kw³: E =
C
Q
2
1
QV
2
1
CV
2
1 2
2
=
=
Pj Zwor
CURRENT ELECTRICITY
 Zwor cÖevn gvÎv: I =
t
Q
 B‡j±ª‡bi Zvob †eM: V =
NAe
I
 †iv‡ai DòZv ¸Yv¼:  =
z
R
R
RZ


−
 †iv‡ai †kªYx mgevq: Rs = R1
–1
+ R2
–1
+ R3
–1
+ ..... + Rn
 †iv‡ai mgvšÍivj mgevq: Rp = (R1
–1
+ R2
–1
+ R3
–1
+ ..... )–1
 mgvšÍivj mgev‡qi †¶‡Î, R1 = R2 n‡j, Rp =
2
R1
 R1 = 2R2 n‡j, Rp =
3
R1
 n msL¨K mggv‡bi †iv‡ai Rb¨ Rs = n2
 Rp
 GKwU Zvi‡K n ¸b j¤^v Kiv n‡j cwieZx© †iva:
R = n2
 Av‡Mi †iva
 Av‡cw¶K †iva:  =
RA
L
 †iv‡ai Kvjvi †KvW, AB10C
[B B R O Y Good Boy Very Good Worker]
 `ywU †iv‡ai g‡a¨ Zzjbv Ki‡j,
2
1
2
2
1
2
1
r
r
L
L
R
R









=
 IÕ †gi m~Î: V = IR
 Af¨šÍixY †iva hy³ _vK‡j, I =
r
R
E
+
 ûBU‡÷vb eªxR:
S
R
Q
P
=
 wgUvi eªx‡Ri wbt¯ú›` we›`y:
r
100
r
Q
P
−
= [r = cm GK‡K n‡e]
 Current divider rule:
I1 = I
R
R
R
2
1
2

+
I2 = I
R
R
R
2
1
1

+
 †kªYx mgev‡qi †¶‡Î, 1
1
1 R
I
V = Ges 2
2
2 R
I
V =
 †Kvb we›`yi we›`y wefe = (eZ©bxi wefe – H we›`yi Av‡Mi †iv‡ai wefe)
Zwor cÖev‡ni †PŠ¤^K wµqv I Pz¤^KZ¡
MAGNETIC EFFECT OF CURRENT & MAGNETISM
 A¨vw¤úqvi m~Î t  = I
dl
B 0
.  |
 ev‡qvU m¨vfv‡U©i m~‡Îi MvwYwZK iæc: 2
sin
r
dl
l
dB


 Zwor cÖev‡ni d‡j m¤úbœ KvR W = I2
Rt = VIt = Pt
 Zv‡ci hvwš¿K mgZv: J =
H
W
=
H
VIt
 ¶gZv P = VI =
R
V 2
 Zvcxq Zwor”PvjK kw³: E = a + b2
 Zwor we‡køl‡b Aegy³ fi: W = ZQ = ZIt
 Zwor ivmvqwbK Zzj¨vsK: Z =
cvigvbweKfi
†hvRbx96500
 d¨viv‡Wi m~Î,
2
2
1
1
m
W
m
W
=
 ZvcgvÎv e„w× n‡j, mst = I2
Rt = VIt = Pt
 `ywU †iva †kªYx‡Z hy³ _vK‡j Drcbœ Zv‡ci AbycvZ:
2
1
2
1
R
R
H
H
=
 `ywU †iva mgvšÍiv‡j _vK‡j Drcbœ Zv‡ci AbycvZ:
1
2
2
1
R
R
H
H
=
 we`y¨r wej, B = Wb (cÖwZ BDwb‡U LiP)
Zzj¨ aviKZ¡ wbY©q
avi‡Ki aviKZ¡
Pv‡R©i ZjgvwÎK NbZ¡
avi‡Ki mwÂZ kw³
I1
R1
I
I2 R2
R1
R2
R3 V2
V
RP
I I
I2
I3
I1
†iv‡ai mgevq
Av‡cw¶K †iva
Zzj¨ †iva
In‡gi m~‡Îi e¨envi
ûBU‡÷vb eªx‡Ri e¨envi
wgUvi eªx‡Ri e¨envi
eZ©bx m¤úwK©Z mgm¨v
Zvob †eM I Zwor cÖevn wbY©q
e¨wqZ Zwor kw³ wbY©q
Zv‡ci hvwš¿K mgZv
Aegy³ fi wbY©q
Drcbœ Zv‡ci AbycvZ
we`y¨r wej wbY©q

10. SHADATH’S PHYSICS CARE Academic and Admission Physics Solution
Contact: 01725176911
 cÖevn NbZ¡: J =
A
I
 †PŠ¤^K åvgK m = NIA
 M¨vjfv‡bvwgUv‡ii Zwor cÖevn , I = k
 C
B
E
0
0
=
 †mvRv cwievnxi wbK‡U †Kvb we›`y‡Z B Gi gvb: B =
a
2
I
0


 e„ËvKvi cwievnxi †K‡›`ª B Gi gvb: B =
r
2
NI
0

 MwZkxj Pv‡R©i Dci †PŠ¤^K ej: B
V
N
F 
=
 †mvRv Zv‡ii Dci †PŠ¤^K ej: B
I
F 
=  sin
 `ywU mgvšÍivj Zv‡ii ga¨ w`‡q Zwor cÖevwnZ n‡j, Zv‡`i g‡a¨
wµqvkxj ej: F =
r
2
I
I 2
1
0

 
 nj wefe cÖv_©K¨: V = Bvd
 ¶z`ª eZ©bxi Dci †PŠ¤^K †¶‡Îi UK©: B
m
B
A
Ni 
=

=

 M¨vjfv‡bvwgUv‡ii g‡a¨ w`‡q cÖevwnZ Zwor, Ig =
S
G
S
+
I
 mv‡›Ui †iv‡ai gvb, S =
1
n
r
−
f~-Pz¤^‡Ki AvYyf~wgK Dcvsk: H = B cos
f~-Pz¤^‡Ki Dj¤^ Dcvsk: V = B sin
webwZ , tan  =
H
V
†gvU cÖvej¨, I = 2
2
H
V +
 †`vjb g¨vM‡bvwgUv‡i Pz¤^‡Ki †`vjbKvj T = 2
MH
I
 Ab¨vb¨: tan =
H
V
I = 2
2
V
H +
 K =
H
I
M = IA
Zvwor‡PŠ¤^Kxq Av‡ek I cwieZ©x cÖevn
ELECTROMAGNETIC INDUCTION &
ALTERNATING CURRENT
  = 0 sin t
 I = I0 sin t
 Mo e‡M©i eM©g~j gvb Irms =
1
2
 kxl©gvb

p
s
s
p
p
s
n
n
I
I
E
E
=
= 
p
s
E
E
K =
  = – N
dB
dt
  = – M
dL1
dt
  = – L
dI
dt
 L =
I
N B

 M =
1
1
1
I
N 
R¨vwgwZK Av‡jvKweÁvb
GEOMETRICAL OPTICS
1. 
=
r
i
sin
sin
2. r
i r
i sin
sin 
 =
 b~¨bZg wePz¨wZi kZ© t
1. b~¨bZg wePz¨wZi †ÿ‡Î 2
/
)
(
2
1 m
A
i
i 
+
=
= n‡e|
2. b~¨bZg wePz¨wZi †ÿ‡Î 2
/
2
1 A
r
r =
= n‡e|
¶xY `„wó‡`i Pkgvi ¶gZv, P =
d
1
−
`~i`„wó A_©vr eq¯‹‡`i Pkgvi ¶gZv, P =
d
1
25
.
0
1
−
E
 mij AYyex¶Y hš¿/ AvZmx KvP: weea©b, m =
f
D
1+
 b‡fv `~iex¶Y hš¿:
(a) ¯^vfvweK †dvKvwms Gi †¶‡Î, b‡ji ˆ`N©¨ L = f0 + fe, weea©b
m =
fe
f0
(b) wbKU we›`y‡Z †dvKvwms L = f0 +
D  fe
D + fe
weea©b m = 
f




1
D
+
1
fe
.
 †dvKvm `~iZ¡ f =
2
r
 `c©‡Yi mgxKib,
u
1
v
1
+ =
f
1
r
2
=
 †dvKvm `~i‡Z¡i mgxKib, f =
v
u
uv
+
  †Kv‡Yi `ywU `c©‡Yi mvg‡b GKwU e¯‘ ai‡j we¤^ m„wó n‡e,
1
360
n
−

=
 weea©b m = –


=
u
v
 e¯‘i `~iZ¡, u = f
m
1
m


[ev¯Íe = +, Aev¯Íe = –]
 DËj `c©Y f = (–), AeZj `c©Y f = (+)
 we‡¤^i ˆ`N©¨ 
 
−
=

f
u
f
cÖevn NbZ¡ I †PŠ¤^K åvgK wbY©q
†PŠ¤^K †¶‡Îi gvb wbY©q
†PŠ¤^K ej wbY©q
nj wefe msµvšÍ mgm¨v
mv›U RwbZ mgm¨v
Pz¤^‡Ki Dcvs‡ki gvb wbY©q
†PŠ¤^‡Ki †`vjbKvj wbY©q
kxl©gvb wbY©q
UªvÝdigvi RwbZ mgm¨v
Avweó Zwor PvjK kw³ wbY©q
¯^Kxq Av‡ek ¸YvsK wbY©q
†Pv‡Li ÎæwU RwbZ mgm¨v
AYyex¶Y hš¿ RwbZ mgm¨v
`c©‡bi mgxKib
we‡¤^i AvK…wZi wbY©q
msKU †KvY wbY©q

11. SHADATH’S PHYSICS CARE Academic and Admission Physics Solution
Contact: 01725176911
  =
1
sinc
 B gva¨g ¯^v‡c‡¶ A gva¨†gi cÖwZmiv¼,
c
a
b
a
c
b


=

 A gva¨g ¯^v‡c‡¶ B gva¨†gi cÖwZmiv¼,
b
a
b
a
C
C
=

 wcÖRg Dcv`v‡bi cÖwZmiv¼:  =
2
A
sin
2
A
sin m

+
 miæ wcÖR‡g wePz¨wZ:  = ( – 1) A
 weea©b: m = –
u
v
 †j‡Ýi mgxKiY,
f
1
u
1
v
1
=
+
 †j‡Ýi ¶gZv: p =
)
m
(
f
1
 Zzj¨ †j‡Ýi ¶gZv, p = n
3
2
1 p
.....
..........
p
p
p +
+
+
+

n
2
1 f
1
...
..........
f
1
f
1
P +
+
+
=
 mgZzj¨ †j‡Ýi †dvKvm `~iZ¡: F =
2
1
2
1
f
f
f
f
+
  =
cÖK…Z MfxiZv
AvcvZ MfxiZv
 cÖwZwe‡¤^i Ae¯’vb,
r
1
u
1
v
−

=
+

 †jÝ cÖ¯‘Z Kvi‡Ki m~Î: 







−
−

=
2
1 r
1
r
1
)
1
(
f
1
‡fŠZ Av‡jvKweÁvb
PHYSICAL OPTICS
 g¨vjv‡mi m~Î t ÒmgewZ©Z Av‡jv we‡køl‡Ki ga¨ w`‡q Mg‡bi d‡j Gi
ZxeªZv mgeZ©K I we‡køl‡Ki wbtmiY Z‡ji ga¨eZ©x †Kv‡Yi cosine
Gi e‡M©i mgvbycvwZK|Ó
 Av‡jvi ZxeªZv, 
 2
0
2
2
cos
cos I
Ka
I 
=
 k~Y¨¯’v‡b Zwor †PŠ¤^Kxq Zi‡½i MwZ‡eM, C =


0
1
 c‡qw›Us †f±i H
E
S




=
 E = h
 C = 
 wd‡Rvi c×wZ‡Z Av‡jvi †eM, C = 4mnd
 Av‡jvi †eM Ges Gi cÖwZmiv‡¼i g‡a¨ m¤úK©, ab =
b
a
C
C
 Zi½‰`N©¨ Ges gva¨‡gi cÖwZmiv‡¼i g‡a¨ m¤úK©, ab =
b
a


 Bqs Gi wØwPf cix¶vq m„ó †Wvivi cÖ¯’: x =
a
nd
GLv‡b, n = KZ Zg, d = c`©vi `~iZ¡, a = wPi؇qi e¨veavb
 GK wP‡oi Rb¨ AceZ©b; a sin  = n
GLv‡b, a = f P‡ii cÖ¯’,  = AceZ©b †Kvb
 †Kw›`ªq Pi‡gi [Dfq ¯ú‡k©] n Zg n = KZ Zg
 Ae‡gi †KŠwbK `~iZ¡ = 2
 m‡e©v”P Ae‡gi msL¨v wbY©‡qi †¶‡Î sin = 1 n‡e|
 †MÖwUs aªæe‡Ki Rb¨ AceZ©b: 
=
 n
sin
N
1
 `kv cv_©K¨ =


2
 c_ cv_©K¨
(`kv cv_©K¨ 2 A_ev 2 (`yB Gi) ¸wYZK n‡Z cv‡i bv)
 A gva¨g mv‡c‡¶ B gva¨‡gi cÖwZmivsK,
b
a
b
a
C
C
=

AvaywbK c`v_©weÁv‡bi m~Pbv
INTRODUCTION TO MODERN PHYSICS
 AvBb÷vB‡bi Av‡jvK Zwor mgxKiY t 0
2
2
1
W
hf
mv −
=
0
W = Kvh© A‡cÿK|
`¨ eªMwj Zi½, ]
[ mv
P
mv
h
p
h
=
=

= 


 K¤úUb cÖfve,
)
cos
1
(
)
cos
1
(
0






 −
=


−
=

=
−
 c
c
m
h
 nvB‡Rbev‡M©i AwbðqZv bxwZ t h
P
x
h
P
x 





 .
2
.

 Av‡cw¶K ˆ`N©¨ , L = Lo  2
2
c
v
1−
 Av‡cw¶K fi , m =
2
2
c
v
1
m
−

 Av‡cw¶K mgq , t =
2
2
c
v
1
t
−

 MwZkxj KvVv‡gvi †eM, v = c  2
)
1
(
1 
−
 b‡fvPvixi eZ©gvb eqm = Av‡Mi eqm + ågbKvj 
2
c
v
1 





−
 fi kw³ iƒcvšÍi m~Î, E = mc2
 K…òe¯‘i †¶‡Î, CS =
S
R
gm
2
cigvYyi g‡Wj Ges wbDwK¬qvi c`v_©weÁvb
ATOM MODEL & NUCLEAR PHYSICS
 fi ÎæwU t M
Nm
Zm
m n
p −
+
=
 )
(
 eÜb kw³ t 2
mc
E 
=
 ‡ZRw¯ŒqZvi ÿqm~Î t
N
dt
dN
N
dt
dN
N
dt
dN

−
=

−



−
†ZRw¯Œq iƒcvšÍi mgxKiY t t
Oe
N
N 
−
=
 Aa©vqy 2
1
T =

693
.
0
[ = ¶q-aªæeK]
Av‡cw¶K fi, ˆ`N©¨, mgq wbY©q
MwZkxj KvVv‡gvi †eM wbY©q
kw³i iƒcvšÍi
cÖwZmiv¼ wbY©q
wcÖRg RwbZ mgm¨v
†j‡Ýi †dvKvm `~iZ¡ wbY©q
†j‡Ýi ¶gZv wbY©q
cÖwZmiv¼ RwbZ mgm¨v
cÖwZmiv¼ wbY©q
Zi‡½i †eM I kw³ wbY©q
wPi RwbZ mgm¨v
`kv cv_©K¨ I c_ cv_©K¨
Aewkó cigvYyi fi

12. SHADATH’S PHYSICS CARE Academic and Admission Physics Solution
Contact: 01725176911
 Aa©vqy 2
1
T =
InN
InN
t
693
.
0
0 −
 A¶Z ev Aewkó cigvbyi fi: N = N0
t
e 
−
 N = N0 (0.5)
2
1
T
t
 Mo Avqy ,  =

1
=
693
.
0
T
 H cigvYyi n K¶ c‡_i kw³ En = eV
n
6
.
13
2
−
 H cigvYyi n K¶c‡_i e¨vmva© rn = n2
 0.53

A
 AvcwZZ Av‡jvK kw³ Kvh©v‡c¶‡Ki Zzjbvq †ewk n‡j,
 hf = 0 + Ek f =
h
10
6
.
1
)
E
( 19
k
−


+

 wewKwiZ Av‡jvi K¤úv¼, f =
h
10
6
.
1
)
E
E
( 19
1
2
−


−
 −
e Gi `yB cÖv‡šÍ V wefe w`‡j, −
e Gi MwZkw³ E = −
e V
 wbe„wZ wefe Vs Gi †¶‡Î, V
e
mv
2
1 2
=
 v =
m
eV
2
‡mwgKÛv±i I B‡jKUªwb·
SEMICONDUCTOR & ELECTRONICS
 MZxq †iva t
I
V
R


=
 cxU cÖevn, C
B
E I
I
I +
=
 cÖevn jvf ,  =
B
C
I
I


=

−

1
 weea©b ¸YK ,  =
E
C
I
I


 MZxq †iva, R =
I
V


kw³¯Í‡ii kw³ I e¨vmva© wbY©q
K¤úv¼ wbY©q
wKQz K_v...
wcÖq D”Pgva¨wgK I fwZ© cÖZ¨vkx wk¶v_©xiv,
GBP.Gm.wm cix¶vi c‡iB †Zvgv‡`i D”P wk¶v AR©‡bi Avkvq
AeZxY© n‡Z nq wek¦we`¨vjq fwZ© hy‡×|BwÄwbqvwis e‡jv Avi
cvewjK wek¦we`¨vjq,fwZ© cix¶vq c`v_©weÁvb †Zv me †¶‡ÎB
Avek¨K|Avi c`v_©weÁv‡b m‡e©v”P cÖ¯‘wZi Rb¨ cÖ‡qvRb
mg‡qi m‡e©v”P mبenvi Ges mwVK w`Kwb‡`©kbv|c`v_©weÁv‡b
fv‡jv wcÖcv‡ikb †bqvi Rb¨ kU©KvU †Kv‡bv dg©zjv †bB|
c`v_©weÁv‡b fv‡jv cÖ¯‘wZi Rb¨ Rvb‡Z nq A‡bK wKQz, eyS‡Z
nq Zvi‡P‡q †Xi †ewk|
Avgvi `xN© mg‡qi GKv‡WwgK I GWwgkb cov‡bvi AwfÁZv
†_‡K †Zvgv†`i‡K c`v_©weÁv‡b m‡e©v”P cÖ¯‘wZi wbðqZv w`‡Z
Avwg wbqwgZ †Póv K‡i hvw”Q|c`v_©weÁv‡bi LyuwUbvwU Rvb‡Z I
wkL‡Z AvMÖnx Ges c`v_©weÁv‡b m‡e©v”P cÖ¯‘wZi mv‡_ mvdj¨
cÖZ¨vkx‡`i ÒSHADATH’S PHYSICS CAREÓ G ¯^vMZg|
ïfKvgbvq,
bvRgym mv`vZ
c`v_©weÁvb wWwmwc-b
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