9 notes comp 9l) by Ayubحمزہ

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3.2

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3.6

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3.7

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3.10

Hamzahçm] ( 03234515251)

H -4E 5! ?ì Hyâ ‡»czg +Æ ê Gñ

3.11

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3.12

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3.13

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3.16

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ó Xó ÷C™¿~‚„q -ZgzZÜZc s Wwg ¯à Zzä™¿6,V,x ÓŠ ñ~”Ë ;wV

wg ¯ÅjgzZyizà Zzä™¿6, Lq Â -Z‰ ñ\ dÐ ~gze ;wV X ÷wg ¯ÜZca -ÑyZ

X ÷wg ¯ÜZca -Ñ¨-¤ /

:¯gzZug * N X2

û 2013eg1gƒÑü ~z)~g Zl wg ¯ÜZca -ÑyZ+ZzŠ L L

:ug * N

û 2013eg1gƒÑü

:¯

ó Xó ÷ë kg ¯s W4ñc* ug N* ÃW, ZÙŠ¤ / Ækg ¯Ë L L

ó ó÷C™Za ¯ÔVƒ:~íÑq -Zp ¯ = (F1xL1) + (F2xL2)

;Ññg Ã

ug N* =F x L

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:*_~r Z, k, 8x ª h‚à ©{z¤ /Zì @* ƒ~ª qÅ*_~r Zk , 8, x ªŸq -Z L L ó Xó ñYW~ci7«KZ:ZzÐ ähg™

ó Xó ì @* ƒ~ª qÅ*_~r ZwR, E KZt, Š hg™h‚ ZhðÃtXì ~ 7, 6,R|Zq -Ztq -ZÙ n Û ;wV

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Xì ~ª qÅ*_

Xì ~ª qÅ*_~r Zk , 8, x ªt:X ÏñYW

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H 4Ém,g » BgzZ AVâzŠ RIztXì Š ïH3E Hc* 3Š~^ā 6XA Ð ŠÆ~y WŠgzZÐ ‚Å¬‚ÅkZā{ Æ b§kZÃ RIz[ Z

XìIz û 2015eg1gƒÑü

?ì @* ƒ~*_~r Z“ ŸðÃ : 4.6

4Ém, 3H ó Xó ƒ#ïHE g »wg ¯x Óà Zzä™¿6, kZ¤ /Z Çƒ~ª qÅ*_~r ZŸðÃ L L

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H 4Ém, ó Xó ƒ#ïH3E g »wg ¯x Óà Zzä™¿6, kZ¤ /Z Çƒ~ª qÅ*_~r ZŸðÃ L L

WnÐêxg p-g ZŠ, 'MYq -Z :# sŸz oÑ«Å*_~r ZŸZ åE<XÅì Cƒ#kg ¯, MaÆkZèa F = 0 : a = 0 ªì @* Xì @* ™~g7

?ì @* ™~g7oÑ«Å*_~r ZŸðÃ¤ /Zì ]gz¢HÅoÑ~uzŠ Å*_~r Z : 4.8 Ÿq -Z~wVˆ~Šnā‰X C¯7D** ƒ~*_~r Z »ŸËoÑ«Å*_~r Z X ÷C™¿~íÑ„q -ZgzZ÷wg ¯ÜZca -Ñwg ¯VâzŠX ÷„g™¿ F2gzZ F1wg ¯zŠ6, X ðƒ~g7oÑ« a = 0 aÆy Z Z åE<XÅ ÷$ Ë ™ Za ug N* ~ŸtÂ( ì Š Hc* 3Š~b^ā 6) ñY~Š™sp(Åwg ¯VâzŠ¤ /Z Xì ~gz¢oÑ~uzŠ Z åE<XÅƒ~*_~r ZŸÑZzä™~g7oÑ«ā7~gz¢t: = 0 ª

?ì HoÑ~uzŠ Å*_~r Z : 4.9

:oÑ~uzŠ Å*_~r Z

4Ém, 3H ó Xó ƒ#ug N* ïHE g ÑZzä™¿6, kZ¤ /Z Çƒ~ª qÅ*_~r ZŸðÃ L L = 0

Ô, 6gî! ˆ

Xì ~ª qÅ*_~r Z ØŠwVÅŸuÃ, Z Ë

: 4.10

._ÆoÑ«Å*_~r Z Z åE<XÅì Cƒ#kg ¯, MaÆkZèa F = 0 : a = 0 ªì @* WnÐêxg p-g ZŠ, 'MYq -Z Xì @* ƒ~ª qÅ*_~r Zg ZŠ', MYZƒ@* WnÐêxg p-

Xƒ:~*_~r Zpƒ~ª qÅÆg ØŠwVÅŸ,Z : 4.11 wkg ¯Åyiz~uzŠÔ Š H²6, zZÃŸÐ TFkg ¯{zq -ZX ÷C™¿wg ¯zŠ6, kZ~]gßsàW Âì * @ Y ²+ $YÅ, 6zZ UŠÀÃŸËZ #

Ÿ6, ~—ð•ZXì ~ÆgaÆxq -ZŸ6, ~—ð•Z Z åE<XÅXì C™¿+ $YÅnwkg ¯Åyizpì CYƒ# Fkg ¯à Zzä™¿6, Xì @* ƒ7~ª qÅ*_~r ZŸÐzzÅÏŠ ñÅkg ¯Œpì @* YW û 2015eg1gƒÑü

?ƒ„g™¿kg ¯Œ6, kZ¤ /Z Yƒ7VY~ª qÅ*_~r ZŸðÃ : 4.12

Xì Cƒ7#kg ¯M ,6,Ÿ~ÏŠ ñÅkg ¯ŒèY Xì Yƒ7~ª qÅ*_~r ZŸðÃ~ÏŠ ñÅkg ¯Œ:Xì @* ™7~g7oÑ«Å*_~r ZŸZ åE<XÅ û 2013eg1gƒÑü

?ì CY¿gVY ÁJ -ueð™zZÅV-h Ç : 4.13

~h Ç„Ú Z Çƒ$ dÛŒÆ}i {Š c* i A¨-/ ¤s Wn W»ŸèYXì CY¿g ÁJ -ueð™zZÅV-h ÇaÆp pg6, R+ , F-¨- ¤ /s WW n Xì Lg Á„ Ú Z {ç»e cZÆ~h Çñƒ3»hñZ åE<XÅX Ïƒ~ª qÅ*_~r Z, k, 8x ª

XØŠwVÅq -ZC Ù ?ìŠ Z%HÐ*_~r ZwR, EgzZ *_~r Zk , 8, x ª)Ô *_~r Zk , 8, x ª : 4.14 ó Xó ñYW~ci7«KZ:ZzÐ ähg™h‚à ©{z¤ /Zì @* ƒ~ª qÅ*_~r Zk ,8, x ªŸq -Z L L :*_~r Z, k, 8x ª

Hamzahçm] ( 03234515251)

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:*_~r Zw, RE ó Xó ì @* ƒ~ª qÅ*_~r ZwR, E{zÂñYI~ci75C Ù 6, ähg™h‚à ©ŸðÃ¤ /Z L L wR, Et:X ÏñW76, ci7«:ZzgzZ ÏñYI6,ci75KZt, Š hg™h‚ ZhðÃtXì ~ 7, 6, R|Zq -Ztq -ZÙ n Û :w V Xì ~ª qÅ*_~r Z

05[ !*

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EI4H & ?ìŠ Z%HÐÐkg ¯ÿ5kG~-¤ /

EI4H " 5G ó Xó ì CBkg ¯ÿ5kG- ¤ /Ôì ms§KZÃŸ}uzŠŸC Ù Š ñ~] Ñ»ÐzzÅTkg ¯{zL L F =

5.2

EI4H & ;kg ¯ÿ5kG~- / ¤ :Ññg Ã

G m1 m 2 d2

?ì mÐkg ¯{Š c* iyÃ ?ì ¤Ã\W}i c* ÷qÃ}i\WH

5.3

Ô._Æyâ ‡ÆŸ~-¤ / ÆHE [¢ÿLuqÆw âÆyZ ì mÐ kg ¯+Zq -Z+ $YKZÃŸ}uzŠŸC Ù ~] Ñ» L L I I E E H½& ó Xó ì Cƒ ÿ5_g7z6, }gâ ZÆ,%Æ, ÃyxgŠÆœ /Z%ÆyZgzZ ÿ5_g7z6,öÐ5G],Z eÆ X ÷qÐ kg ¯Üq -ZÃ}uzŠq -Z}igzZë:

?ì CƒHkg ¯ì

5.4

ó Xó ì CBkg ¯ìì @* Î%ñƒµ6,Ÿ}uzŠŸq -Z kg ¯+Z L L :kg ¯ì EI4H & /Å~i ;wV Xì kg ¯ìq -Zkg ¯ÿ5kG~-¤

EI4H & ?VYXìgÜ‡ÐäÎ{ i Z0 +Z »kg ¯ÿ5kG~-¤ /yZ0‚*Š

5.5

EI4H " 5G ?ì kg ¯ìq -Zkg ¯ÿ5kG-¤ / ā÷M hÈ b§¾\W

5.6

EI4H & yZŠb‚*Šāìzz¸X YYH7kC ˜À&Xì CƒÁð•Zkg ¯ÿ5kG~-¤ /yxgŠÆx ZÆw â Lg¹Š ñŠ¤ / Šg Z}g ø EI4H & XìgÜ‡ÐäÎ{ i Z0 +Z »kg ¯ÿ5kG~-¤ / EI4H & Æ™¿6, kZ ì ¯ ) !* Ækg ¯ÿ5kG~-¤ /Å}itXì CY¬f(, êÅkZ6, 3Zz²ì CY¬CƒÁêÅŸ‰9s§Å6, zZ

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EI4H & :Ü‰¤Åìÿ5kG~- / ¤

EI4H EI4&H EI4H & & ó Xó ì CB‰ Ü ¤Åìÿ5kG~-¤ / Æ}i(kZkg ¯ÿ5kG~- ¤ /à Zzä™¿6, kâ . $-(Ë~ìÿ5kG~-¤ / Æ}i L L EI4H " 5G Ü ¤Åìÿ5kG- ¤ / 6,}i R ;7 Xì Cƒ 10Nkg-1 ‰

?ì ë ZVYa}gøyâ ‡»Ÿ~-¤ /

5.8

;÷M h™ÝqZ +Z ¯sfzgqëÐŠæÅyâ ‡ÆŸ~-¤ / H I E 4& X ÷M h™x¥kg ¯ÿ5kG~-¤ /àZzä™¿yxgŠÆx ZëÐŠæÅyâ ‡kZ ( 1 X ñƒ[ x»~ä™x¥kâ »}iëÐŠæÅyâ ‡kZ ( 2 45_¦¡gzZ CgŠ…yâ ‡t ( 3 5H G Xì @* ƒ" $U* yzç~KÃ×ñŠ¤ / Æ}iÅQÕäG

XÙ s # ŸzÅyâ ‡ÆŸ~-¤ / ÆHE

û 2013,14eg1gƒÑü

5.9

:yâ ‡»Ÿ~- / ¤ [¢ÿLuqÆw âÆyZ ì mÐ kg ¯+Zq -Z+ $YKZÃŸ}uzŠŸC Ù ~]Ñ» L L I I E E H& ó Xó ì Cƒ ÿ5_g7z6, }gâ ZÆ,%Æ, ÃyxgŠÆœ /Z%ÆyZgzZ ÿ5_g7z6,öÐ5½G], Z eÆ F =

:Ññg Ã

G m1m 2 d2

û 2013eg1gƒÑü

?ì YYHx¥b§¾kâ »}i

5.10

;ì YYHx¥Æ™wEZ Ññg ÃsfzgqÐŠæÅy â ‡ÆŸ~- ¤ /kâ »}i gR2 Me = G

& EI4&H cæÎh½GZ ÿ5kG~- ¤ /= g

Ô öi +g »}i = R

Ô kâ »}i = Me

?ì Cƒ]gz¢Åq¾Ã\WaÆä™x¥tÂV;¤ /Z ?÷M h™x¥kâ »0 +e\WH

5.11

;ì YYHx¥ÐŠæÅÑñg Ãsfzgqkâ »0 +e! V;Y Mm =

gm x (Rm)2 G

& ½& EI4H cæÎh GZ ÿ5kG~-¤ /»0 +e = gm

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;²

Hamzahçm] ( 03234515251) ?ì CƒVYZ6, V»Z7Å g GMe

gh =

5.12

;._Æá ñg Ã

(R + h)2

1 gh (R + h)2

Xì CYƒspÌ7Å ghÐ%$ +Æ h~—āìC Ùª

?ì Cƒspb§¾B‚Æ~—7Å g GMe

gh =

5.13

;._Æá ñg Ã

(R + h)2

b§ÏZXì CY{g ðåaq -Z7Å g6, ~—h +' × ', Z', Hq k -ZÆöi +gÆ}iÐ RÅ}iXì CYƒÁ7Å ghÐ "(, Æ h~— ~—h +' × ', Z', HzŠÆöi k +gÆ}iÐRÅ}i Xì CY{gzVZâ7Å g6, û 2013eg1gƒÑü

45_¦¡ 5.14 5H G ?÷HQÕäG

45_¦¡ 5H G :$ V äÕG

4]g Ñ" äVâ ZŠb‚ L L 5G4]¦¡7ZX ÷R˜Š¤ G ó Xó ÷ëQÕäH / Æ}i¼Ð~y ZX ÷Ç~ÜQÕä5H " I4»G 5E 45_á Zzt˜Š¤ G 5H X ÷DƒwEZaÆ èEjG ñQÕäG / Æ}iÐ ¹ ;]ÑEZ

45_yâ ‡»Ÿ~-¤ 5H G ?ì @* ™Šæ~g øb§¾~KÃ×ñÅQÕäG /»HE

5.15

45_Ë 5H G ?ì Cƒ«6, VzqÁ×ñŠ¤ / Æ}iÅV $ ÕäG

5.16

EI4H HF & 4&~ç~gz¢ÃV 4&~çaÆt˜Š¤ 45_¦¡Xì Cƒ]gz¢Åkg ¯ÿH F 45_C 5G G G 5H 5H kg ¯ÿ5kG~-¤ /à Zzä™¿6,yZkg ¯Ô ÿ5G $ ÕäG / Æ}iÃV $ ÕäG Ù 45_Z åE<XÅXì C™½ 5H G XìæWg » ð•Zy â ‡»Ÿ~- ¤ / aÆKÃ×ñÅV $ ÕäG vo

gh x r o

Ô._ÆÑñg Ã

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45_¦¡ 5H G ?÷D YÇVY~# $g W~eæV $ ÕäG

5.17

45_¦¡ G 5H ÷D YÇ~# $g W~eæV $ ÕäG X ñW:ËZ, 6ðÃ~−}ā @* " 5E 4»G jG 45_èEI 5H G X ÷D™å~V[ R 246q -Z CZŠ¤ / Æ}iQÕäG ñ ;s # Ÿz E " 5 4»G jG & ZKZ Ì}ièa 4G 5_èEI 5H QäÕG ñakZì C™å6q -Z~] 24Š¤ / ÆçEl½G

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6.2

:ugz ó Xó }™ð~‚Åkg ¯, Ã¼Ÿ{zgzZ}™¿kg ¯ðÃ6,ŸËZ # Çƒ~]gßkZugzL L

:Ññg Ã

W=F x S

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XÙs # Ÿz?ì C™ugz“ kg ¯

6.3

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?ì CƒVY]gz¢ÅY3, Z…

6.4

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Ôèa Xì Cƒ]gz¢ÅY3, ZaÆä™ugz… Z åE<XÅ

4G 5 ½$ 1E X Cx lZ ÅY3, Z ÿ¹G XÙp°ÅY3, Z

6.5

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4E &ð» 5G XÙ ~ .Z Ññg Ã»kZgzZÙp°ÅY3, Z ëH û 2014,15**eg1gƒÑü 4E &ð»Y3,Z àZzäYð0* 5G ó Xó ì CBY3, Z ëH ¯* ) !Æ×ñÅkZ~ŸË L L K.E. =

1 mv2

6.6

4E &ð» 5G : Y, 3Z ëH :Ññg Ã

IE " 457H 6.7 XÙ ~ .Z Ññg Ã»kZgzZÙp°ÅY3, Z ÿhG

û 2013**eg1gƒÑü

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û 2013eg1gƒÑü

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6.8

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Xì k 7¯ ) !* »ä™{Šß WÃwj ât /

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J 45½$ G 1E X ÷D™sp~Y3, Z ÿ¹G ÃY3, Zp¼Z Kx ** Æ çEl$Z-e õ0* ,Z

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6.11

6 ( 1)

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6.12

E 45_I ?ì * @Y1ÈHÐ ögG hZ ÅÄË

6.13

45½$ G 1E ªXì @* ™sp~Y3,Zu¼ZÃY3, Z ÿ¹G ì!W(Zq -Zñ¾u¼Z E 5½$ 14G ñ¾u¼Z Y3, Zp¼Z Y3, Z ÿ¹G û 2014eg1gƒÑü

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Y3,Z2 $yS À

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E 45_I ögG hZ = E 45_I ögGhZ % =

:Ññg Ã 6.14

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E 45_I ÔaÆ ögG hZ‚

?ìŠ Z%HÐgz0*6.15

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;÷˜V-~^! ˆÃgz0* :Ññg Ã

û 2014eg1gƒÑü

XÙp°Å^ Zz

6.16

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[!*

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7.3

: ªq¶aÅ{Š â Xì)i ö ª q¶aÅ{Š â 5ÅâgzZÅZ6,Z/h +”ð•Z L L D Yƒ`g {yz¼Z~ËÆî Z”y xgŠÆ²ðG3½G

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HE 4& ; ö-oGe

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7.4

a, -Y °x Z¤ / ³ (kgm-3)¢

H-oE 4& $- » ö Ge~SI .

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û 2015eg1gƒÑü

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= F/A

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7.8

Zƒ~g ‚Ð}g ½gzZì Ät6, %Åì»}g ½gzZì @* ƒ{Š c* fÐb6,uÉ é)H-#GZÆC Ù !* b6, äì CY~½Zƒc* ’Œ˜~}g ½ Xì @* ƒÂð•Z * *™ `g {ZƒÐ~kZÐzzÅTì @* ƒAb6, uÉ é)H-#GZ î !* Š » ZƒŠ ñ~L Þ 1²Xì CYƒ`g {

?ì @* ƒH¢ azÛ

7.9

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7.11

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7.13

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7.22

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8.3

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8.4

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8.5

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8.6

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8.7

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8.9

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9.7

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