Intermediate physics 1st paper

1. , , , , - , , , - / pdf Menu Bar View Auto /Automatically Scroll ( Ctrl + Shift + H ) up Arrow down Arrow 1. (Vector)2. (Linear-Motion)3. (Motion-In-Two-Dimensions)4. (Laws-Of-Motion)5. (Laws-Of-Angular-Motion)6. , (Work-Energy-And-Power)7. (Gravitation)8. (Simple-Harmonic-Oscillation)9. (Elasticity)10. (Fluid)11. (Heat-And-Gas)12. (Temperature)13. (First Law Of Thermodynamics)14. (Heat Radiation)15. (Change Of State)16. (Second Law Of Thermodynamics)17. (Waves & Sound)18. (Sound)19. (Speed Of Sound)Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

2. / , , , , , , , , , - , , , , , , / , , , , , , ,, , , , , , Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

3. fi ivwk (Vector Quantities):h mKj fZ ivwkK m~Yic cKvk Kivi Rb gvb I w`K Dfqi cqvRb nq ZvìK fi ivwk ej|hgb- miY, IRb, eM, ZiY, ej BZvw`|jvi ivwk (Scalar Quantities):h mKj fZ ivwkK ay gvb viv m~Yic cKvk Kiv hvq ZvìK jvi ivwk ej| hgb- `wZ, fi,KvR, `N BZvw`|jvi ivwk I fi ivwki ga cv_K (Distinction between Scalar and Vector Quantities):wgK jvi ivwk fi ivwk1|h mKj fZ ivwkK ay gvb viv m~YiccKvk Kiv hvq ZvìK jvi ivwk ej|h mKj fZ ivwkK m~Yic cKvk Kivi Rbgvb I w`K Dfqi cqvRb nq ZvìK fi ivwkej|2|`wZ, fi, KvR, `N BZvw` jvi ivwkiD`vniY|miY, IRb, eM, ZiY, ej BZvw` fi ivwkiD`vniY|3|Kgc GKwU ivwki gvb k~b bv nj bdjk~b nZ cvi bv|Kvb ivwki gvb k~b bv njI bdj k~b nZcvi|4| gvb AvQ wK w`K bvB| gvb I w`K AvQ|5|hvM, weqvM, b, I fvM ^vfvweK wbqg Kivhvq|hvM, weqvM, b, I fvM ^vfvweK wbqg Kiv hvqbv|6|`ywU Aw`K ivwki bdj me`v GKwU Aw`K ivwknq|`ywU w`K ivwki myweav RbK bdj GKwU w`K ivwkev GKwU Aw`K ivwk nq|GKK fi (Unit Vector):h fii gvb GK ZvK GKK fi ej| gvb k~b bq Ggb fiK Gi gvb viv fvM Kij H w`K ivwkwUi w`KGKwU GKK fi cvIqv hvq| gb Kwi AGKwU fi ivwk; 0A A Gi w`K GKK fi aAA (awi)mxgve fi (Restricted Vector):h fii Avw` we`y Kv_vq _vK Zv wi _vK ZvK mxgve fi ej| O we`yZPej OB iLv eivei wqv Ki eySvj fi Pmxgve fi hvi cv` we`y O |mgvb fi (Equal Vector):GKB w`K wqviZ `ywU mgRvZxq fii gvb mgvb nj ZvìK mgfiev mgvb fi ej| wP PI Qmgvb fi|k~b ev bvj fi (Zero or Null Vector):h fii gvb k~b ZvK k~b ev bvj fi ej| bvj fii Avw` I kl we`y GKB we`yZ AewZ|Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

4. 01| fi (Vector) 2m`k fi ev mgvivj fi (Like Vector):mgRvZxq `yB ev ZZvwaK fi hw` GKB w`K wqv Ki Ze ZvìK m`k fi ev mgvivjfi ej| wP AI Bm`k fi ev mgvivj fi|wem`k fi (Unlike Vector):mgRvZxq `yB ev ZZvwaK fi hw` wecixZ w`K wqv Ki Ze ZvìK wem`k fi ej|wP AI Bwem`k fi|mgiL fi (Co-linear Vector):`yB ev ZZvwaK fi hw` GKB mijiLv eivei ev cii mgvivj wqvKi Ze ZvìK mgiL fi ej| wP A,B,CmgiL fi|Aevb fi (Position Vector):cm KvVvgvi g~j we`yi mvc Ab Kvb we`yi Aevb wbYqi Rb h fi eenviKiv nq ZvK Aevb fi ej|evLv t wP O nQ cmsM KvVvgvi g~j we`y Ges h P Kvb GKwU we`y|OP fiwU O we`yi mvc P we`yi Aevb wb`k KiQ| ZvBOP GKwU Aevb fi|Aevb fiK AbK mgq evmva fi rviv cKvk Kiv nq| rOPAvqZGKK fi (Rectangular Unit Vector):wgvwK vbv eevq cii j^ wZbwU A _vK| h_v t X,Y Ges Z A| X Ai w`Kwewfb fiK cKvk Kivi Rb GKwU GKK fi i eenvi Kiv nq| Zgwb j I k h_vgY I Z Ai w`K GKK fi (Wvb cvki wP)| i , j Ges k K AvqZGKK fi ej|evmva fi (Radius Vector): AbK mgq Kvb we`yi AevbK h fii mvnvh cKvkKiv nq ZvK evmva fir ej| myZivs Kvb we`y P-Gi vbvsK (x,y,z) nj, evmvafi kzjyixOPrviv cKvk Kiv nq| Ges Gi gvb nq 222zyxrr fi ivwki mvgvwiK m~ (Law of Parallelogram) eYbv I evLv :eYbv: Kvb KYvi Dci GKB mgq wqvkxj `ywU fi ivwkK hw` Kvb GK we`y _K AswKZ mvgvwiKi `ywUmwbwnZ ev viv wb`k Kiv hvq Ze H we`y _K AswKZ mvgvwiKi KYB fi `ywUi jwi gvb I w`K wb`k Ki|gbKwi GKwU KYvi Dci GKB mgq `ywU w`Kivwk P I Q, KvY wqv KiQ| OA Ges OC iLv `ywUh_vg P I Q gvb Ges Zxi wP Gì w`K wb`k KiQ| GLvb AOC | GB `ywU w`K ivwki jwi gvb I w`KwbYq KiZ ne|AsKb : mvgvwiK OABC AsKb Ki Kb OB hy Kwi| Zvnj OB KbB w`Kivwk `ywUi gvb I w`K wb`kKie| gb Kwi jwi gvb R Ges KvY GKwU myKvY| GLb B we`y _K OA Gi ewaZ Aski Dci BN j^ Uvwb|Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

5. 01| fi (Vector) 3jwi gvb wbYqt AB I OC mgvivj| AOC | OBN wfyRi ONB GK mgKvb| OB2= ON2+ BN22OB =(OA+AN)2+BN22OB = OA2+2OA .AN +AN2+BN22OB = OA2+(AN2+BN2) +2OA .AN2OB = OA2+AB2+2OA.ABAN.AB2OB = OA2+OC2+2OA.OC Cos R2= P2+Q2+2PQ Cos(1).........PQCos2QPR 22jwi w`K wbYq: gbKwi jw R, P Gi mv_ Kvb Drcb Ki| A_vr AOB OBN mgKvYx wfyRONBNtan ANOABN tanABANABOAABBNABtanQCosPQSintan(2).........QCosPQSintan 1 (1) bs mgxKiY jwi gvb I (2) bs mgxKiY jwi w`K wb`k Ki|GKB mgq GKB we`yZ wqviZ `ywU w`Kivwki jwi mevP I mewb gvb ivwk `ywUi hvMdj I weqvM dji mgvb tP I Q, KvY wqv Kij mvgvwiKi m~vbyhvqx Avgiv cvB,(1).........PQCos2QPR 22 R2= P2+Q2+2PQ Cos R2 P2Q2= 2PQ CosPQ2QPRCos222 Avevi Avgiv Rvwb, CosGi gvb1 _K +1 Gi ga mxgve| A_vr, 1Cos1 1PQ2QPR1222 [CosGi gvb ewmq]PQ2QPRPQ2 222PQ2QPRPQ2QP 22222 [Dfq c P2+Q2hvM Ki]222)Q~P(R)QP( )Q~P(R)QP( KvRB GKB mgq GKB we`yZ wqviZ `ywU w`K ivwki jwi mevP I mewb gvbivwk `ywUi hvMdj I weqvM dji mgvb| Ab fveI ejv hvq, GKB mgq GKB we`yZ wqviZ `ywU w`K ivwki jwimevP gvb ivwk `ywUi hvMdj nZ eo nZ cvi bv I mewb gvb ivwk `ywUi weqvM dj _K QvU nZ cvi bv|Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

6. 01| fi (Vector) 4`ywU fi ivwk P I Q cii KvY AvY&Z| Gì jvi Yb I fi Yb tjvi Yb ev WU Yb t `ywU w`K ivwki jvi Yb GKwU Aw`K ivwk Ges Gi gvb w`Kivwk `ywUi gvbiYdj Ges Gì gaeZx KvYi Cosine Gi Y dji mgvb ne|evLvt gb Kwi, PI Q`ywU w`K ivwk cii KvY AvbZ& A_vr P I Q Gi gaeZx KvY | Gì WUYb A_vr jvi Yb PQCosQ.PwPvbyhvqx, ;OAP ;OBQ BM, OA Gi Dci j^ I AN, OBGi Dci j^ | myZivs OM =OB Cos ev, OM =Q Cos )QCos(PQ.P = (PGi gvb) (OM)= (PGi gvb) ( PGi DciQGi j^ Awfci gvb)Abyicfve, )(. PCosQQPCosPQ = (QGi gvb) (QGi DciPGi j^ Awfci gvb) A_vr `ywU fiivwki jvi A_vr WU Ydj ejZ Gì h Kvb GKwU fi ivwk viv Dnviw`K Aci fi ivwkwUi AwfciYdj evSvq|(K) hw` fi ivwkq cii mgKvb AvbZ& _vK Ze 090CosPQQ.P AZGe `ywU fiivwk mgKvY AvbZ&_vKj Gì jvi bdj k~b ne wecixZg `ywU fi ivwki jvi bdj k~b nj ivwk `ywU ciii Dci j^ne|awi wZbwU AvqZKvi fi ivwk j,i I k cZK ciii Dci j^|myZivs Gì h Kvb `ywUi jvi bdj k~b ne| A_vr 0... ikkjji(L) hw` `ywU fi ivwk GKB w`K wqv Ki Ze Gì gaeZx KvY = 0;m PQCosPQQP 0.ne| GKK w`K ivwki cvB, 1... kkjjii(M) hw`PIQ`ywU fi ivwk cii wecixZgyLx nq Ze Gì gaeZx KvY = 180nq Ze m PQCosPQQP 180.ne|fi Yb ev m Yb t `ywU w`K ivwki fi (m) Yb GKwU fi ivwk hvi gvb w`Kivwk `ywUi gvbi Ydj GesGì gaeZx KvYi Sine -Gi Y dji mgvb Ges GB bdj ivwk `ywUi Zj j^fve vwcZ GKwU Wvb cvKi KKzK 1g fi ivwk _K 2q fi ivwki w`K z`Zi KvY Nyivj GUv h w`K AMmi nq mB w`K wqv Ki|evLvt gb Kwi, PI Q`ywU w`K ivwk cii KvY AvbZ& A_vr P I Q Gi gaeZx KvY | Gì mYb A_vr fi Yb PQSinQP GLvb GKwU GKK w`K ivwk hv )( QP Gi jwi w`K wb`k Ki|hw` RQP aiv nq Ze R Gi AwfgyL PI QGi mgZji mv_ Awfj^ eivei ne| PQSinQPR( P Gi gvb) ( P Gi j^ eivei Q Gi gvb )Avevi, )(QPSinPQ QPSinPQPQ ( Q Gi gvb) ( Q Gi j^ eivei P Gi gvb )PQQP A_vr fi Yb wewbgq m~ gb Pj bv|Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

7. 01| fi (Vector) 5Avgiv Rvwb, Wvb cvKi KK zK evgw`K Nyivj GwU Dcii w`K Lyj Avm Avi Wvb w`K Nyivj wbPi w`K AMminq, Z`c PI QGi fi Yb evgveZx nj Gì jw RGi AwfgyL Da w`K nq Ges PI QGi fi Yb`wbveZx nj Gì jw RGi AwfgyL wbgyLx ne hv c~ei AwfgyLi Dv w`K ne|Dciv eYbv Abymvi,1) = 0 nj 0QP ne KviY Sin 0 = 02) QP|| nj 0QP ne KviY Sin 0 = 03) QP nj PQQP ne KviY Sin 90 = 14) j,i I k mgKvY wqv Kij jik,ikj,kji I j,i I k mgvivj wqv Kij 0kkjjii jvi Yb wewbgq m~ gb Pj wK fi Yb wewbgq m~ gb Pj bv:gb Kwi `ywU fi PI Q, KvY AvbZ& (1).........PQCosQ.P Avevi, QPCosP.Q(2).........PQCosP.Q (1) I (2) nZ cvB, P.QQ.P A_vr jvi Yb wewbgq m~ gb Pj| Acic, )QP( I )PQ( Gi gvb GKBnjI Gì w`K wecixZ A_vr (3).........SinPQQP Avevi, )(SinPQPQ (4).........SinPQPQ (3) I (4) nZ cvB, )PQ()QP(PQQP A_vr fi Yb wewbgq m~ gb Pj bv|fi hvMi wfyR m~ (Triangle Law) t`ywU fiK GKwU wfyRi `ywU mwbwnZ ev viv GKB g w`K I gvb wb`kKij wfyRwUi ZZxq ev wecixZ g w`K I gvb Dnvì jw wb`k Ki|evLv t awi PI QGKB RvZxq `ywU fi| ABC wfyRi AB Ges BCev h_vg fi PI Qwb`k Ki| m~vbymvi, BCABACQPR [ RACb,GLv ]Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

8. 01| fi (Vector) 6fii hvMi wewbgq m~ (Commutative Law) t ABBAcgvb t aiv hvK AOP Ges BOR `ywU fi O we`yZ wqv Ki OPQRmvgvwiK c~Y Ki wfyR m~vbymvi cvB,(1)............OQPQOPGes (2)............OQRQOR(1) I (2) _K cvB, RQORPQOPA_vr, ABBA myZvivs fi hvM wewbgq m~ gb Pj|fii hvMi mshvM m~ (Associative Law) : )CB(AC)BA(cgvb t aiv hvK AOP , BPQ Ges CQR | GLb OQ, PR Ges OR aiwf~R m~vbymvi cvB, )BA(OQPQOPGes )CB(PRQRPQGLb ORQROQ A_vr DC)BA(Avevi, ORPROP A_vr D)CB(A)CB(AC)BA( myZvivs fi hvM mshvM m~ gb Pj|eUb m~: C.AB.A)CB.(A Gi cgvY:cgvY: gb Kwi,CB,A I fi wZbwU h_vg OP,OQI QR viv m~wPZ Kiv nqQ| GLb wP _K AvgivcvB, )QROQ(.A)CB.(A OR.A)CB.(AcAwf^jGiDciGi OROPA)CB.(AONA)CB.(A )MNOM(A)CB.(A Figure 1MNAOMA)CB.(A cAwf^jGiDciGicAwf^jGiDciGi QROPAOQOPA)CB.(A QR.AOQ.A)CB.(A C.AB.A)CB.(A (cgvwYZ)Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

9. 01| fi (Vector) 7wgvwK vbv eevvq GKwU Aevb fii gvb wbYq:A_vr 222zyxr Gi cgvY :wgvwK vbv eevq cii wZbwU iLv OX, OY I OZ h_vg X, Y IZ, A wb`k Ki Ges i, jI kA wZbwU eivei GKK fi| rGKwU Aevb fi| awi, OPrGes P we`yivbv (x,y,z)| XZ Zji Dci PN Ges N we`y nZ X I Z Ai Dci h_vg NA I NB j^ AvuwK|wP nZ, BN =OA= x, AN=OB = z Ges NP = ywfyR m~ Abymvi, NPONOP NPBNOBOP OBNPBNOPkzjyixr Avevi, OPN wfyR nZ, OP2=ON2+NP2 OP2= OB2+BN2+NP2 OP2= BN2+ NP2+OB22222zyxr )(222cgvwYZzyxr zzyyxx BABABAB.A Gi cgvY:awi, kAjAiAA zyx I kBjBiBB zyx dj, )kBjBi) . ( BkAjAi(AB.A zyxzyx )k.k(BA)j.k(BA)i.k(BA)k.j(BA)j.j(BA)i.j(BA)k.i(BA)j.i(BA)i.i(BAB.Azzyzxzzyyyxyzxyxxx)1(BA)0(BA)0(BA)0(BA)1(BA)0(BA)0(BA)0(BA)1(BAB.A zzyzxzzyyyxyzxyxxx zzyyxx BA000BA000BAB.A oved)Pr(BABABAB.A zzyyxx kAjAiAA zyx I kBjBiBB zyx njWant more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

10. 01| fi (Vector) 8BA wbYq :)kBjBi(B)kAjAi(ABA zyxzyx )kk(BA)jk(BA)ik(BA)kj(BA)jj(BA)ij(BA)ki(BA)ji(BA)ii(BABAzzyzxzzyyyxyzxyxxx0)i(BA)j(BA)i(BA0)k(BA)j(BA)k(BA0BA yzxzzyxyzxyx )k(BA)k(BA)j(BA)j(BA)i(BA)i(BABA xyyxzxxzyzzy k)BAB(Aj)BAB(Ai)BAB(ABA xyyxzxxzyzzy zyxzyxBBBAAAkjiBA (Ans.)fi wefvRb ev fi weklb (Resolution Of Vectors) tGKwU fi ivwkK `yB ev ZZvwaK fi ivwkZ wef Kivi cwZK fii wefvRb ev fii weklb ej|gbKwi, wP OC iLv RfiwUi gvb I w`K wb`k Ki| GLb RfiwUK Ggb `ywU Ask wef KiZ ne h, Gjv OC Gi mv_ h_vg I KvY Drcb Ki| GLb O we`y _K OC iLvi mv_ Gi `yB cvk I KvY Ki OB I OA iLv Uvbv nj| OACB mvgvwiKwU c~Y Kiv nj mvgvwiKim~vbymvi OA Ges OB ev `ywU Rfii `ywU Dcvsk wb`k Kie|gbKwi, wefvwRZ Dcvsk XOA Ges YOB |(K) wP, OCABOC Ges -180OAC GLb OAC wfyR weePbv Ki Avgiv cvB,)](180[SinOCSinACSinOAY)OBAC()(SinRSinYSinX )(SinRSinX Ges)(SinRSinY R fiK hw` mgKvY wefvwRZ Kiv hvq [wP (L)] A_vrDcvsk `ywU hw` cii j^ nq Ze Zvnj,+90 Sin+Sin 90 = 1X = R SinGesY = R Sin hnZz +90 90Sin Sin () = Cos dj, X = R Cos GesY = R SinWant more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

11. c_g ci AsKi mgvavbFirst Paper Math Solution1| fi (Vector)1| fi1| hw` k2ji3A I kj3i2B nq Ze |BA|KZ?132213kjiBA k11j7i5)29(k)43(j)61(i Ans.)96.13121492511)7(5|BA| 222(2| hw` k2j3i6A I kj2i2B nq ZeKZ?B.Azzyyxx BABABAB.A )(Ans.82612)1)(2()2)(3()2)(6( 3| k3-j2i5A I |k9-jai15B a Gi gvb KZnj AI Bcii mgvivj ne?AI Bcii mgvivj ne hw` 0BA nq|9-a15325kjiBA )30a-5(k)4545(-ja)318(iBA )30a5(k)18a3(iBA 2)30a5(2)18a3(BA ckgZ, AI Bcii mgvivj nj 0BA 0)30a5()18a3( 22i]KMeKc[Dfq 0)30a5()18a3( 220)6(a5)6(a3 22220)53()6(a 222iKfvMvivKcDfq )53(0)6(a 222.)Ans(6a 4| k5-j3i2A I |k10-j2imB m Gigvb KZ nj AI Bcii j^ ne|AI Bcii j^ nj 0B.A ne|0 zBzAyByAxBxAB.A0506m2)10)(5()2)(3()m)(2( (Ans.)28-m256-m 5| kj2i2A I k2j3i6B nj BAIGi gaeZx KvY wbYq Ki| cosABB.ABAI Gi gaeZx KvY,BAB.ACos 142-6-12)2)(1(-)3)(-2()6)(2(BABABABA zzyyxx.39)1(22A 22274949362)3(6B 222(Ans.)02.79214Cos)7)(3(4CosBAB.ACos 11-1 6. fi k2j3i6B Gi Dci fikj2i2A Gi j^ Awfc wbYq Ki| cosABB.AA Gi j^ Awfc,BB.AcosA 826-12)2)(1()3)(-2()6)(2(BABABAB.A zzyyxx74949362)3(6B 222A Gi j^ Awfc =78BB.A7| k3j2iB,kj2i3A I k2jiC nj cgvY Ki h, C).BA()CB.(A211321kjiCB k-j5-i7)2-1(k)32(j)34(iCB ev,Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

12. 1| fi (Vector) 21011021)1)(-1()5)(-2()7)(3()CB. (AL.H.S3-21123kjiBA GLb,k4j10i8)2-6(k)19(j)26(i=BAev,108108-)2)(4()1)(10()1)(8(-C) .BA(R.H.SR.H.SL. H. S A_vr, oved.)Pr(C).BA()CB.(A8| ,k2j3iA kj2iB I k4j3i2C nj cgvY Ki h, ACABA)CB(k3ji3k)41(j)32(i)21()CB( 231313kjiA)CB(L.H.S k10j3i11)19(k)36(j)92(i 231121kjiAB Avevi,kj3i7)2-3(k)12(j)34(i 231432kjiAC k9i18)36(k)4-4(j)126(i k10j3i11kj3i7ACABR.H.S k9i18 A_vr, oved.)Pr(ACABA)CB(9| k6-ji9A Ges k5j6i4B fi `ywUiMybdj wbYq Ki `LvI h, Giv ciii Dci j^|zzyyxx BABABAB.A 030636)5)(6()6)(1()4)(9( 0ABCosB.A 0CosC0, B0A wK9090CosCos , evAZGe AI ciii Dcii j^|10| hw` kAjAiAA zyx I kBjBiBB zyx nqZe `LvI h, zzyyxx BABABAB.A )kBjBi) . ( BkAjAi(AB.A zyxzyx )k.k(BA)j.k(BA)i.k(BA)k.j(BA)j.j(BA)i.j(BA)k.i(BA)j.i(BA)i.i(BAB.Azzyzxzzyyyxyzxyxxx)1(BA)0(BA)0(BA)0(BA)1(BA)0(BA)0(BA)0(BA)1(BAB.Azzyzxzzyyyxyzxyxxxzzyyxx BA000BA000BAB.A oved)Pr(BABABAB.A zzyyxx 11| hw` k5j4i2A I k3j2iB fi qi jwfii mgvivj GKK fi wbYq Ki|k3j2ik5j4i2BAR k2j6i3R R Gi mgvivj GKK fiRRa 7494369)2(63R 222(Ans.)k72j76i737k2j6i3RRa 12| GKB we`yZ wqvkxj `ywU mgvb gvbi fii gaeZx KvY KZnj G`i jwi gvb h Kvb GKwU fii mgvb ne?R2=P2+Q2+2PQCosev, X2= X2+X2+2X.X.Cosev, X2- X2-X2=2X2Cosev, -X2=2X2Cos22X2XCos, ev 21Cos, ev 21Cos, 1ev (Ans.)120GLvb,awi, fi, P=Q=Xjw, R= XAf~ KvY, Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

13. 1| fi (Vector) 313| Aevb fi kzjyixr K eeKjb KiwKfve eM I ZiY cvIqv hvq?Avgiv Rvwb,eM,dtrdv)kzjyi(xdtd(Ans.)kdtdzjdtdyidtdxAvevi, ZiY kdtdzjdtdyidtdxdtddtvda(Ans.)kdtzdjdtydidtxd22222214| k)1t2(jtitP 2I ktjtit5Q 3?)Q.P(dtd?)QP(dtd)t)(1t2()t)(t()t5)(t(Q.P 323423tt2tt5Q.P 234tt4t2Q.P )tt4t2(dtd)Q.P(dtd 234t2t12t8)Q.P(dtd 2332ttt51t2ttkjiQP)t5t(k)tt5t10(j)tt2t(iQP235224235224t5t(k)tt5t10(j)tt2t(idtd)QP(dtd k)t5t(dtdj)t5t10t(dtdi)tt2t(dtd)QP(dtd232524(Ans.)k)t10t3(j)5t20t5(i)1t4t4()QP(dtd24315| k3j2-iQ,k4j3i2P fi q h ZjAevb Ki Zvi Dj^w`K GKwU GKK fi wbYq Ki|Avgiv Rvwb,`ywU fii m bdj fi `ywU viv MwVZ mgZji Dci j^ nq| mBj^ fii mgvivj GKK fiB ne mgZji Dj^ w`K GKKfi| awi, mB fi a ,QPQPa )34(k)46(j)89(i321432kjiQP k7j10iQP PI Qh Zj AewZ Zvi Dj^ w`K fi222)7()10()1()k7j10i(QP)QP(a .)(150)k7j10i(a Ans16| Kvb GKwU KYvi Aevb fij][5.3msi4.2m])t[(3.5msr 11 njeM V wbYq Ki|Avgiv Rvwb,dtrdV jt][5.3msi4.2m])t[(3.5msdtdV 11 j5.3i3.5V (Ans.)17| cgvY Ki t 2222BAB.ABA 22.BABALHS 22cossin ABAB 2222222cosBAsinBA 222222cosBAsinBA.1 2222cossinBA22221. BABA (Proved).... SHRSHL 18| kj2iP Ges k3j6i3Q nj `LvI h, PIQcii mgvivj|PI Qcii mgvivj ne hw` 0QP nq|)66(k)33(j)66(i363121kjiQP 0000)0(k)0(j)0(iQP Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

14. 1| fi (Vector) 40 QP0 QP PI Qcii mgvivj|(cgvwYZ)19| k4j3i2P Ges k3ji2Q fi q hZj AewZ Zvi Dj^w`K GKwU GKK fi wbYq Ki|Avgiv Rvwb,`ywU fii m bdj fi `ywU viv MwVZ mgZji Dci j^nq| mB j^ fii mgvivj GKK fiB ne mgZji Dj^w`K GKK fi| awi, mB fi n ,QPQPn )62(k)86(j)49(i312432kjiQP k8j2i13QP Avevi, 2228213QP 237QP 2378213kjiQPQPn .)(2378237223713 Ansjin 20| kj4i4P Ges kj2i2Q fiqGKwU mgvwiKi `ywU mwbwnZ ev wb`k Kij Gi dj wbYqKi|Avgiv Rvwb, `ywU fi GKwU mgvwiKi `ywU mwbwnZ ev wb`kKij H mgvwiKi dj ne fi `ywUi m Ydji gvbimgvb| QPmgvwiKi dj|GLb,)88(k)24(j)24(i122144kjiQP j6i6QP 49.87266 22 QPGKK (Ans.)21| k3-jmi2P I |k15-j5i10Q m Gi gvb KZ njPIQcii mgvivj ne?PI Qcii mgvivj ne hw` 0QP nq|15-5103m2kjiQPm)10-10(k)3030(-j)15m15(iQP m)1010(k)15m15(iQP 2m)1010(2)15m15(QP ckgZ, PIQcii mgvivj nj, 0QP 02m)1010(2)15m15( i]KMeKc[Dfq 0m)1010()15m15( 220)1(m10)1(m215 2220)1015()1(m 222iKfvMvivKcDfq )1015(0)1(m 222.)Ans(1m 22| kjiA 22 Ges kjiB 236 `ywU fi ivwk|G`i j^ AwfgyL GKwU GKK fi wbYq Ki|Avgiv Rvwb,`ywU fii m bdj fi `ywU viv MwVZ mgZji Dci j^ nq| mBj^ fii mgvivj GKK fiB ne mgZji Dj^ w`K GKKfi| awi, mB fi n ,QPQPn )126()64()34(236122 kjikjiQPkjiQP 1810 Avevi, )18()10(1 222QP425 QP4251810kjiQPQPn (Ans.)Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

15. , - - , : : () () : () () (i) - (ii) - , (iii) . . , ,. , . , , , . , Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

16. MoeM (Average Velocity) :msv: h Kvb mgq eeavb Kvb ei Mo cwZ GKK mgq h miY nq ZvK ewUi Mo eM ej|eLv: t mgq eeavb Kvb ei miY r nj Mo eMtrvne|eM (Velocity):msv: mgq eeavb k~bi KvQvKvwQ nj mgqi mv_ ei miYi nviK eM ej|eLv: t mgq eeavb Kvb ei miY r nj eMtrlimv0t wKtrnQ Mo eM v| myZivs vlimv0tA_vr mgq eeavb k~bi KvQvKvwQ nj Mo eMi mxgvwK gvbKB eM ej|mgeM ev mylg eM (Uniform Velocity) :hw` Kvb ei MwZKvj Zvi eMi gvb I w`K AcwiewZZ _vK Zvnj mB ei eMK mgeM ej| A_vr Kvb ehw` wbw` w`K mgvb mgq mgvb c_ AwZg Ki Zvnj eieMK mgeM ej| ki eM, Avjvi eM, cfwZ mgeMi cKcvKwZK D`vniY|AmgeM (Variable Velocity) tKvb ei MwZKvj hw` Zvi eMi gvb ev w`K ev DfqB cwiewZZ nq Zvnj mB eMK AmgeM ej| AvgivmPvivPi h MwZkxj e `wL Zv`i eM AmgeM|ZvrwbK eM (Instantaneus Velocity) :GKwU e mij ev e c_ AmgeM Pjj cwZwbqZ Gi eMi cwieZb nq| Gfve AmgeM Pj Kvb ei hKvb gyZi eMK H ei ZvrwbK eM ej| ZvrwbK eMi w`K ewUi H gyZi Aevb AswKZ MwZc_ikK eivei|ZiY (Acceleration) :mgqi mv_ eM ewi nviK ZiY ej| t mgq eeavb ei eMi cwieZb v nj ZiYtva ne| Abfveejv hvq mgq eeavb k~bi KvQvKvwQ nj mgqi mv_ ei eM ewi nviK ZiY ej| t mgq eeavb ei eMicwieZb v nj ZiYtvlim0t a ne|mgZiY ev mylg ZiY (Uniform Acceleration) :GKB w`K GKB mgq eeavb eMi ewi nvi mgvb nj ZvK mgZiY ev mylg ZiY ej| AwfKli Uvb gyfveco ei eM ewi nviK AwfKlR ZiY ej| AwfKlR ZiY, mgZiY wewk MwZi GKwU cK D`vniY| mgZiY,ZiYi gvb I w`K mgqi mv_ AcwiewZZ _vK| mgZiY MwZkxj eZ mgej wqvKi ei cici mKieMiWant more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

18. 02| iwLK MwZ (Linear Motion) 3 t0xxvvx dtdvxxoeKaaa toxvvx tvxx0a 0tvv xxox atvv xxox a mgxKiYwU cwZcv`b Kiv nj|(L) t)vv(21xx xxoo cwZcv`b:gbKwi, X A eivei GKwU e mylg ZiY MwZkxj| Aviv awi, GB MwZi cviwK kZvw` nj mgq Mbbvi iZA_vr hLb t = 0 ZLb Avw` Aevb x = x0 Ges Avw`eM vx = vxo | Aviv awi, t mgq ci ewUi Aevb x Ges GeskleM vx | MoeMi msv nZ Avgiv Rvwb, z`vwZz` mgq eeavb eM I mgq eeavbi bdji mgw wbqZvK gvU mgq w`q fvM Kij H mgqi MoeM ej| myZivs KYvwUi t mgq ci MoeM xv nj,dtvtvt0xx 1dtdxxvdtdtdxt1vt0x (1)............tvxx xo mymg ZiY Pjgvb ewUi eM xv mgqi mv_ mymgfve cwiewZZ nq ej h Kvb mgq eeavb Zvi Mo gvb Hmgq eeavbi i I kli eMi gvbqi mgwi AaK| A_vr xxxox v),vv(21v Gi GB gvb (1) bsmgxKiY ewmq cvB, t)vv(21xx xxoo t)vv(21xx xxoo mgxKiYwU cwZcv`b Kiv nj|(M) 2xxoo21tatvxx cwZcv`b:gbKwi, X A eivei GKwU e ax mylg ZiY MwZkxj| Aviv awi, GB MwZi cviwK kZvw` nj mgq Mbbvi iZA_vr hLb t = 0 ZLb Avw` Aevb x = xo Ges Avw`eM vx = vxo | Aviv awi, t mgq ci ewUi Aevb x = x GesGes eM vx = vx| hnZz h Kvb gyn~Zi mgqi mvc Kvb KYvi eM ewi nviK ZiY ej|myZivs,dtdva xx dtadv xx hLb t = 0 ZLb vx = vxo Ges x = xo Avevi, hLb t = t ZLb vx = vx Ges x = x GBmxgvi ga mgxKiYK mgvKjb Ki cvB, t0xxxxoeKaadtadvvvx tovv tav xxo xx 0xxox tavv(1)...............xxox tavv h Kvb gyZ ei miY ewi nviK eM ej| D(1) mgxKiYdtdxv x ewmq cvB, tavdtdxxxo Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

19. 02| iwLK MwZ (Linear Motion) 4xxo dttadtvdx tot dtxatodtxovxxodx tatvxtoxtoxoxxo 22 0210 2 tatvxx xxoo221tatvxx xxoo mgxKiYwU cwZcv`b Kiv nj|ev,221tatvxx xxoo 221tatvS xxo mgxKiYwUI cwZcv`b Kiv nj| wiAevb _K mgZiY Pjgvb ei , 0xov Ges eKaxa ,dj2210 tS eKa 2tS eKa2tS KvRB, wi Aevb _K mgZiY Pjgvb ei AwZv `yiZ mgqi eMi mgvbycvwZK|(N) )xx(2vv ox2xo2x a cwZcv`b :awi, GKwU e X A eivei ax mylg ZiY MwZkxj| GB MwZi cviwK kZvw` nj hLb mgq Mbbvi iZ hLb t = 0ZLb Avw` Aevb x = xo Ges Avw`eM vx = vxo Avevi, t mgq ci KYvwUi Aevb x Ges eM vx | hnZz h Kvbgyn~Z mgqi mvc ei eM ewi nviK ZiY ej|myZivsdtdvxx aiYZdtdxxddvxx a xxxx vdtdxvxddvadxdvv xxx ahLb x = xo ZLb vx = vxo Ges hLb x = x ZLb vx = vx GB mxgvi ga Dciv mgxKiYK mgvKjb Ki cvB, xxxvvxxoxoxdxdvv a xxxovv2xx2vxxoa)xx(2vvox2xo2x a)xx(2vv ox2xo2x a mgxKiYwU cwZcv`b Kiv nj|Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

20. 02| iwLK MwZ (Linear Motion) 5(O) )1t2(a21vs ot ev, a2)1t2(vs ot cwZcv`b :gbKwi, vo Avw`eM Ges a mgZiY AB mijiLv eivei Pjgvb KYvwUi Avw` Aevb A we`yZ| (t-1) mK Ges tmK hw` Gi Aevb h_vg C I B we`yZ nq Ze t Zg mK e KYvwU BC `~iZ AwZg Kie| MwZim~vbyhvqx t mK e KZK AwZv `~iZ AB(1)...............at21tvAB 20 (t-1) mK e KZK AwZv `~iZ AC(2)...............)1t(a21)1t(vAC 20 KvRB t Zg mK e KZK AwZv `yiZ st njst = CBACABst )1t(a21)1t(vat21tvs 2020t)1t(a21)1t(vat21tvs 2020t )1t2t(a21vtvat21tvs 20020t a21atat21vtvat21tvs 20020t a21atvs 0t a21atvs 0t )1t2(a21vs ot ev, a2)1t2(vs ot mgxKiYwU cwZcv`b Kiv nj|Lvov Dcii w`K wbw ei mevwaK DPZv wbYq :gbKwi, Kvb GKwU eK Lvov Dcii w`K v0 eM Qvov nj| G ei Dci wqviZ ZiY = g, KviY gcw_exi K`vwfgyLx| KvRB h DPZvq v MwZeM ARb Kij MwZi mgxKiY _K Avgiv cvB, gH2vv 2o2 KvRBewU Da DVZ _vKj Gi kl eMi gvb gkt KgZ _vKe| KvRB h we`yZ wbw ei eM k~b H we`yBei MwZ c_i mevP we`y wb`k Ki| myZivs h we`yZ ei kl eM k~b, mB we`yi DPZv H nj ,gH2v0 2o2g2vH2o KvRB Lvov Dcii w`K wbw ei g2v2o-B nj e KZK AwZv mevPDPZv|Lvov Dcii w`K wbw ei mevwaK DPZvq cQZ mgq wbYq :gbKwi, Kvb GKwU eK Lvov Dcii w`K vo eM Qvov nj| G ei Dci wqviZ ZiY = -g, KviY gcw_exi K`vwfgyLx| t mgq ci Kvb wbw` DPZvq ewUi eM v nj, MwZi mgxKiY nZ cvB, v = vo gt KvRB`Lv hvQ h, Dcii w`K wbw ei eM axi axi KgZ _vK| Kvb wbw` DPZvq hLb gt Gi gvb vo Gi mgvbZLb kl eM v = 0 ne| A_vr ewU Avi Dci DVZ cvie bv| GB DPZvB mvP DPZv| awi, mevP DPZvqWant more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

21. 02| iwLK MwZ (Linear Motion) 6MgbKvj t, myZiv&s 0 = vo gtgvt o KvRB Lvov Dcii w`K wbw ei gvo-B nj e KZK AwZvmevP DPZvq cQbvi mgq|Lvov Dcii w`K wbw ei Dvbi, cZbi, Dvb cZbi mgq wbYq :gbKwi, Kvb GKwU eK Lvov Dcii w`K vo eM Qvov nj| G ei Dci wqviZ ZiY = g, KviY gcw_exi K`vwfgyLx| t mgq ci h DPZvq ewUi eM v nj MwZi mgxKiY nZ cvB,v = vo gt ... ... ... ... (1)Ges )2(.........gH2vv 2o2myZivs `Lv hvQ h, Dcii w`K wbw ei eM axi axi KgZ _vK| GB eM GK mgq 0 (k~b) ne| A_vrewU Avi Dci DVe bv| dj ewU h DPZvq DV ZvB-B e KZK AwZv mevwaK DPZv H| awi GB DPZvqhZ mgq jvM t1 myZivs (1) bs mgxKiY nZ cvB,0 = vo gt1)3(...............gvt o1 mevwaK DPZvq Dvb Kvjgvt o1 , Avevi (2) mgxKiY nZ cvB,gH2v0 2o )4(............g2vH2o mevwaK DPZvq ei kleM k~b| KvRB mevP DPZv nZ f~wgZcovi mgq Gi Avw`eM ne k~b Ges ay AwfKlR ZiY ewU wbP coZ _vKe| mevP we`y _K f~wgZ wdiAvmZ t2 mgq jvMj, MwZi mgxKiY _K cvB,222 gt21t0H g2vHgt21 2022 22o22gvt )5(............gvt o2 Dvb cZbi gvU mgq T nj T = t1+t2gvgvT oogv2T o BnvB Dvb cZbi gvU mgq|Lvov Dcii w`K wbw e fywgZ wdi Avmvi mgq wbYq :gbKwi, Kvb GKwU eK Lvov Dcii w`K vo Avw`eM Qvov nj| G ei Dci wqviZ ZiY = g,KviY g cw_exi K`vwfgyLx| dj ewUi eM axi axi KgZ _vKe Ges GKwU wbw` DPZvq eM k~b ne A_vrewU Avi Dci DVebv| KvRB GB DPZvq e KZK AwZv mevP DPZv| awi mevP DPZv H, dj MwZimgxKiY _K cvB, gH2vv 2o2gH2v0 2o Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

22. 02| iwLK MwZ (Linear Motion) 7(1).........g2vH2oAvevi mevP DPZv _K fywgZ cZveZbKvj ei Avw`eM k~b ne Ges ay gv AwfKlR ZiY ewU wbP coZ_vKe| mevP we`y _K fywgZ wdi AvmZ ei t mgq jvMj MwZi mgxKiY _K cvB,2gt21t0H 22ogt212gv2o2gvt (2)............gvt o BnvB mevP DPZv nZ cZbKvj|awi, fywgZ wdi AvmZ h mgq jvM mB mgqi kl ei eM = vmyZivs v = 0 + gtgvgv oovv myZivs f~wg _K eK h eM Dciiw`K wbc Kiv nq, ewU wdi Gm mB eM f~wgZ AvNvZ Ki|co ei m~ eYbv (Laws of falling bodies) :evavnxb fve co e wbv wZbwU m~ gb Pj| 1589 wLv wevbx MvwjwjI m~ wZbwU Avwevi Kib t1g m~t e mgvb mgq mgvb c_ AwZg Ki|2q m~t wbw` mgq e h eM jvf Ki Zv H mgqi mgvbycvwZK| t mgq v eM jvf Kij, m~vbyhvqx eM ne,tv3q m~t wbw` mgq e KZK AwZv `~iZ H mgqi eMi mgvbycvwZK| t mgq AwZv `yiZ h nj, m~vbyhvqxDPZv ne, 2th^bgy`v I cvjK cixv:hcvwZt (K) j^v GKwU k, gvUv I duvcv `yBgyL Lvjv KvPbj B| (L) GKwU Uzwc C(M) GKwU c KK S (N) GKwU cvjK |cixvi weeiY: KvPbji GKcvGKwU Uzwc C Ges Aci cvGKwU c KK S _vK|Uzwc Lyj GKwU ^bgy`v G Ges GKwU cvjK F bji ga XyKvbv nq| cKKi Pvwe Lyjcvi mvnvh bjwUK evqyc~b ev evqyk~b Kiv hvq| bjwUK nVvr Dwq gy`v I cvjKKwbPiw`K coZ `Iqv nq| cixvq `Lv hvq h (1) evqyc~b Aevq gy`vwU cvjKi AvMwbPi cvco| (2) evqyk~b Aevq gy`v I cvjK GKB mv_ wbPi cv co|djvdjt evqyk~b vb mKj e mgvb mgq mgvb c_ AwZg Ki|Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

23. 02| iwLK MwZ (Linear Motion) 8mgZiY MwZi eM ebvg mgq (v t)jLwP AsKb Ges jLwP nZ 2o at21tvs mgxKiYwU cwZcv`b:mgZiY MwZkxj Kvb ei X Ai w`K mgq t Ges Y Ai w`K eM v wbq v ebvg t jL wP AsKbKiv nj| GwU Y AK Q`Kvix GKwU mij iLv nq hv, v = vo+at mgxKiY gb Pj| GB jLwP _K t mgqei AwZv `~iZ s wbbq Kiv hvq| AB iLvi Dci h Kvb we`y P bqv nq| P _K X Ai Dci PQ j^ Uvbvnq| Zvnj OQ = t mgq AwZv `~iZ s ne AOQP idj| aiv hvK, KYvwUi mgZiY aGes Avw`eM, vo = AOAwZv mgq, t = OQGes t mgq AwZv `~iZ , s = AOQP i dj|= AOQR i dj ARP i dj|= AOOQ + 21ARPRs = AOOQ + 21OQPR [ AR = OQ ]wK AB iLvi Xvj nQ KYvwUi ZiY a,ARPRa PR = aAR= aOQs = AOOQ + 21OQaOQ s = AOOQ + 21aOQ2 2o at21tvs mgxKiYwU cwZcv`b Kiv nj| Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

24. c_g ci AsKi mgvavbFirst Paper Math Solution2| iwLK MwZ (Linear Motion)1| GKwU e`yKi wj Kvb Ìqvji ga 0.04m cek Kivici AaK eM nvivq | MywjwU Ìqvjiga Avi KZUzKz cek Kie?gb Kwi,jj ceki gyn~Z wji AvwèM = uGes wjwU AviI x wgUvi `~iZ cek Kie|0.04 m cek Kivi ci eM ne =2uGes kl eM ne 0 (k~b)|Avgiv Rvwb, c_g Aski Rb2a(0.04)u2u 224uu0.08a22)1(...............0.323u0.0843ua22wZxq Aski Rb,ax22u02x32.0u322u0,22ev4u0.32x6u,22ev(Ans.)m0.0133460.32x 2| 50 wgUvi DPuy _K GKwU e f~wgZ cwZZ nq|(K) fywgZ cuQZ Gi KZ mgq jvMe?(L) fywgZ cuQevi c~e gyn~Z Gi eM KZ ne?(K) 2gt21uth 2t9.821005 2t9.405 9.450t29.450t t = 3.19 s (Ans.)Avevi,(L) v = u + gt v = 0 + 9.8 3.19v = 31.26 ms-1(Ans.)3| 20ms-1eM MwZkxj GKwU ei eM cwZ mK 3ms-1nvinvm cvq| _g hvIqvi AvM ewU KZ `~iZ AwZg Kie?Avgiv Rvwb, v2= u2 2asev, 0 = 202 2(3)sev, 6s = 4006400s ev,(Ans.)m66.7s 4| Dcii w`K wbw GKwU ej Uwjdvb ZviK 0.70ms-1`wZZAvNvr Ki| Qvovi vb _K ZviwUi DPZv 5.1m nj ejwUi Avw``wZ KZ wQj?Avgiv Rvwb,2ghuv 225.19.82u(0.7) 225.19.82(0.7)u 2296.9949.0u245.100u2(Ans.)ms10.0245.100u -15| GKwU Ub 3ms-2mgZib PjQ Ges AvwèM 10m/s UbwU hLb60m c_ AwZg Kie ZLb Gi eM KZ ne|Avgiv Rvwb,2as2u2v 603210v 22360100v2460v2)Ans(1ms45.21447.21460v 6| GKwU eK 98 ms-1eM Lvov Dcii w`K wbc Kiv nj`LvI h, 3 Sec I 17 Sec mgq ei eMq mgvb wK w`KwecixZ gyLx|Avgiv Rvwb,3 mt ci eMv1 = u gt1ev, v1 = 989.83ev, v1 = 9829.4v1 = 68.6ms-1Avevi, 17 mt ci eMv2 = u gt2ev, v2 = 98 9.817ev, v2 = 98 166.6v2 = 68.6 ms-13 mt I 17 mt ci eR q mgvb I wecixZ (cgvwYZ)GLvb,AvwèM, u = 20 ms-1g`b, a = 3 ms-2kleM, v = 0_vgvi AvM ewU KZKAwZv `~iZ, s = ?GLvb,DPZv, h =50mAvwèM, u = 0g = 9.8 ms-2(K) mgq, t = KZ?(L) kl eM, v = KZ ?GLvb,DPZv, h =5.1mg = 9.8 ms-2kl eM, v =0.70ms-1Avw` `wZ, u =?GLvb,ZiY, a = 3ms-2AvwèM, u = 10 ms-1miY, s = 60mkleM, v = ?GLvb,AvwèM, u = 98 ms-1mgq, t1 = 3Smgq, t2 = 17SkleM, v1 =?kleM, v2 =?Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

25. 2| iwLK MwZ (Linear Motion) 27| t3t31s 3 m~vbymvi GKwU e mij iLvq PjQ|2 mK ci Gi eM KZ ne?Avgiv Rvwb,dtdsv t3t31dtdv 33t331v 23tv 232v 2 [t Gi gvb ewmq]7v GKK (Ans.)8| 54 kmh1eM Pj GKwU ij MvwoZ mb _K wKQy `yi0.75ms-2g`b mwKvix eK Ìqvq MvwowU mb Gm _g Mj|mb _K KZ `~i eK Ìqv nqwQj Ges MvwowU _vgZ KZmgq jMwQj?Avgiv Rvwb,v2= u22ass75.02150 2m75.021515s(Ans.)m150s Avevi, v = u att75.0150 s75.015t (Ans.)s20t 9| GKwU e wi Aevb nZ hvv i Ki c_g mK 1m`~iZ AwZg Ki| cieZx 1m `~iZ AwZg KiZ KZ mgqjvMe|Avgiv Rvwb,2111 at21uts 2)1(a2101 2a1 2ms2a GLb c_g _K s2 = (1m+1) =2m `~iZ AwZg KiZ mgqjvM = t22222 at21uts 22t22102 2t22 s414.12t2 kli 1m `~iZ AwZg KiZ mgqjvM, .)Ans(s414.0s)1414.1(ttt 12 10| GKwU Ub wi Aevb nZ 10ms-2ZiY PjZ Avi Kij| GKBmgq GKwU Mvwo 100ms-1mgeM Ubi mgvivj Pjv i Kij| UbMvwowUK KLb wcQb dje?gb Kwi, t mgq ci Ub MvwowUK wcQb dj Pj hve,t mgq Ub KZK AwZv `~iZ,2at210x 2t1021x (1).........t5x 2t mgq Mvwo KZK AwZv `~iZ, Vtx (2).........t100x kZgZ Ub hLb MvwowUK AwZg Kie ZLb xx ne|t100t5 25100t (Ans.)s20t 11| wivev _K PjZ Avi Ki 625m `~iZ AwZg Kij GKwUei eM 125ms-1nj| ZiY wbYq Ki|Avgiv Rvwb,as2uv 22625a20125222ms6252125a .)Ans(ms5.12a 212| 64m DuPz `vjvbi Qv` _K 5kg fii GKwU cv_i Qo w`jf~wgZ cuQvZ Gi KZ mgq jvMe?Avgiv Rvwb,2gt21uth 2t8.921064 2t9.464 .)Ans(.s61.3t9.464t GLvb,mgq, t = 2 SeceM, v =?GLvb,AvwèM, u = 54 kmh-11ms3600100054 =15ms-1g`b, a = 0.75ms-2kleM, v = 0mgq, t = ?miY, s=?GLvb,AvwèM, u = 0mgq, t1 = 1smiY, s1 =1mZiY, a=?GLvb,Mvwoi mgeM, V = 100ms-1Ubi ZiY, a = 10ms-2mgq, t = ?GLvb,AvwèM, u = 0AwZv `~iZ, s = 625mkl eM, v = 125 ms-1ZiY, a =?GLvb,AvwèM, u = 0AwZv `~iZ, h = 64mfi, m= 5kgmgq, t =?Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

26. 2| iwLK MwZ (Linear Motion) 313| wi Aevb nZ hvv Avi Ki GKwU e c_g mK 2m`~iZ AwZg Ki| cieZx 2m `~iZ AwZg KiZ ewUi KZmgq jvMe|Avgiv Rvwb,2111 at21uts 2)1(2102 a22a2ms4a GLb c_g _K s2 = (2m+2m) = 4m `~iZ AwZg KiZmgq jvM = t22222 at21uts 2242104 t2t22 s414.12t2 kli 2m `~iZ AwZg KiZ mgqjvM, .)Ans(s414.0s)1414.1(ttt 12 14| GKwU e c_g `yB mK 30m I cieZx Pvi mK 150mMj| ZiY AcwiewZZ _vKj ewU Gi ci GK mK KZUv c_AwZg Kie?Avgiv Rvwb,2111 at21uts 2221230 au)1(..........15 auc_g _K t2= (2+4)= 6 mK ewU hvq s2=(30+150)m=180m222221atuts 26216180 au)2(..........303 au)1(..........15 auweqvM Ki, 2a= 15 25.7 msaGLb (1) bs mgxKiY a Gi gvb ewmq,155.7 u 15.7 msu6 mKi cii mK A_vr 7g mK AwZv `~iZ,)12(2 taust)172(25.75.77 s1325.75.77 s75.485.77 s)(25.567 Ansms GLvb,Avw`eM, u = 0mgq, t1 = 1smiY, s1 =1mZiY, a =?GLvb,`~iZ, s1 = 30mmgq, t1 = 2smiY, s2 = (30+150)=180mmiY, s7 =?Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

27. ckt wbwjwLZ mgxKiYwj mivmwi fi ic cwZcv`b Ki|)rr(a2vvta21tvrr)tvv(21rrtavv0200000022 N)M)L)K) ((((|cwZcv`bK)( tavv0awi, GKwU e a mgZiY Kvb Zj MwZkxj| GB MwZi cviwK kZvw` nj hLb oit ZLb Avw` Aevb fi0rr Ges Avw`eM 0vv Avevi, ttf mgq ewUi Aevb fi rGes eM v|h Kvb gyn~Z mgqi mvc ei eM ewi nviK ZiY ej|dtdvaiYZdtavdev,hLb t = 0 ZLb 0vv Ges hLb t = t ZLb vv GB mxgvi ga Dciv mgxKiYK mgvKjb Ki cvB, t0dtd0avvv tvv tav o 0 )(0 otavv tavv 0tavv 0)(21rr00|cwZcv`b(L) tvvawi, GKwU e a mgZiY Kvb Zj MwZkxj| GB MwZi cviwK kZvw` nj hLb 0it ZLb Avw` Aevb fi0rr Ges Avw`eM 0vv Avevi, ttf mgq ewUi Aevb fi rGes eM v|myZivs KYvwUi t mgq eeavb MoeM VnjtdtvtV01 tdtrdvdtdtrdtV0][1rrrdtV01rrrtV0][1)(10rrtVtVrr 0tvvrr )( 0210 )( 021vvV tvvrr )( 0210Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

28. 3| wgvwK MwZ (Motion In Two Dimention) 2|cwZcv`b(M)200t21rr atvawi, GKwU e a mgZiY Kvb Zj MwZkxj| GB MwZi cviwK kZvw` nj hLb oit ZLb Avw` Aevb fi0rr Ges Avw`eM 0vv Avevi, ttf mgq ewUi Aevb fi rGes eM v|h Kvb gyn~Z mgqi mvc ei eM ewi nviK ZiY ej|dtdvaiYZdtavdev,hLb ti = 0 ZLb 0vv Ges hLb tf = t ZLb vv GB mxgvi ga Dciv mgxKiYK mgvKjb Ki cvB, t0dtd0avvv tvv tav o 0 )(0 otavv tavv 0tavv 0Avevi, hnZz Kvb gyn~Z mgqi mvc ei Aevb fi ewi nviK eM ej, ZvB msvbymvi,dtrdv ewmq cvB, tavdtrd 0tdtadtvrd 0hLb ti = 0 ZLb 0rr Ges hLb tf = t ZLb rr GB mxgvi ga Dciv mgxKiYK mgvKjb Ki cvB, t0t00rrtdtadtvrd0 tttrr atvr 0200 ][][20 )0(2)0( 200 tatvrr22100 tatvrr22100 tatvrr2020|cwZcv`b(N) )rr(avv2 awi, GKwU e a mgZiY Kvb Zj MwZkxj| GB MwZi cviwK kZvw` nj hLb oit ZLb Avw` Aevb fi0rr Ges Avw`eM 0vv Avevi, ttf mgq ewUi Aevb fi rGes eM v|h Kvb gyn~Z mgqi mvc ei eM ewi nviK ZiY ej|dtdvaiYZdtavdev,hLb t = 0 ZLb 0vv Ges hLb t = t ZLb vv GB mxgvi ga Dciv mgxKiYK mgvKjb Ki cvB, t0dtd0avvv tvv tav o 0 Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

29. 3| wgvwK MwZ (Motion In Two Dimention) 3)(0 otavv tavv 0tavv 0Dfq cK GB mgxKiY w`q Y Ki cvB,)).((. 00 tavtavvv20000 ..... taatavtavvvvv2000 ..2.. taatavvvvv)21.(2.. 2000 tatvavvvv )(21.2.. 020000 rrtatvrravvvv 0202.2 rravvckt cvm KvK ej?Dit Kvb eK AbyfywgKi mv_ wZhKfve Kvb vb wbc Kiv nj ZvK cvm ej| wZhKfve wbwwXj, eyjUi MwZ BZvw` cvm MwZi D`vniY|ckt AbyfywgKi mv_ wZhKfve wbw cvmi MwZc_i mgxKiY wbbq Ki Ges `LvI h, GB MwZc_ AwaevKvi|Dit gbKwi, evqygawZ O we`y nZ GKwU cvmK wbc Kiv nj|wbc eM ev AvwèM = vowbc KvY = g wbPi w`K wqvkxj| AZGe ay = -g; ax = 0;wbc we`y I g~j we`y GKB nIqvq xo = yo = 0 AvwèMi Abyf~wgK Dcvsk = voCosoGes AvwèMi Dj^ Dcvsk = voSinoX A eivei MwZi cwieZb D A eivei ZiYi Dci wbfikxj| Y A eivei MwZi cwieZb D Aeivei ZiYi Dci wbfikxj| G `ywU A eivei MwZi cwieZb Awbfikxj|awi t mgq cvmwU P(x,y) Aevb _vK| ZLb Gi eM = vAbyf~wgKi w`K ZiY, ax= 0Abyf~wgKi w`K miY = xx = voCoso t + 21axt2ev, x = voCoso t + 0 [ax= 0]ev, x = voCoso t)1...(....................ooCosvxtDj^ w`K ZiY ay=g;Dj^ w`K miY y; Abyicfvey=voSinot 21gt2Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

30. 3| wgvwK MwZ (Motion In Two Dimention) 42o 21ooooo CosvxgCosvxSinvyev, [t Gi gvb ewmq]2222tan xCosvgxyooo ev, coCosovgbcxbxy o 2222tan, GeseKaawiDciv mgxKiYwU GKwU Awaei mgxKiY| cvmi MwZc_ GKwU Awae (cvivevjv)|ckt cgvY Ki, evqynxb Aevq f~wg nZ DPZvq AewZ h Kvb Aevb nZ Abyf~wgK AwfgyL wbw ei MwZc_GKwU Awae|gbKwi, k~b AewZ O we`y nZ vo eM f~wgi mgvivj GKwU eKYv wbw nj| e KYvwU g Gi cfvebxP coe| awi ccb Zj Abyf~wgK OX iLv X A Ges OY iLv Y A| awi t mgq ci e KYvwU MwZ c_iP(x,y) we`yZ gyn~Zi Rb Aevb Kie| g bxPi w`K wqvkxj|AZGe ay = g; ax= 0 ;Avw`eMi Abyf~wgK Dcvsk = voGes Avw`eMi Dj^ Dcvsk = 0tmgq AwfKlRZiYnxb Abyf~wgK miY x = vot)(tvx ... ...... ...... ...o1222tmgq Dj^ miY y = 0.t + 21gt2y = 21gt2... .... .... .... .... .... .... (2)(1) K (2) viv fvM Ki cvB221222gttvyx ogv2yx 2o2ygvx o22 2 eKaawi avayx 4g2,42o2Dciv mgxKiYwU GKwU Awaei mgxKiY| ZvB wbw ei MwZc_ GKwU Awae (cvivevjv)|ckt AbyfywgKi mv_ wZhK fve wbw ei (K) mevP DPZvq cQZ mgq (L) mevP DPZv (M) wePiYKvj (N) cvjv (O) mevwaK cvjv wbbq Ki|gb Kwi, evqygawZ O we`y nZ GKwU cvmK ov eM o KvY wZhKfve wbc Kiv nj| cvmwU t mgq mevPDPZv P(x,y) G Aevb Kie Ges ZLb Gi eM ne v|(K) mevP DPZvq cQZ mgqt vo eMi Dj^ Dcvsk voSinot mgq ci P we`yZ eM, vy = voSino gt.................(1)P we`yMvgx mevP DPZvq vy= 0..................................... (2)Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

31. 3| wgvwK MwZ (Motion In Two Dimention) 5(1) bs mgxKiY vy= 0 ewmq cvB0 = voSino gt)3....(..............................gSinvt oo (L) mevP DPZvtgbKwi, mevP DPZv = H H = voSinot 21gt2 qewmgvbGiZnbs t(3)221gSinvggSinvSinvH oooooo 222gSinvgSinvH oooo (4).....................2gSinvH o22o (M) Dqb (wePiY) Kvj (Time of Flight) tgb Kwi wePiY Kvj T A_vr T mgq cvmwU mgZj wdi Avm| t mgq Dj^ w`K miY y = voSinot 21gt2GB mgxKiY mgq t = T Ges miY y = 0 ewmq cvB,0 = voSinoT 21gT2ev, 21gT2 = voSinoT(5)..................2TgSinv oo (N) cvjv (Range)tgb Kwi cvjv R A_vr T mgq cvmwU AbyfywgKi w`K h `~iZ AwZg Ki ZvBB cvjv R R = ( voCoso ) TgSinvCosvR oooo2 [(5) bs nZ T Gi gvb ewmq]gCosSinvR ooo 22.......(6)....................22gSinvR oo (O) mevwaK cvjv (Maximum Range) tgbKwi mevwaK cvjv Rmax| wbw` vo Gi Rb, Sin20 Gi gvb mevwaK nj cvjv ne mevwaK| Sin20 GimevwaK gvb = 1A_vr Sin20 = 1ev, Sin20 = Sin900ev, 20 = 900 0 = 450myZivs wbc KvY0 = 450nj cvjv mevwaKWant more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

32. 3| wgvwK MwZ (Motion In Two Dimention) 6 mevwaK cvjv4522maxgSinvRoo 092maxgSinvRoo12maxgvR o (7)...............2maxgvR ockt iwLK eM I KwbK eMi msv `vI Ges G`i ga mK vcb Ki| |Kicgvbev, , rvrv ev|KicgvYev, rv iwLK eM (Linear Velocity)t wbw` w`K iwLK c_ Kvb e GKK mgq h `yiZ AwZg Ki ZvK H ei iwLKeM ej| iwLK eMK v viv cKvk Kiv nq| wbw` w`K e t mgq d `~iZ AwZg Kij eMtdv ne| eMGKwU fi ivwk| iwLK eMi GKK ms-1KwYK eM (Angular Velocity) t mgq eeavb k~bi KvQvKvwQ nj Kvb we`y ev AK K` Ki evKvi c_Pjgvb Kvb ei mgqi mv_ KwbK miYi nviK KwbK eM ej| Ab K_vq evKvi c_ Kvb e GKK mgqh KwbK `~iZ AwZg Ki ZvK H ei KwbK eM ej| KwbK eMK viv cKvk Kiv nq| wbw` w`K e tmgq KvY Drcb Kij KwbK eMt ne| KwbK eMi GKK rad s-1Gi gvv nQ 1-TTLLmgqevmvaPvcmgqKvYmK (Relation) tgbKwi GKwU eKYv OC= OB = r evmva wewk GKwU eicwiwa eiveiKwbK eM NyiQ| hw` T mK e KYvwU ei cwiwaeivei GKevi Nyi Avm Ze KwbK `~iZ = iwWqvb ne|KwbK eM,T2 ev, )1...(............2T GLb e KYvwU hw` evKvi c_ bv Nyi H GKB mgq mij iLv eivei PjZ Ze T mgq eKYvwU ewUicwiwai mgvb c_ r `~iZ AwZg KiZ| iwLK eM2Trv )2...(............2vrT (1) bs I (2) mgxKiYq nZ cvBvr22 Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

33. 3| wgvwK MwZ (Motion In Two Dimention) 7vr1 v = r A_vr iwLK eM = KwbK eM ei evmva|v = r mgxKiYi fi ic:gb Kwi, (3).........ru ufii gvb ][r90sin rru m Ybi wbqg Abymvi, u,evr fii AwfgyL Ges vfii AwfgyL Awfb| Avevi v = r| `Lv hvQ h,gvb I w`K weePbvq vuI fi Awfb|(4).........vu(3) I (4) nZ rv (cgvwYZ)ck: KwbK eM I iwLK eMi ga cv_K eYbv Ki|KwbK eM I iwLK eMi ga cv_K (Distinction between Angular Velocity and Linear Velocity)wgK KwbK eM iwLK eM1|KwbK c_ ei KwbK mibi nviK KwbK eMej|wbw` w`K iwLK c_ Kvb GKwU ei vbcwieZbi nvi K iwLK eM ej|2| GK viv cKvk Kiv nq| GK viv v cKvk Kiv nq|3| Gi mgxKiYt Gi mgxKiYtsv 4| Gi gvv mgxKiY [ T-1] Gi mgxKiY [ LT-1]5| Gi GKK iwWqvb/ mK Gi GKK wgUvi/ mKK`gyLx ej (Centripetal Force): hLb Kvb e evKvi c_ NyiZ _vK ZLb h ej ei Dci H ei K`AwfgyL wqv Ki ewUK evKvi c_ MwZkxj ivL ZvK K`gyLx ej ej| m fii e r evmva wewk evKvic_v mg`wZZ NyiZ _vKj Zvi K`gyLx ejrvm2 |K`wegyLx ej (Centrifugal Force): hLb Kvb e evKvi c_ NyiZ _vK ZLb h ej H ei K`i wecixZw`K cqvM Ki ZvK K`wegyLx ej ej| m fii e r evmva wewk evKvic_ v mg`wZZ NyiZ _vKj ZviK`wegyLx ejrvm2 |m fi wewk GKwU e r emvai evKvi c_ v mg`wZZ NyiQ| (1) `LvI h, j^ ZiY rrva 22 ev (2)j^ ZiYi ivwkgvjv wbbq Ki| (3) cgvY Ki h, K`gyLx ej rmrvmF 22 ev, (4) evKvi c_ mg`wZZN~bvqgvb Kvb ei Dci wqvkxj K`gyLx eji gvb I w`K wbYq |aiv hvK, m fii Kvb e r evmvai evKvi c_ v mg`wZZ Ges KwbK eM AveZbiZ AvQ| awi AwZ z`mgq t eeavb ewU A nZ B we`yZ Am| A we`yZ ewUi eM H we`yZ kK AC eivei| B we`yZ ewUi eMH we`yZ kK BD eivei| BD K cQb ewaZ Kij AC I BD Gi wgjb we`y nq E|Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

34. 3| wgvwK MwZ (Motion In Two Dimention) 8GLb, OAEB PZzf~R, AEB+ AOB = `yB mgKvY|Avevi, AEB+ BEC = `yB mgKvY| AOB = BEC = awi,A we`yZ ei eMi Dj^ Dcvsk, vy = 0Ges AbyfywgK Dcvsk, vx = vB we`yZ ei eMi AC eivei eMi Dj^ Dcvsk, vsinvy Ges AbyfywgK Dcvsk, vcosvx t AwZ z` mgq myZivs AwZ z`| sin Ges 1c osB we`yZ ei eMi eMi Dj^ Dcvsk, vvy Ges AbyfywgK Dcvsk, vvx GZ `Lv hvQ, AbyfywgK eivei eMi Dcvski Kvb cwieZb nq bv|eMi Dj^ Dcvski cwieZbi KviY ZiY, a nj,tva0tvv trvv rvrrrrva 2222K`gyLx ej, rmrvmmaF 22 (cgvwYZ)ck: Awfj^ ZiY ev evmvagyLx ZiY ev K`gyLx ZiY:Awfj^ ZiY ev evmvagyLx ZiY ev K`gyLx ZiY tKvb e hLb evKvic_ NyiZ _vK ZLb ei evmva eivei ei K`i w`K wqvkxj AwfK` eji Rb hZiYi mw nq ZvK evmvagyLx ZiY ev Awfj^ ZiY ev K`gyLx ZiY ej| Gi GKK wgUvi/mK2|ck: KwbK ZiY KvK ej?KwbK ZiYt hLb Kvb eKYv Amg KwbK eM Nyi, ZLb ewUi KwbK eM cwieZbi nviK KwbK ZiYej A_ev, mgqi mv_ Amg KwbK eM cwieZbi nviK KwbK ZiY ej| GK viv cKvk Kiv nq| Gi GKKiwWqvb/mK2|gbKwi, evKvi c_ Nybvqgvb eKYvi Avw`KwbK eM i Ges t mgq ci Gi kl KwbK eM f KvRBKwbK ZiYtif Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

35. 3| wgvwK MwZ (Motion In Two Dimention) 9ck: mg`wZZ Pjgvb ei Zib _vK bv, wK evKvi c_ mg`wZZ Pjgvb ei ZiY _vK Kb? evLv Ki|mg`wZZ Pjgvb ei Zib _vK bv, wK evKvi c_ mg`wZZ Pjgvb ei ZiY _vK teMi gvb nQ `wZ Ges eMi cwieZbi nvi nQ ZiY| Kvb e hLb mij c_ mg `wZZ Pj ZLb eMigvbi Kvb cwieZb nq bv Avi mij c_ Pjvi Rb w`Ki I Kvb cwieZbnq bv| dj ei Kvb ZiY _vK bv|wK evKvi c_ Nyievi mgq ei wbqZ w`Ki cwieZb nq, KviYeMi AwfgyL me`vB ei kK eivii nq| Gfve AbeiZ w`K cwiewZZnZ _vK ej e mg`wZZ PjjI eM mgvb _vKbv| eMi GB cwieZbidj ZiYi mw nq| GB ZiYi AwfgyL evKvi c_i K` eivei nq _vK|G Rb evKvi c_ mg`wZZ Pjgvb ei ZiY _vK|Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

36. c_g ci AsKi mgvavbFirst Paper Math Solution3| wgvwK MwZ (Motion In Two Dimention)1| GKwU cvmi AbyfywgK cvjv 96m Ges AvwèM 66 ms-1|wbc KvY KZ?Avgiv Rvwb,g2SinvR o2o 20ovgRSin2,ev2o669.896Sin2ev,(0.2159)Sin2, 1oev)Ans.(24.647.122ooev,2| GKwU eK 40ms-1eM Ab~fywgKi mv_ 60 KvY wbcKiv nj| mevwaK DPZv Ges Abyf~wgK cvjv wbYq Ki|Avgiv Rvwb,g2)Sin (vH2oo 8.92260Sin40H 8.92260Sin40H 8.92286602.040H 8.9226408.34H8.929850.1199H.)m (Ans22.61H go2SinvR20Avevi,8.9)602Sin (40R28.9)602Sin (40R28.9)120Sin1600R8.986602.01600R8.9632.1385R m (Ans.)39.141R 3| nvBWvRb cigvbyi gWji GKwU BjKUb GKwU cvUbi Pviw`K5.2 10 -11m evmvai GKwU evKvi c_ 2.18 106ms-1eMc`wb Ki| BjKUbi fi 9.1 10-31kg nj K`gyLx ej KZ?Avgiv Rvwb,rmvF211-2631-102.5)1018.2(101.9FN (Ans.)10316.8F 84| 0.250kg fii GKwU cv_i LK 0.75m j^v GKwU myZvi GKcv eua evKvi c_ cwZ wgwbU 90 evi Nyivj myZvi Dci KZ Uvbcoe|Avgiv Rvwb,rmF 2rtn2mF275.060901416.3225.0F2 (Ans.)N65.16F 5| 9.2 ms-1eM GKwU z` eK Lvov Dcii w`K wbc Kiv nj|GwU KZ mgq ci f~-c wdi Avme?Avgiv Rvwb,gSinv2T oo 8.990Sin2.92T8.912.92T8.94.18T .)Ans(s877.1T 6| AbyfywgKi mv_ 30KvY f~-c _K 50ms-1eM GKwU eyjUQvov nj| eyjUwU 50m `~i AewZ GKwU ÌqvjK KZ DPZvqAvNvZ Kie|Avgiv Rvwb,22000 x)cosv(2gx)(tany220)50()30cosv(2gx)30(tanyGLvb,AbyfywgK cvjv, R = 96 mAvwèM, vo = 66ms-1AwfKlR ZiY, g = 9.8ms-2wbc KvY, = ?GLvb,AvwèM, v0 = 40ms-1wbc KvY 60AwfKlR ZiY,g = 9.8ms-2mevwaK DPZv, H = ?AbyfywgK cvjv, R = ?GLvb,fi, m = 0.250 kgevmva, r = 0.75 mmgq t = 1 min.= 60s.cvKmsLv, n = 90 cvK|Uvb, F = ?GLvb,AvwèM, vo = 9.2 ms-1wbc KvY, 0AwfKlR ZiY,g = 9.8ms-2Dvb cZbi gvUmgq T =?GLvb,AvwèM, vo = 50 ms-1wbc KvY, AwfKlR ZiY,g = 9.8ms-2AbyfywgK `~iZ, x=50mDj^ `~iZ, y=?Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

37. 3| wgvwK MwZ (Motion In Two Dimention) 2220)50()30cosv(2g50)30(tany 22)50()866025403.050(28.950577350269.0y 533333345.686751346.28y (Ans.)m33.22y 7| GKwU cvmi AbyfywgK cvjv 79.53 m Ges wePiYKvj 5.3 snj wbc KvY I wbc eM KZ?Avgiv Rvwb,g2SinvR o2o 8.92Sinv53.79 o2o (1).....394.7792Sinv o2o Aevi,gSinv2T oo 8.9Sinv23.5 oo (2).........94.51Sinv2 oo (1) bs mgxKiYK (2) bs mgxKiY viv fvM Ki cvB,94.51394.779Sinv22Sinvooo2o94.51394.779Sinv2CosSin2voooo2o(3)........15Cosv o0 (2) bs mgxKiYK (3) bs mgxKiY viv fvM Ki cvB,1594.51CosvSinv2o0oo2463.3tan o 732.1tan o 732.1tan 1o.)Ans(60o (3) bs mgxKiY 0 Gi gvb ewmq cvB,1560Cosv0 1521v0 (Ans.)ms30v 108| GKwU ejK f~wgi mv_ 30KvY Ki Dcii w`K wbc Kiv njGwU 20m `~i GKwU `vjvbi Qv` wMq coj| wbc we`y _K Qv`iDPZv 5m nj ejwU KZ eM Qvov nqwQj|Avgiv Rvwb,22000 x)cosv(2gx)(tany2220)20(30cos28.92030tan5v75.024008.902577350269.05 20 v5.1392054.115 20 v54.65.1v3920205.154.63920v20 .)Ans(ms20v 109| GKRb jvK 48 ms-1eM GKwU ej Lvov Dcii w`K wbcKi| ejwU KZ mgq k~Y _vKe Ges mevP KZ Dci DVe?Avgiv Rvwb,gSinv2T oo 8.990Sin482T8.91482T.)(.795.9T Anss Avevi,2gSinvH o22o 9.82)90Sin(48H22 (Ans.)117.5mH 10| GKwU Mvgvdvb iKW cwZ wgwbU 45 evi Nyi| Gi K` _K9cm `~i Kvb we`yi `wZ KZ?Avgiv Rvwb,rv rtn2v6009.04514.32v.)Ans(ms42.0v 1GLvb,AbyfywgK cvjv, R = 79.53 mwePiYKvj, T=5.3swbc eM, vo = ?wbc KvY, = ?GLvb,wbc KvY, AwfKlR ZiY,g = 9.8ms-2AbyfywgK `~iZ, x=20mDj^ `~iZ, y=5mAvw`eM, vo = ?GLvb,eM, v0 = 48 ms-1wbc KvY, =Dvb cZbi gvU mgq,T =?DPZv, H =?GLvb,mgq, t = 1m =60scvKmsLv, n=45evmva,r =9cm=0.09m`wZ, v =?Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

38. 1 = 7.2324 1 = 13825.728 - ) () () () () 1:1030:1040:1042[ 1] Gravitation Intermediate vector bosons Photon , , , , Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

39. RoZv (Inertia):c`v_ h Aevq AvQ mB Aevq _vKZ PvIqvi h ceYZv ev mB Aev ivLZ PvIqvi h ag ZvK RoZv ej|RoZv `yB cKvi: h_v (1) wwZ RoZv (2) MwZ RoZv(1) wwZ RoZv (Inertia of rest) t wi e wi _vKZ Pvq ei GB bK ei wwZ RoZv ej|D`vniYt wi Mvwo nVvr Qo w`j hvwiv wcQb w`K nj co| KviY Mvwo Pvjy nIqvi msM msM hvwìkixii wbPi Ask Mvwoi mv_ mshy _vKvq mvgbi w`K GwMq hvq| wK kixii Dcii Ask wwZ RoZvi RbwcwQq co|(2) MwZ RoZv (Inertia of motion) t MwZkxj e MwZkxj _vKZ Pvq ei GB bK ei MwZ RoZv ej|D`vniYt Pj Mvwo nVvr eK Kij hvwiv mvgbi w`K SzK co| KviY Mvwo eK Kivi KviY Mvwo _ghvIqvi mv_ mv_ hvwì kixii wbPi Ask Mvwoi mv_ mshy _vKvq _g hvq wK kixii Dcii Ask MwZRoZvi Rb mvgbi w`K GwMq hvq|ej (Force):hv wi ei Dci wqv Ki eK MwZkxj Ki ev KiZ Pvq A_ev MwZkxj ei Dci wqv Ki MwZi cwieZb Ki evKiZ Pvq ZvK ej ej| ejK F viv cKvk Kiv nq| m fii ei ZiY a nj ej F=ma ne| ej GKwU fiivwk|gwjK ej (Fundamental Forces) th mKj ej ^vaxb A_vr h mKj ej Ab Kvb ej _K Drcb nq bv ZvK eis Abvb ej GB mKj eji Kvb bvKvb ici cKvk ZvìK gwjK ej ej| gwjK ej Pvi cKvi, h_v: (1) gnvKl ej (2) ZvwoZ P^K ej (3)mej wbDwKq ej I (4) `~ej wbDwKq ej(1) gnvKl ej t gnvweki h Kvb `ywU ei gaKvi cviwiK AvKlb ejK gnvKl ej ej|(2) ZvwoZ P^K ej t `ywU PvwRZ KYv Zvì PvRi KviY GK Acii Dci h AvKlY ev weKlb ej cqvM KiZvK ZvwoZ P^K ej ej|(3) mej wbDwKq ej t cigvbyi wbDwKqvm wbDwKq Dcv`vb Z_v wbDwKqbjvK GK Ave ivL h kwkvjx ejZvK mej wbDwKq ej ej|(4) `~ej wbDwKq ej t h ^ cvjvi I ^ gvbi ej wbDwKqvmi ga gwjK KYvwji ga wqv Ki AbKwbDwKqvm AwwZkxjZvi De NUvq ZvK `~ej wbDwKq ej ej|Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

40. 04| MwZm~ (Laws Of Motion) 2gwjK ej mg~n AvcwK wZeZv cvjv1) gnvKl ej 1 Amxg2) ZvwoZ P^K ej 1039 Amxg3) mej wbDwKq ej 104110-15m4) `~ej wbDwKq ej 103010-16mfieM (Momentum) t fi I eMi bdjK fieM ej| fieMK P viv cKvk Kiv nq| m fii Kvb ei eMv nj fieM P = mv ne| fieMi GKK kg-ms-1| Gi gvv [MLT-1]wbDUbi MwZi 1g m~ (Newtons 1stLaw of Motion) teYbvt evwnK ej cqvM bv Kij wi e wPiKvj wi Ges MwZkxj e mgeM mij c_ PjZ _vKe|eLvt evBi _K ej chy bv nj (1) wi e wPiKvj wi _vKe Ges(2) MwZkxj e mgeM mij c_ PjZ _vKe|myZivs `Lv hvq h, MwZi c_g m~i `ywU Ask| c_g Ask _K wi ei wwZkxj _vKvi ceYZv mK aviYv cvIqv hvq| GB ceYZvK wwZ RoZv ej| Avevi wZxq Ask MwZkxj ei MwZkxj _vKvi ceYZv jbxq |GB ceYZvK MwZ RoZv ej| G KviY wbDUbi MwZi 1g m~K RoZvi m~ I ejv nq| G m~ _K eji msv IcvIqv hvq|wbDUbi MwZi 2q m~ (Newtons 2ndLaw of Motion)teYbvt ei fi eM cwieZbi nvi ei Dci chy eji mgvbycvwZK Ges ej h w`K wqv Ki ei fi eMicwieZb I mB w`K NU|eLvt G m~i evLv nj amF cwZcv`b|amF cwZcv`b tgb Kwi, Kvb MwZkxj eKYvi fieM P| Feji wqvq z`vwZz` mgq eeavb dt AeKvk KYvi fieMicwieZb Pdnj fieM cwieZbi nvidtPdne| MwZi 2q m~vbymvi, fieM cwieZbi nvi chy ejimgvbycvwZK| A_vr, FdtPd eKYvi fi m Ges eM v nj fieM vmP ewmq cvB,Fdt)vm(d FdtvdmdtvdaFmaiYZ(1)................Fkma GLvb k GKwU mgvbycvwZK aeK; hvi gvb GKK ejimsv viv wbaviY Kiv hvq| h ej GKK fii Dci wqv Ki GKK ZiY mw Ki ZvK GKK ej ej|A_vr 1F , m=1 Ges 1a nq Ze mgxKiY (1) nZ cvB|11=k1 k=1 mgxKiY ewmq cvB, FamWant more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

41. 04| MwZm~ (Laws Of Motion) 3A_vr amF Kvb ei Dci ^Z ejwj hw` nq h_vg n321 F,..F,F,FBZvw` wqviZ _vKj Avgiv cvB,maF....FFF n321 amF GLvb, FnQ jw ej ev bxU ej hLvb, n321 F....FFFF (cgvwbZ)eji GKK wbDUb t h ej 1kg fii Dci wqv Ki 1ms -1ZiY mw Ki ZvK 1 wbDUb ej ej|A_vr 1 wbDUb = 1kg 1ms -2|wZxq m~ _K c_g m~ cwZcv`b twbDUbi MwZi 1g I 2q m~ Zzjbv Ki `Lv hvq h, 1g m~ nQ 2q m~i GKwU ic| amF _K `Lv hvqh, ei Dci wbU ej k~b nj A_vr hLb 0FZLb 0am ,wK ,0m 0a nq| myZivs hLb evBi _Kej cqvM bv nq A_vr wbU ej k~b nq ZLb,0a 0dtvdvGi wWdviwqmvb k~b v = aeK|myZivs evBi _K ei Dci ej wbU ej k~b nj ei eM AcwiewZZ _vK A_vr e h Aevq wQj mB AevqB_vK| A_vr evwnK ej cqvM e Aevb cwieZb KiZ eva bv Kij wi e wPiKvj wi Ges MwZkxj e wPiKvjmgeM mij c_ PjZ _vKe| GwUB wbDUbi MwZi c_g m~|NvZej (Impulsive Force) tLye A mgq h ej chy nq ZvK NvZ ej ej| nvZzwo viv KvV ciK cvZv, evU viv wKU ej AvNvr Kiv,BZvw` NvZ eji D`vniY|eji NvZ (Impulse of Force) tKvb ej I eji wqv Kvji b djK eji NvZ ej| Kvb ej Fhw` Kvb ei Dci it mgq _K ft mgq chwqv Ki, Zvnj eji NvZ ne, fittdtFJ][ ea FdtFJfitt ]t-[tFtFJ ifttfitFJ eji NvZi mv_ fieMi mK (Relation with Impulse of Force and Momentum ) tchy ej Fnj eji NvZ fittdtFJ dtPdFdtdtPdJfittWant more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

42. 04| MwZm~ (Laws Of Motion) 4 fifiPPPpPPdJ if PPJPJ A_vr, eji NvZ fieMi cwieZbi mgvb|wbDUbi MwZi ZZxq m~ (Newtons 3rdLaw of Motion) teYbv: cZK wqviB GKwU mgvb I wecixZ cwZwqv AvQ|wbDUbi MwZi ZZxq m~vbymvi hw` GKwU e A, Aci e B Gi Dci ej cqvM Ki, Ze B eI A ei Dci mgvbI wecixZ ej cqvM Kie| awi A e B ei Dci F1 ej cqvM Ki Ges B e A ei Dci F2 ej cqvM Ki|m~vbymvi, F1 = F2 , A_vr ej qi gvb mgvb wK wecixZgywL| G `ywU eji h Kvb GKwUK wqv GesAbwUK cwZwqv ej| Dcii `v wqv I cwZwqv mgvb I wecixZ|fieMi msib m~ (Law of Conservation of Momentum) tGKvwaK ei ga wqv cwZwqv ej Qvov Ab Kvb ej wqv bv Kij, H e mg~ni gvU fieMi mgw ae _vK|MvwbwZK fve, eKaPcwZcv`b: 1 I 2 `ywU e weePbv Kwi| awi Kvb GK mgq eqmsNl wj nj| aiv hvK, GB msNl F1 nQ c_g ei Dci wZxqe KZK chy ej Ges F2 nQ wZxq ei Dci c_g e KZK chy ej| Kvb GK mgq t Z c_g ei fieM 1PGes wZxq ei fieM 2P| Avgiv cwZwU ei wbDUbi 2q m~ cqvM Ki cvB,dtPdF 11 GesdtPdF 22wbDUbi MwZi ZZxq m~ _K cvB, 21 FFdtPddtPd 210dtPddtPd 21 0PPdtd21 0dtPd21 PP[ nQ eevi gvU fieM ev ]PhnZz mgqi mvc gvU fieM 21 PPP , PGi cwieZbi nvi k~b, ZvB gvU fieM Pae _vK, A_vr21 PPP = aefi PPf2f1i2i1 PPPP myZivs `Lv hvQ h, msNli AvM Kvb eevi fieMifi mgw Avi msNli ci fieMi fi mgw me`v mgvb _vK| GwUB fieMi msib m~|Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

43. 04| MwZm~ (Laws Of Motion) 5iKUi MwZ (Motion of Rocket) tawi iKUwU AwfKli AvIZvgy gnvk~b MwZkxj| hLb iKUi Bwb KZK MvmwbMZ nqZLb mB Mvmi GKwU fieM _vK| ZLb fieM msiwZ _vK ej iKU wecixZ w`KMwZkxj nq| iKU _K Mvm hLb GKwU wbw` nvi wbMZ nZ _vK, ZLb Mvmi MwZiwecixZ w`K iKUwU GKwU wi ej jvf Ki| GB ejK avv ej|wnmve: gbKwi iKU _K Rvjvwb Z_v Mvm v eM wbMZ nQ| t mgq wbMZ Mvmifi m nj, wbMZ Mvmi fieM ne,P=(m)vwbMZ Mvmi GB fieM iKU Rvjvwbi fieMi cwieZbi mgvb| fieMi msibm~vbymvi Rvjvwbi fieMi GB cwieZb iKUwUi fieMi cwieZbi mgvb| Avgiv Rvwb,Kvb ei fieMi cwieZbi nvi Zvi Dci chy eji NvZi mgvb| myZivs iKUi Dcichy avv F nj P = Ft(m)v = Ft vtmF, ev GLvbtmnQ Rvjvwb eenvii nvi|Kvb gyn~Z iKUi fi M nj Ges H gyn~Z Zvi ZiY a nj, F Gi gvb F= Ma ewmq cvB,vtmMa vtmMa 1iY,Zeji fvimvg (Equilibrium of Force) tei Dci eji jw k~b nIqvK A_vr, 0FnIqvK eji fvimvg ej| fvimvg Aevq ei Dci ZiY k~bnq| fvimvg Aevq ei eM ae _vK| A_vr eMi gvbi ev w`Ki Kvb cwieZb nq bv| fvimvg `yB cKvi| h_v-(1) wi fvimvg (2) MwZq fvimvgjvwgi Dccv` (Lamis Theorem) tKvb ei Dci wZbwU Amgvivj ej wqv Ki fvimvg Aevi mw Kij cZKwU ej Aci `ywU eji AfyKvbi mvBbi mgvbycvwZK|gbKwi, Q,PI RwZbwU ej O we`yZ wqv Ki fvimvg mw Ki| QI RGiAfy KvY , RI PGi Afy KvY , PI QGi Afy KvY | myZivs jvwgi Dccv` Abymvi, SinRSinQSinPne|NlY (Friction) t`ywU e ciii msk _K hw` GKi Dci w`q AciwU PjZ Pv Kij e qik Zj GB MwZi wei h evavi Drcw nq ZvK NlY ej| NlY mvaviYZ Pvi cKvii nq _vKt(1) wwZ NlY (Static Friction),(2) MZxq NlY (Kinetic Friction),(3) AveZ NlY (Rolling Friction),(4) cevwn NlY (Fluid Friction),Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

44. 04| MwZm~ (Laws Of Motion) 6NlY ej t`ywU e ciii msk _K hw` GKi Dci w`q AciwU PjZ Pv Kij e qi k Zj GB MwZi weih eji mw nq ZvK NlY ej ej|wwZNlY ev mxgvwK NlY (Static Friction) tchy eji mevP h gvbi Rb GKwU wwZkxj e MwZi Dcg nq, ZvK wwZ NlY ev mxgvwK NlY ej&|wwZ Nlbi gvb k~b _K mxgvwK gvb ch nZ cvi|wwZNlY ej th Nlb ej viv Kvb e chy ejK cwZnZ Ki wi _vKZ cqvm cvq ZvK wwZNlb ej ej|NlY KvY I wwZ KvYi ga mK twwZ NlY Yv t wwZ NlYi mxgvwK gvb Ges Awfj^ cwZwqvi AbycvZK wwZ NlY Yv ej| GK s vivcKvk Kiv nq| wwZ NlYi mxgvwK gvb fs Ges Awfj^ cwZwqv R nj wwZ NlY Yv ne(2)..................Rfss fs I R Gi GKK GKB| KvRB s Gi Kvb GKK bB|NlY KvY (Angle of Friction) twwZ NlYi mxgvwK gvb fs Ges Awfj^ cwZwqv R K mg^q Kih jw cvIqv hvq ZvK j cwZwqv S ej| GB j cwZwqv Awfj^cwZwqvi mv_ h KvY Ki ZvK NlY KvY ev wwZ NlY KvYej| NlY KvYK viv cKvk Kiv nq| Wvbcvki wP Gi Aevb `Lvb nqQ| wPvbymvi cvB,(3)..................cosSR (4)..................sin Sfs (4) bs mgxKiYK (3) bs mgxKiY viv fvM Ki cvB, (5)............tanRfsAvevi, (2) bs mgxKiYRfss K (5) bs Gi mv_ Zzjbv Ki cvB, (6).........tans A_vr NlY KvYiUvbRU -Gi gvb wwZ Nlb bvi mgvb| BnvB NlY KvY I wwZ NlY Yvi ga mK|Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

45. 04| MwZm~ (Laws Of Motion) 7wwZ KvY ev wbj Kvb (Angle of Repose) tKvb AvYZ ZjwZ e Zji h AvbwZi Rb MwZi Dcg nq ZvK wwZ KvY ev wbj KvY ej| GK vivcKvk Kiv nq| wPvbymvi, OY Zji DcwiwZ e Zji AvbwZi Rb MwZi Dcg nq| myZivs ne wwZ KvY|GB Aevq W Lvov wbPi w`K wqv Kie Ges Zji Awfj^ cwZwqv R-Gi wqv iLvi mv_ KvY bZ _vKe|wP c`wkZ fi eev Abymvi, CosWR SinWfs(7)............Rftan swK (2) bs mgxKiY nZ cvB, ...(2)Rfss Avevi (7) I (2) bs mgxKiY _K cvB,(8).........tans Avevi, (6)............tans dj (6) I (8) _K cvB, tantan AZGe, NlY KvY Ges wbj KvYi gvb mgvb| Ze NlY KvY mechvR; wK wbj KvY aygv AvbZ Zji Rb chvR|MwZq NlY (Kinetic Friction) tKvb Zji Dci w`q MwZkxj e MwZi wei h evav Abyfe Ki ZvK MwZq NlY bv ej Ges h ej MwZZevavi mw Ki, ZvK MwZq NlY ej ej|MwZq NlY bv tMwZq NlY ej Ges Awfj^ cwZwqvi AbycvZK MwZq NlYbv ej| GK viv cKvk Kiv nq|Rfkk GLvb, fk = MwZq NlY ej I R Awfj^ cwZwqv|Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

46. c_g ci AsKi mgvavbFirst Paper Math Solution4| MwZm~ (Laws Of Motion)1| 10kg fii GKwU e`yKi wUMvi Pvc ÌqvZ e`yKi bjnZ 20g fii GKwU eyjU 400ms-1eM ei nq Mj|e`yKwUi cvr eM KZ?Avgiv Rvwb,m1v1 = m2v240010200v1 31 ev,104001020v31ev,(Ans.)0.8msv 112| 40kg I 60kg fii `ywU e h_vg 10ms-1I 5ms-1eM cii wecixZ w`K _K Avmvi mgq GK AciK avvw`j| avvi ci e q GK hy nq KZ eM Kvb w`K Pje?Avgiv Rvwb,m1u1+m2u2 = m1v1+m2v2ev, 4010+ 60(-5)= 40v + 60 vev, 400300 =100vev, 100v =100100100vev,ms1v 1 v abvZK nZz avvi ci e q GK hynq 1ms-1eM 1g ei AwfgyL Pje|3| GKwU e wi Avevq wQj| 15 wbDUbi GKwU ej Gi Dci 4mK wqv Kivi ci eji wqv e nq hvq| ewU Gi ci 4mK 48m `~iZ Mj| ewUi fi KZ?ej _vKv Kvjxb 4 mK ewU h kl eM jvf KimB kl eMK Mo eM wbq cieZx 4 mK ewU 48m `~iZhvq|Avgiv Rvwb,s = v t2tsv2ev,448v ev,ms12v -1Avevi,v = u + at1ev, 12 = 0 + a (4)412aev,a = 3 ms-2Avevi, F = maaFm ev,315m ev,(Ans.)kg5m 4| 10N Gi GKwU ej 2kg fii GKwU wi ei Dci wqv Ki| hw`4s ci eji wqv e` nq hvq Ze c_g _K 8s G ewU KZ `~ihve?ej _vKv Kvjxb 4 mK ewU h kl eM jvf KicieZx (8 4) = 4 mK mB kl eMK Mo eM wbq ewUPje|Avgiv Rvwb,F = m amFaev,210aev,-2ms5 a2111 at21uts Avevi,21 45210s m40s1 1-1ms20v450vtuv aAvevi,m80s420stvs2222Avevi,s = s1+s2 = (40+80)m =120m (Ans.)5| 100kg Ges 200kg fii `wU e cii wecixZ w`Kh_vg 20ms-1Ges 10ms-1eM hvIqvi c_ GK AciKavv w`j| avvi ci e `ywU GK hy _K KZ eM Kvbw`K Pje?Avgiv Rvwb,m1u1+m2u2 = m1v1+m2v2 10020+200(-10)=100v+200v 100v+200v =2000 2000 300v =0v = 0hnZz kl eM k~b dj e `ywU GK hy nq _g hve|GLvb,e`yKi fi, m1 = 10 kgeyjUi fi,m2 = 2010-3kgeyjUi eM, v2 = 400ms-1e`yKi cvr eM, v1 =?GLvb,1g ei fi, m1 = 40kg2q ei fi, m 2 = 60kg1g ei AvwèM, u1 = 10ms-12q ei AvwèM, u2 =-5ms-1hy eqi kl eM,v1 = v2 = v = ?GLvb,AvwèM, u = 0ej, F = 10 Nfi, m = 2 kgmgq, t1 = 4smgq, t2 = (84) s = 4sgvU `yiZ, s = s1+s2 = ?GLvb,AvwèM, u = 0ej, F = 15 Nmgq, t1 = 4smgq, t2 = 4skleM = MoeM = vmiY, s = 48mfi, m = ?GLvb,1g ei fi, m1 = 100kg2q ei fi, m2 = 200kg1g ei eM, u1 = 20 ms-12q ei eM, u2 = -10 ms-1GK hy eM v1=v2=v=?Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

47. 4| MwZm~ (Laws Of Motion) 26| 4 kg fii GKwU eK 10ms-2ZiY MwZkxj KiZ KZej cqvM KiZ ne? c_i Nlb ej 2.5N kg-1|Avgiv Rvwb,F1 = ma F1 = 410 NF1 = 40 NAvevi 4kg Z NlY ej F2= F 4 NF2= 2.5 4 N = 10 NAvevi, F = F1+F2F = (40+10)N=50N (Ans.)7| 70kg fii evK 500N AbyfywgK ej gSi Dci w`qUvbv nQ| evwU hLb Pj ZLb ev I gSi gaeZx NlY mnM0.5| evi ZiY wbYq Ki|Avgiv Rvwb,MZxq NlY mnM,RFkk RF kk 6865.0Fk N343Fk Avevi, F = P-Fk F =(500 343)N F =157 NAvevi, F = ma 157 = 70 a1ms70157 a(Ans.)ms24.2 2a8| 1N Gi GKwU ej 0.1kg fii GKwU wi ei Dci wqvKi| hw` 1s ci eji wqv e` nq hvq Ze c_g _K 2s GewU KZ `~i hve?ej _vKv Kvjxb 1 mK ewU h kl eM jvf KicieZx (2 1) = 1 mK mB kl eMK Mo eM wbq ewUPje|Avgiv Rvwb,F = m amFaev,0.11aev,-2ms01 a2111 at21uts Avevi,21 101210s m5s1 1-1ms10v1010vtuv aAvevi,m10s110stvs2222Avevi,s = s1+s2 = (5+10) m =15m (Ans.)9| 36 kg fii GKwU ei Dci KZ ej cqvM Kij 1 wgwbUGi eM 15kmh-1ew cve?Avgiv Rvwb,ej F=matuvmF)( NF60360010001536).(5.2 AnsNF 10| 36 kg fii GKwU ei Dci KZ ej cqvM Kij wgwbUGi eM NUvq 12km ew cve?Avgiv Rvwb,ej F=matuvmF)( NF60360010001236).(2 AnsNF GLvb,fi, m = 4 kgZiY, a = 10ms-2NlY ej, F =2.5 N kg-1ej, F = ?GLvb,MZxq NlY mnM 5.0k evi fi m = 70kgAwfj^ cwZwqv.R=mg=709.8N=686NAbyfywgK ej P=500Nevi ZiY a =?GLvb,Avw`eM, u = 0ej, F = 1 Nfi, m = 0.1 kgmgq, t1 = 1smgq, t2 = (21) s = 1sgvU `yiZ, s = s1+s2 = ?GLvb,fi, m =36 kgmgq, t = 1m=60seM ew,(v-u)=15kmh-13600100015 ms-1ej,F=?GLvb,fi, m =36 kgmgq, t = 1m=60seM ew,(v-u)=12kmh-13600100012 ms-1ej,F=?Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

48. 1| GKwU PvKvi fi 5kg Ges PMwZi evmva 25cm | GiRoZvi vgK KZ? PvKvwUK 4 rad s-2KwbK ZiY mw KiZKZ gvbi UK cqvM KiZ ne?Avgiv Rvwb,RoZvi vgKI = MK2= 5(0.25)2= 0. 3125 kg m2( Ans.)Avevi,UK 0. 3125 4 Nm=1.25Nm (Ans.)2| GKwU KYv 1.5m evmvai evKvi c_ cwZ wgwbU 120 eviAveZb Ki| Gi mij iwLK eM wbYq Ki|Avgiv Rvwb,v = rrtn2v ev,1.5601203.142v ev,Ans.)(ms18.84v 13| evKvi c_ 3.14ms-1mg`ywZZ AveZbiZ GKwU KYv cwZmK 10 wU c~b AveZb mb Ki| evKvi c_i evmva wbYqKi|Avgiv Rvwb,v = rrtn2v ev,n2v trev,103.14213.14rev,r 0.05m (Ans.)4| 13ms-1eM GKwU MvwoK wbivc` 30m evmvai GKwUeuvK AwZg KiZ nj euvKwUK KZ KvY Xvjy KiZ ne?Avgiv Rvwb,rgvtan219.83013tan21 0.57tan 1(Ans)29.89 5| GKwU Zvgvi MvjKi fi 0.05 Kg| GwUK 2m `xN GKwU myZviGK cv ea cwZ mK 5 evi Nyivb nQ| MvjKwUi KwbKfieM KZ?Avgiv Rvwb,RoZvi vgKI = MK2= 0.05(2)2= 0.2 kg-m2Avevi,tn 151432rad s-1= 31.4 rad s-1Avevi, L = IL =0.231.4 = 6.28 Kg-m2s-1(Ans.)6| evKvi c_ 72Kmh-1mg`ywZZ Pjgvb Kvb gvUi Mvoxi K`gyLxZiY 1ms-2nj evKvi c_i evmva KZ?Avgiv Rvwb,.)Ans(m400rr2201r2va7| 75m evmvai evKvi c_ Kvb gUi mvBKj Avivnx KZ eMNyij Dj^ Zji mv_ 30KvY AvbZ _vKe?Avgiv Rvwb,rgvtan 2rgtanv28.97503tanv28.97503tanv235.424v235.424v2)Ans(ms20.635.424v -1GLvb,fi, M = 5kgPMwZi evmva, K= 25cm=0.25mRoZvi vgK, I = ?KwbK ZiY, = 4 rad s-2UK, ?GLvb,iwLK `ywZ, v = 3.14ms-1mgq, t = 1 sec.cvK msLv, n = 10 cvKevmva, r =?GLvb,evmva, r = 1.5mmgq, t = 1 min = 60 sec.cvK msLv, n = 120 cvKiwLK eM, v =?GLvb,eM, v =13 ms-1evmva, r = 30mg = 9.8 ms-2KvY, =?GLvb,fi, M = 0.05 kgPMwZi evmva, K= 2mRoZvi vgK, I = ?cvKmsLv, n = 5mgq, t = 1 SecKwbK fieM, L =?GLvb,v = 72 Kmh-11-20ms3600100072 va = 1ms-2evmva, r = ?GLvb,evmva, r = 75mg = 9.8 ms-2KvY, =30eM, v =?Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

49. 5| KwbK MwZm~ (Laws Of Angular Motion) 28| 0.1kg fii GKwU cv_iK 0.5m j^v myZvi mvnvh evKvic_ Nyivb nQ| cv_iwU cwZwgwbU 30 evi c~Y NyYb mb Ki|myZvi Uvb KZ?Avgiv Rvwb,rmF 2rtn2mF2 N5.0603014.321.0F2 F = 0.49298 N (Ans.)9| cw_exi Pvwiw`K P`i Kc_i emva cvq 3.85105km|GKevi c`wb KiZ mgq jvM 27.3 w`b| Pv`i KwbK `wZwbYq Ki|Avgiv Rvwb,tn23600243.2711416.32.)Ans(rads1066.2 16 10| 200m evmva wewk GKwU euvKv c_ 50.4 km.h-1eM MvwoPvjvZ c_wUK KZ KvY KvZ Ki ivLZ ne? ivvwUi c 1m nj,evBii cvk wfZii cvk Acv KZ DuPz nZ ne? (g = 9.8 ms-2)Avgiv Rvwb,rgvtan219.820014tan21 0.1tan 1(Ans)71.5 1h71.5sin 1h0995.0 .)(1.00994.0 Ansmmh GLvb,fi, m = 0.1kgevmva, r = 0.5mcvKmsLv, n = 30mgq, t = 1 min= 60secmyZvi Uvb ej, F = ?GLvb,emva r=3.85105km=3.85108mmgq t= 27.3 w`bcvK msLv=1cvKKwbK `wZ =?GLvb,eM, -1kmh50.4=v1-ms3600100050.4=v-1ms14=vevmva, r = 200mg = 9.8 ms-2KvY, =?x=1m, h=?Want more Updates: https://www.facebook.com/tanbir.ebooksfacebook /gmail/skype: -tanbir.cox Web: http://tanbircox.blogspot.com

50. , W = F. S FS cos: : , p = : : : , : , - : W = k. , . : F. P. S Ft-poundal C. G. S erg M. K. S S.I Jole. = . . : Jol/sec watt.. : : [ML2T-2] : [ML2T-2] : [ML2T-3]. 25 27 . 0.143 H.P. 900 . 0 < < 900 900

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Intermediate physics 1st paper