Title 3. P1C3 HSC Prep Papers গতিবিদ্যা (With Solve) .pdf ✅

MwZwe` ̈v  HSC Prep Papers 1 MwZwe` ̈v Dynamics Z...Zxq Aa ̈vq Topicwise CQ Trend Analysis UwcK 2015 2016 2017 2018 2019 †gvU AwZμvšÍ `~iZ¡ I Mo‡eM msμvšÍ 2 1 2 1 1 7 †eM ebvg mgq †jLwPÎ Ñ 1 2 Ñ 1 4 Ae ̄ vb ebvg mgq †jLwPÎ Ñ 1 1 Ñ 1 3 cošÍ e ̄‧ 1 1 Ñ Ñ 1 3 wbw`©ó mg‡q cÖv‡mi †eM 4 3 4 1 7 19 Avbyf‚wgK cvjøv msμvšÍ 3 4 2 Ñ 2 11 DÇqbKvj msμvšÍ 2 4 3 Ñ 3 12 e„ËvKvi MwZ I †K›`agyLx Z¡iY Ñ Ñ 1 Ñ 2 3 *we.`a.: 2020-24 mvj ch©šÍ MwZwe` ̈v mswÿß wm‡jevm Gi AvIZvfz3 wQj bv| ̧iæZ¡c~Y© m„Rbkxj cÖ‡kœvËi 1| wμ‡KU †Ljvi gv‡V wicb e ̈vU w`‡q ej‡K AvNvZ Kivq ejwU 30 m/s †eM cÖvß nq Ges m‡e©v”P Avbyf‚wgK `~iZ¡ AwZμg K‡i| m‡1⁄2 m‡1⁄2 GKRb wdìvi K ̈vP aivi Rb ̈ 10 m/s †e‡M †`.o ïiæ K‡i Ges 40 m AwZμg K‡i| [g = 9.8 m/s2 ] (K) cÖv‡mi cvjøv Kx? [Xv. †ev. 19] (L) cÖv‡mi †ÿ‡Î †Kvb mg‡q †eM m‡e©v”P n‡e? e ̈vL ̈v `vI| [Xv. †ev. 19] (M) 2 s c‡i ejwUi †eM KZ? [Xv. †ev. 19] (N) ejwU gvwU‡Z covi Av‡M wdìvi K ̈vP ai‡Z †c‡i‡Q wKÑ bv? MvwYwZKfv‡e we‡køl‡Yi gva ̈‡g gZvgZ `vI| [Xv. †ev. 19] DËi: (K) Abyf‚wg‡Ki mv‡_ Zxh©Kfv‡e wbwÿß †Kv‡bv e ̄‧ Avw` D”PZvq wd‡i Avm‡Z †h mgq jv‡M, †mB mg‡q †mwU †h Avbyf‚wgK `~iZ¡ AwZμg K‡i Zv‡K cÖv‡mi cvjøv e‡j| (L) cÖv‡mi †ÿ‡Î ïiæ‡Z I †kl gyn~‡Z© †eM m‡e©v”P nq| KviY cÖv‡mi †ÿ‡Î Avbyf‚wgK Dcvsk vx = v0cos wbw`©ó Avi Djø¤^ Dcvsk vy = v0sin – gt cwieZ©bkxj Ges GwU mgq (t) Gi Dci wbf©ikxj| cÖv‡mi †ÿ‡Î ïiæ‡Z t = 0 nIqvq v0sin m‡e©v”P nq| Avevi, †kl gyn~‡Z© (f‚wg‡Z cZb ev AvNv‡Zi gyn~‡Z© †eM), vy = v0sin – gt = v0sin – g  2v0sin g     t = T = 2v0sin g = – v0sin A_©vr cÖv‡mi †ÿ‡Î †kl gyn~‡Z©I †e‡Mi gvb m‡e©v”P, Z‡e wecixZgyLx nq| myZivs cÖv‡mi †ÿ‡Î ïiæ‡Z I †kl gyn~‡Z© †eM m‡e©v”P nq| (M) Z_ ̈ Abyhvqx, mgqKvj, t = 2 s cÖvß †eM, v0 = 30 ms–1 †h‡nZz m‡e©v”P Avbyf‚wgK `~iZ¡ AwZμg K‡i, †m‡ÿ‡Î, wb‡ÿcY †KvY,  = 45 Avgiv Rvwb, cÖv‡mi ZvrÿwYK †eM, v = v 2 y + v 2 x = (v0sin – gt) 2 + (v0cos) 2  2s c‡i ejwUi †eM, = (30sin45 – 9.8  2) 2 + (30cos45) 2 = 2.60243 + 450 = 21.27 ms–1 (Ans.) (N) ejwU Zvi wePiYKvj, T Gi mgvb mgq a‡i k~‡b ̈ DÇqgb Av‡Q| GLv‡b, cÖv‡mi wb‡ÿcY †eM, v0 = 30 ms–1 wb‡ÿcY †KvY,  = 45 [∵ m‡e©v”P Avbyf‚wgK `~iZ¡] Avgiv Rvwb, T = 2v0sin g = 2  30sin45 9.8 = 4.33 s Avevi, wdìv‡ii †ÿ‡Î, s = vt  t = s v = 40 10 = 4 sec GLv‡b, wdìv‡ii †eM, v = 10 ms–1 wdìv‡ii AwZμvšÍ `~iZ¡, s = 40 m †h‡nZz, T > t A_©vr wdìvi hw` ej cZ‡bi ̄ vb n‡Z 40 m `~‡i _v‡K Z‡e, ejwU gvwU‡Z covi c~‡e©B wdìvi D3 ̄ v‡b †cu.‡Q hvIqvq gvwU‡Z covi Av‡M †m ejwU K ̈vP aiv m¤¢e| (Ans.)
2  HSC Physics 1st Paper Chapter-3 2| †jLwP‡Î GKwU Mvwoi hvÎvKvjxb cÖ_g 10 wgwb‡U †e‡Mi cwieZ©b †`Lv‡bv n‡q‡Q| A B C 0 2 4 6 8 10 t(min) v (m/s) 20 15 10 5 (K) †K›`agyLx Z¡i‡Yi †f±i iƒcwU †jL| [iv. †ev. 19] (L) evqycÖevn bv _vK‡jI GKRb mvB‡Kj Av‡ivnx evZv‡mi SvcUv Abyfe K‡ib †Kb? e ̈vL ̈v K‡iv| [iv. †ev. 19] (M) Mo †e‡Mi †fŠZ msÁvbyhvqx MvwowUi MwZKvjxb cÖ_g Pvi wgwb‡U Mo †eM wbY©q K‡iv| [iv. †ev. 19] (N) ÔMvwowUi 10 wgwb‡U AwZμvšÍ `~iZ¡ †jLwP‡Îi AšÍfz©3 †ÿ‡Îi †ÿÎd‡ji mgvbÕÑ Dw3wUi h_v_©Zv MvwYwZKfv‡e we‡kølY K‡iv| [iv. †ev. 19] DËi: (K) †K›`agyLx Z¡i‡Yi †f±ii~c: a  = –  2 r  = – v 2 r 2 r  GLv‡b ( – ) wPý †_‡K †`Lv hvq †K›`agyLx Z¡i‡Yi w`K e ̈vmva© †f±i Z_v Ae ̄ vb †f±‡ii wecixZ w`‡K A_©vr e ̈vmva© eivei †K‡›`ai w`‡K| (L) hLb mvB‡Kj Av‡ivnx MwZkxj nq, ZLb evqycÖevn bv _vK‡jI MwZkxj mvB‡Kj Av‡ivnxi mv‡c‡ÿ w ̄ i evqy Avi w ̄ i _v‡K bv, mvB‡Kj Av‡ivnxi mv‡c‡ÿ evqyi Av‡cwÿK †eM m„wó nq Av‡ivnxi wecix‡Z| d‡j Av‡ivnx evZv‡mi SvcUv Abyfe K‡i| D`vniY ̄^iƒc: PjšÍ iv ̄Ív OB c‡_ Pjgvb mvB‡Kj Av‡ivnxi Dci QO c‡_ e„wói SvcUv co‡e| †Kbbv Av‡cwÿK †eM wμqv K‡i| vR (e„wói †eM) B (e ̈w3i †eM) Q O (M) MvwowU 1g 2 min G mgZ¡i‡Y P‡j| Gmgq AwZμvšÍ `~iZ¡ s1 n‡j, s 1 =     u + v 2 t1 =     0 + 10 2 ×120 = 600m GLv‡b, †eM, v = 10 ms1 mgq, t1 = 2 min = 120s MvwowUi cieZ©x 2min G 10 ms1 mg‡e‡M AwZμvšÍ `~iZ¡ s2 n‡j, s2 = vt2 = 10 × 120 = 1200m  Mo‡eM vavg n‡j, vavg = s t = s1 + s2 t1 + t2 = 600 + 1200 120 + 120  vavg = 7.5 ms1 (Ans.) GLv‡b, Avw`‡eM, u = 0 ms1 †kl‡eM, v = 10 ms1 mgq, t2 = 2 min = 2 × 60s = 120s (N) ÔMÕ n‡Z cvB, OA As‡k AwZμvšÍ `~iZ¡, s1 = 600 m AB Ges As‡k MvwowU v = 10 ms1 mg‡e‡M t2 = 8  2 = 6 min P‡j| G mgq AwZμvšÍ `~iZ¡ s2 n‡j, s2 = vt2 = 10 × 360 = 3600m GLv‡b, mg‡eM, v = 10 ms1 mgq, t2 = 6 min = 6 × 60 s = 360 s Avevi, BC As‡k MvwowU u = 10ms1 Avw`‡eM wb‡q mgZ¡i‡Y t3 = 10  8 = 2 min P‡j 15 ms1 †kl‡eM cÖvß nq| G mgq AwZμvšÍ `~iZ¡ s3 n‡j, s3 =     u + v 2 t3 = 10 + 15 2 × 120 = 1500m GLv‡b, Avw`‡eM, u = 10 ms1 †kl‡eM, v = 15 ms1 mgq, t3 = 2 min = 2 × 60= 120s  †gvU AwZμvšÍ `~iZ¡, s = s1 + s2 + s3 = 600 + 3600 + 1500 = 5700m A B C O D X 4 6 8 10 E 15 10 5 v (m/s) 2 F t(×60s) Avevi wP‡Î, †jLwP‡Îi AšÍfz©3 †ÿ‡Îi †ÿÎdj n‡jv OABE UavwcwRqvg I BCFE UavwcwRqv‡gi †ÿÎd‡ji †hvMd‡ji mgvb| GLb, OABE UavwcwRqv‡gi †ÿÎdj = 1 2 (AB + OE) × AD = 1 2 (6 × 60 + 8 × 60) × 10 = 4200m Ges BCFE UavwcwRqv‡gi †ÿÎdj = 1 2 (BE + CF)× EF = 1 2 (10 + 15) × 2 × 60 = 1500 m  †jLwP‡Îi AšÍfz©3 †ÿ‡Îi †ÿÎdj = 4200 + 1500 = 5700 m hv AwZμvšÍ `~iZ,¡ s = 5700 m Gi mgvb| (Ans.) 3| GKwU evm Pj‡Z ïiæ Kivi mv‡_ mv‡_ ev‡mi 16m wcQb †_‡K GKRb hvÎx evmwU aivi Rb ̈ †`u.o †`q| hvÎx I ev‡mi mgq ebvg †eM †jLwPÎ wb‡P †`Iqv nj: 0 1 3 6 mgq (s)  †eM (ms 1 ) 10 8 6 4 2 2 4 5 6 wPÎ: ev‡mi †eM ebvg mgq †jLwPÎ 0 1 3 6 mgq (s)  †eM (ms 1 ) 10 8 6 4 2 2 4 5 6 wPÎ: hvÎxi †eM ebvg mgq †jLwPÎ
MwZwe` ̈v  HSC Prep Papers 3 (K) j¤^ Z¡iY Kv‡K e‡j? (L) cÖwZcv`b Ki   =    r  (M) evmwU KZ...©K 4 s-G AwZμvšÍ `~iZ¡ wbY©q K‡iv| [Kz. †ev. 19] (N) DÏxc‡Ki hvÎx evmwU ai‡Z cvi‡e wK? MvwYwZK we‡kølYmn gZvgZ `vI| [Kz. †ev. 19] DËi: (K) e„ËvKvi c‡_ MwZkxj e ̄‧i †K‡›`aiw`‡K †h Z¡iY wμqv K‡i Zv‡K †K›`agyLx Z¡iY ev j¤^ Z¡iY e‡j| (L) g‡b Kiv hvK, r  e ̈vmv‡a©i e„ËvKvi c‡_ MwZkxj GKwU e ̄‧ KYvi •iwLK †eM r mgq v1  †_‡K cwiewZ©Z n‡q v2  nj Ges IB GKB mg‡q †K.wYK †eM 1  cwiewZ©Z n‡q 2  nj|  v1 = 1   r  Ges v2  = 2   r  myZivs •iwLK Z¡iY, a  = v2  – v1  t = 2   r  – 1   r  t = 2   1  t  r  Avevi, †K.wYK Z¡iY,   = 2   1  t  a  =    r  (M) DÏxc‡Ki ev‡mi mgq-†eM †jLwPÎ †_‡K cvB| Avw`‡eM, v0 = 0 ms1 4s ci †eM,v = 8 ms1 mgqKvj, t = 4 sec AwZμvšÍ `~iZ¡, s = ? AwZμvšÍ `~iZ¡, s = v + v0 2 t = 8 + 0 2 × 4 = 16 m (Ans.) (N) DÏxc‡Ki hvÎxi mgq-‡eM †jLwPÎ †_‡K †`Lv hvq, hvÎxwU evmwU‡K aivi Rb ̈ mg‡e‡M †`.ovw”Qj Ges D3 mg‡e‡Mi gvb, vp = 8 ms1 g‡b Kwi, evmwUi Avw` Ae ̄ vb n‡Z x m `~‡i t mgq ci †jvKwU evmwU‡K ai‡Z cvi‡e| 16 m B x m A C 8 ms1 v0 = 0 ms2 a = 2 ms2 myZivs, hvÎxi AwZμvšÍ `~iZ¡, 16 + x = vp.t  16 + x = 8t ......... (i) t mg‡q ev‡mi AwZμvšÍ `~iZ¡, x = vb 0 t + 1 2 ab t 2  x = 0 × t + 1 2 × 2 × t2  x = t2 ......... (ii) evmwUi Z¡iY, ab = vv0 t = 8  0 4 = 2ms–2 vb 0 = 0 ms1 mgqKvj = t (i) bs I (ii) bs mgxKiY †_‡K cvB, 16 + t 2 = 8t  t 2  8t + 16 = 0  (t)2  2.t.4 + (4)2 = 0  (t  4)2 = 0  t  4 = 0  t = 4 s GLb, (ii) bs mgxKiY †_‡K cvB, x = (4)2 = 16 m GLv‡b, t I x Gi ev ̄Íe gvb cvIqv †M‡Q| myZivs, D3 hvÎxwU 4s G Zvi Avw` Ae ̄ vb n‡Z (8 × 4) = 32 m †`.ov‡bvi ci evmwU‡K ai‡Z cvi‡e Ges D3 mg‡q evmwU 16m `~iZ¡ AwZμg Ki‡e| (Ans.) 4| weÁvb †gjv‡K AvKl©Yxq Kivi Rb ̈ cÖ‡ekc‡_i `yÕcv‡k cvwbi †dvqviv ̄ vcb Kiv n‡jv| Zv‡`i g‡a ̈ GKwUi cvwbi †dvuUv ̧‡jv 5 ms1 †e‡M Ges 60° †Kv‡Y Qwo‡q co‡Q| Aci †dvqvivi cvwbi †duvUv ̧‡jv 6ms1 †e‡M Ges 30° ‡Kv‡Y Qwo‡q co‡Q| (K) cÖ‡ÿcK Kv‡K e‡j ? [P. †ev.19] (L) e„ËKvi Ua ̈v‡K †Kv‡bv †`uŠowe` mg‡e‡M †`Šov‡Z cv‡i bv †Kb? e ̈vL ̈v K‡iv| [P. †ev.19] (M) 0.6 sec mg‡q 1g †dvqvivi cvwbi †duvUvi †eM wbY©q K‡iv| [P. †ev.19] (N) DÏxc‡Ki †Kvb †dvqvivi cvwbi †duvUv ̧‡jv †ewk AÂj Ry‡o Qwo‡q co‡e? MvwYwZKfv‡e we‡kølY K‡iv| [P. †ev.19] DËi: (K) AwfK‡l©i cÖfv‡e k~b ̈ ̄ v‡b f~wgi mv‡_ Zxh©Kfv‡e wbwÿß e ̄‧‡K cÖwÿß e ̄‧ ev cÖvm e‡j| (L) †e‡Mi gvb I w`‡Ki †h‡Kv‡bv GKwUi cwieZ©b n‡jB †mwU Amg‡eM n‡e| e„ËvKvi c‡_ Pjgvb †Kv‡bv e ̄‧i †e‡Mi gv‡bi cwieZ©b bv n‡jI w`‡Ki cwieZ©b nq| KviY, e„ËvKvi c‡_ Pjgvb †Kv‡bv e ̄‧i †e‡Mi w`K nq H we›`y‡Z ̄úk©K eivei| GLb, e„‡Ëi cÖwZwU we›`yi Rb ̈ ̄úk©‡Ki w`K wfbœ| myZivs e ̄‧i †e‡Mi w`K cÖwZwbqZ cwiewZ©Z n‡Z _v‡K| GKvi‡Y e„ËvKvi Uav‡K †Kvb †`.owe` mg‡e‡M †`.ov‡Z cv‡i bv| (M) †dvqviv n‡Z wbM©Z nIqvi t = 0.60 ci 1g †dvqvivi cvwbi †duvUvi AbyfywgK I Djø¤^ †eM h_vμ‡g vx I vy n‡j, vx = vx0 = V0 cos0 = 5 cos60° = 2.5 ms1 GLv‡b, wb‡ÿcY †Kvb, 0 = 60° AwfKl©R Z¡iY, g = 9.8 ms2 mgq, t = 0.6s Ges wb‡ÿcY †eM, v0 = 5 ms–1
4  HSC Physics 1st Paper Chapter-3 Avevi, vy = v0 y  gt = v0 Sin0  gt = 5 × sin60°  9.8 × 0.6 =  1.55 ms1  t = 0.6 ci cvwbi †duvUvi †eM v n‡j, v = vx 2 + vy 2 = (2.5) 2 + (1.55) 2 = 2.94 ms1 Abyf~wg‡Ki mv‡_ cvwbi †duvUvi †eM  †KvY Drcbœ Ki‡j,  = tan1 vy vx = tan1     1.55 2.5 =  31.8° A_©vr, D3 gyn~‡Z© 1g †dvqvivi cvwbi †duvUv Abyf~wg‡Ki mv‡_ 31.80° †Kv‡Y wb‡Pi w`‡K 2.94 ms1 †e‡M MwZkxj| (Ans.) (N) GLv‡b, cÖ_g †dvqvivi cvwbi †duvUvi wb‡ÿcY †eM, v0 1 = 5 ms1 Ges wb‡ÿcY †KvY, 0 1 = 60° wØZxq †dvqvivi cvwbi †duvUvi wb‡ÿcY †eM, v0 2 = 6 ms1 Ges wb‡ÿcY †KvY, 0 2 = 30° cÖ_g I wØZxq †dvqvivi cvwbi †duvUv h_vμ‡g R1 I R2 ch©šÍ Abyf~wgK `~iZ¡ AwZμg Ki‡j, R1 R2 = v 0 2 1 sin20 1 /g v 0 2 2 sin20 2 /g = 5 2 ×sin(2×60°) 6 2 × sin(2 × 30°) = 0.694  R1 R2 < 1  R1 < R2 A_©vr, wØZxq †dvqvivi cvwbi †duvUv ̧‡jv cÖ_gwU A‡cÿv †ewk AÂj Ry‡o Qwo‡q co‡e| (Ans.) 5| GKw`b GK cÖxwZ g ̈vP †Ljvi mgq wcÖZg e ̈vU w`‡q AvNvZ Kivq ejwU cvk¦©eZ©x GKwU DuPz fe‡bi Qv‡` coj| Wv3v‡ii wb‡la _vKvq wcÖZg 96m Gi †ewk DuPz‡Z DV‡Z A ̄^xK...wZ Rvwb‡q Qv‡` ej Avb‡Z †Mj bv| cøveb Qv‡` D‡V ejwU‡K Djø‡¤^ mv‡_ 60° †Kv‡Y 5 ms1 †e‡M wb‡P †d‡j w`j| ejwU Quy‡o gvivi 3 sec c‡i f~wg †_‡K 2 m DuPz‡Z wcÖZg ejwU a‡i †djj| (K) wbU ej Kx? [wm. †ev. 19] (L) fi‡K RvW ̈fi ejv nq †Kb? e ̈vL ̈v K‡iv| [wm. †ev. 19] (M) ejwU KZ †e‡M wcÖZ‡gi nv‡Z AvNvZ K‡iwQj? [wm. †ev. 19] (N) DÏxc‡Ki Z_ ̈ Abymv‡i wcÖZg Qv‡` DU‡Z cviZ wK bv? MvwYwZK we‡køl‡Yi gva ̈‡g †Zvgvi gZvvgZ `vI| [wm. †ev. 19] DËi: (K) †Kv‡bv we›`y‡Z wμqviZ GKvwaK e‡ji †f±i †hvMdjB n‡jv D3 we›`y‡Z wbU ej ev jwä ej| (L) †Kv‡bv e ̄‧i ga ̈Kvi †gvU c`v‡_©i cwigvY‡K Gi fi e‡j| fi `yB cÖKvit AwfKl©xq fi I RvW ̈fi| `vwocvjøv ev wbw3i mvnv‡h ̈i Avgiv †h fi gvwc, †mwU n‡jv AwfKl©xq fi| wKš‧ †h ̄ v‡b AwfKl© †bB (†hgb: gnvk~b ̈hv‡b), †mLv‡b AwfKl©xq f‡ii welqwU AKvh©Ki n‡q c‡o| ZLb e ̄‧i fi gvcv nq F = ma m~Î e ̈envi K‡i; A_©vr, †Kv‡bv e ̄‧‡Z wbw`©ó gv‡bi ej cÖ‡qvM K‡i G‡Z m„ó Z¡iY gvcv nq| ZLb F I a Gi Abycv‡Zi Øviv e ̄‧i RvW ̈fi gvcv nq| Z‡e †h‡Kv‡bv e ̄‧i •ewkó ̈ Ggb †h, Gi AwfKl©xq fi I RvW ̈fi me©`v mgvb nq| ZvB fi‡K RvW ̈fi ejv nq| (M) ejwU wb‡ÿc‡Yi t = 3s c‡i †e‡Mi Avbyf~wgK I Djø¤^ Dcvsk h_vμ‡g vx I vy n‡j, 60 30 2 m vx = vx 0 = v0 cos0 = 5 cos (30°) = 4.33 ms1 vy = v0sin0 + gt GLv‡b, Avw`‡eM, v0 = 5 ms1 wb‡ÿcY †Kvb, 0 = (90°  60) = 30 = – 5 sin 30 + 9.8  3 = 26.9 ms–1  v = v 2 x + v2 y = (4.33) 2 + (26.9) 2 = 27.25 ms–1  ejwU wcÖZ‡gi nv‡Z 27.25 ms–1 †e‡M AvNvZ K‡iwQ‡jv| (Ans.) (N) ejwUi 3 s G AwZμvšÍ Djø¤^ `~iZ¡ y n‡j, y = – v0 sin0t + 1 2 gt2 = – 5 sin 30  3 + 1 2  9.8  3 2 = 36.6 m †h‡nZz wcÖZg ejwU‡K 3s ci f‚wg †_‡K 2 m D”PZvq a‡i, d‡j f‚wg n‡Z fe‡bi D”PZv (36.6 + 2) = 38.6 m AZGe, wcÖZg Qv‡` DV‡Z cvi‡Zv| (Ans.) 6| O v0 = 30ms1 P M X Y 0 = 40 H m‡e©v”P we›`y f~wg †_‡K v0 MwZ‡Z GKwU e ̄‧ 0 †Kv‡Y wb‡ÿc Kiv n‡jv| f~wg †_‡K e ̄‧wUi m‡e©v”P D”PZv HP|