Title 5. Phy.-1st-Paper-For-FRB-2024_With Solve- Ridoy 11.01.25- OK.pdf ✅

KvR, kw3 I ÿgZv  Final Revision Batch 1 cÂg Aa ̈vq KvR, kw3 I ÿgZv Work, Energy and Power Topicwise CQ Trend Analysis UwcK 2016 2017 2018 2019 2021 2022 2023 2024 †gvU KvR I kw3 Ñ 2 Ñ 4 2 Ñ 1 1 10 MwZkw3 1 Ñ Ñ Ñ Ñ Ñ 2 Ñ 3 w ̄’wZkw3 ev wefe kw3 Ñ Ñ Ñ 3 Ñ Ñ Ñ 3 6 kw3i wbZ ̈ZvbxwZ ev msiÿYkxjZv Ñ Ñ 1 3 3 4 Ñ Ñ 11 ej I miY Ñ Ñ Ñ 1 Ñ 1 3 Ñ 5 cv¤ú, ÿgZv, Kg©`ÿZv 1 1 1 3 10 3 5 5 29 AwfKl© e‡ji weiæ‡× KvR Ñ Ñ Ñ 1 Ñ 1 1 Ñ 3 MwZ‡eM wbY©q 1 1 Ñ Ñ Ñ 1 Ñ Ñ 3 myZvi Uvb 2 Ñ Ñ Ñ Ñ Ñ Ñ Ñ 2 * we.`a.: 2020 mv‡j GBPGmwm cixÿv AbywôZ nqwb| weMZ mv‡j †ev‡W© Avmv m„Rbkxj cÖkœ 1| Nl©Ynxb Abyf‚wgK Z‡ji Dci GKwU `„p Ae ̄’vb †_‡K GKwU w ̄úas Gi GK cÖvšÍ AvUwK‡q Aci cÖv‡šÍ ej cÖ‡qvM K‡i 5cm msKzwPZ K‡i †Q‡o †`qv n‡jv| G‡Z w ̄úaswU Avw` Ae ̄’vq wd‡i Avmj| [w ̄úas aaæeK K = 120 Nm–1 ] [g. †ev. 24] (K) msiÿYkxj ej Kx? (L) ej I miY ïb ̈ bv n‡jI KvR ïb ̈ n‡Z cv‡i wK? e ̈vL ̈v Ki| (M) w ̄úaswU 2.5cm cÖmvwiZ Ki‡j G‡Z mwÂZ wefe kw3 wbY©q Ki| mgvavb: w ̄úas-G mwÂZ wefekw3, U  1 2 kx2 = 1 2  120  (2.5  10–2 ) 2  U  0.0375 J myZivs, w ̄úas-G mwÂZ wefekw3 0.0375 J| (Ans.) (N) DÏxc‡K w ̄úas ejwU wK msiÿYkxj ej? MvwYwZKfv‡e e ̈vL ̈v Ki| mgvavb: g‡b Kwi, x Aÿ eivei w ̄úaswUi m¤úamviY x n‡j w ̄úas-G Drcbœ cÖZ ̈qbx ej F,  †f±iiƒ‡c, F   – kx i ^ [k  w ̄úaswUi w ̄úas aaæeK] Avgiv Rvwb, †Kv‡bv ej F  Gi Kvj© k~b ̈ n‡j ejwU GKwU msiÿYkxj ej nq,     F         i ^ j ^ k ^  x  y  z – kx 0 0  i ^ (0 – 0) – j ^ (0 – 0)  k ^ (0 – 0)  i ^ 0  j ^ 0  k ^ 0  0      F   0  myZivs, DÏxc‡Ki w ̄úas ejwU msiÿYkxj ej| (Ans.) 2| GKwU cvwbi U ̈vs‡Ki MfxiZv 20 m Ges e ̈vm 4 m| U ̈vsKwU‡K cvwbk~b ̈ Kivi Rb ̈ GKwU cv¤ú jvMv‡bv n‡jv| cv¤úwU Pvjy Kivi 10 wgwbU ci U ̈vs‡Ki GK PZz_©vsk Lvwj K‡i cv¤úwU bó n‡q †M‡jv| c‡i Ab ̈ Av‡iKwU cv¤ú Øviv U ̈vs‡Ki evwK cvwb k~b ̈ Kiv n‡jv| [cvwbi NbZ¡ 1000 kg m–3 ] [Xv. †ev. 24] (K) Kg© `ÿZv Kx? (L) w ̄úas Øviv K...Z KvR FYvZ¥K nq †Kb? (M) cÖ_g cv¤úwUi ÿgZv wbY©q Ki| mgvavb: GLv‡b, U ̈vs‡Ki GK-PZz_©vsk cvwbi fi, m  1 4  AvqZb  NbZ¡ = 1 4  r 2 h    m  1 4  1000    2 2  20  62831.85 kg GK-PZz_©vsk cvwbi fi‡K‡›`ai miY, h  0  20 4 2  h  2.5 m 2.5 5 15  cv¤úwUi ÿgZv, P  mgh t  P  62831.85  9.8  2.5 10  60 W  P  2565.633 W myZivs, cÖ_g cv¤úwUi ÿgZv 2565.633 W  2565.633 746 HP  3.44 HP (Ans.) (N) DÏxc‡Ki wØZxq cv¤úwU hw` evwK U ̈vs‡Ki cvwb 20 wgwb‡U k~b ̈ Ki‡Z cv‡i Zvn‡j Dfq cv‡¤úi g‡a ̈ †KvbwUi Ak¦ÿgZv †ewk MvwYwZKfv‡e hvPvB K‡i| mgvavb: ÔMÕ n‡Z cvB, cÖ_g cv‡¤úi ÿgZv, P1  2565.633 W  2565.633 746 HP = 3.44 HP
2  HSC Physics 1st Paper Chapter-5 wØZxq cv‡¤úi †ÿ‡Î, wZb-PZz_©vsk cvwbi fi, m  3 4 v  3 4 r 2 h  m  3 4  1000    2 2  20  m  188495.56 kg fi‡K‡›`ai miY, h  20 4  20 2  h  12.5 m 12.5 m 5m 15m  wØZxq cv‡¤úi ÿgZv, P2  mgh t  188495.56  9.8  12.5 20  60 W  19242.255 W  19242.255 746 HP  P2 = 25.8 HP  P2 > P1 myZivs, Dfq cv‡¤úi g‡a ̈ wØZxq cv‡¤úi Ak¦ÿgZv †ewk| (Ans.) 3| A I B `ywU cvwbc~Y© Kzqv hv‡`i MfxiZv h_vμ‡g 12m I 10m Ges e ̈vm h_vμ‡g 1.8m I 2m| X I Y `ywU cv¤ú hv‡`i Kg©`ÿZv h_vμ‡g 70% I 60%| X cv¤úwU A Kzqv‡K 24 wgwb‡U cvwbk~b ̈ Ki‡Z cv‡i| Y cv‡¤úi ÿgZv 2.4 H.P| [iv. †ev. 24; Abyiƒc e. †ev. 24] (K) MwZkw3 Kv‡K e‡j? (L) k~b ̈ KvR e ̈vL ̈v Ki| (M) X cv¤úwUi ÿgZv wbY©q Ki| mgvavb: GLv‡b, A Kzqvi m¤ú~Y© cvwbi fi, m  V  r 2 h  1000    0.92  12  30536.28 kg fi‡K‡›`ai miY, h  0 + h 2  12 2  h = 6m  X cv¤úwUi jf ̈ Kvh©Ki ÿgZv, Pout  mgh t  30536.28  9.8  6 24  60  1246.89 W Avgiv Rvwb,   Pout Pin  Pin  Pout   1246.89 0.7  Pin  1781.27 W myZivs, X cv¤úwUi cÖK...Z ÿgZv 1781.27 W (Ans.) (N) X I Y cv¤ú Øviv B Kzqv‡K GKB mg‡q cvwbk~b ̈ Kiv hv‡e wK-bv? MvwYwZKfv‡e we‡kølYc~e©K gZvgZ `vI| mgvavb: B Kzqvi m¤ú~Y© cvwbi fi, m  V  r 2 h  1000    1 2  10  31415.92 kg fi‡K‡›`ai miY, h  0 + h 2  10 2  5 m Y cv¤úwUi jf ̈ Kvh©Ki ÿgZv, Pout  mgh t1 ......(i) Avgiv Rvwb,   Pout Pin    Pin  mgh t1 [(i) n‡Z]  t1  31415.92  9.8  5 0.6  2.4  746  1433 s  t1  23.88 min Avevi, ÔMÕ n‡Z cvB, X cv‡¤úi jf ̈ Kvh©Ki ÿgZv, P out  1246.89 W  P out  mgh t2  t2  31415.92  9.8  5 1246.89  t2  1234.576 s  t2  20.58 min  t1  t2 myZivs, X I Y cv¤ú Øviv B Kzqv‡K GKB mgq cvwbk~b ̈ Kiv hv‡e bv| (Ans.) 4| wP‡Îi MvwowUi fi 3000 kg Ges ÿgZv 152.18 kW, [g = 9.8 ms–2 ] [h. †ev. 24] 15 (Nl©Y D‡cÿYxq) A C B 500 m (K) Ak¦ ÿgZv Kv‡K e‡j? (L) cÖ`Ë kw3 I Kvh©Ki kw3i e ̈eavb †ewk n‡j h‡š¿i `ÿZv Kg n‡eÑ e ̈vL ̈v Ki| (M) MvwowU A n‡Z B †Z †h‡Z K...Z Kv‡Ri cwigvY wbY©q Ki| mgvavb: Avgiv Rvwb, K...ZKvR, W  ej  e‡ji Awfgy‡L mi‡Yi Dcvsk  mgsin  s  3000  9.8  sin(15)  500  3.804  106 J myZivs, MvwowU A n‡Z B †Z †h‡Z K...ZKv‡Ri cwigvc 3.804  106 J| (Ans.) (N) ÒAB iv ̄Ív eivei MvwowUi †eM 72 kmh–1 mxgv AwZμg Kiv m¤¢e bqÓÑ MvwYwZKfv‡e Dw3wUi mZ ̈Zv hvPvB Ki| mgvavb: Avgiv Rvwb, ÿgZv, P  W t = mgh t  P  mgABsin15 t  P = mgsin15  AB t  P = mgsin15  v  v = P mgsin15  v = 152.18  103 3000  9.8  sin15  v = 20ms–1 = 20  3600 1000 kmh–1 GLv‡b, Mvwoi fi m = 3000 kg ÿgZv, P = 152.18 kW = 152.18  103 W D”PZv, h = ABsin15 B A C h 15  v = 72 kmh–1 myZivs, ÒAB iv ̄Ív eivei MvwowUi †eM 72 kmh–1 mxgv AwZμg Kiv m¤¢e bqÓÑ Dw3wU h_v_©| (Ans.)

4  HSC Physics 1st Paper Chapter-5 (M) P we›`y †_‡K Q we›`y‡Z †cu.Qv‡Z K...Z Kv‡Ri cwigvY wbY©q Ki| mgvavb: Avgiv Rvwb, K...ZKvR, W  ej  e‡ji Awfgy‡L mi‡Yi Dcvsk  mgsin  s  70  9.8  sin35  5  1967.36 J myZivs, P we›`y n‡Z Q we›`y‡Z †cuŠQv‡Z K...ZKv‡Ri cwigvY 1967.36 J. (Ans.) (N) †Kvb c‡_ †m Kg ÿgZv e ̈‡q Q we›`y‡Z †cu.Qv‡Z cvi‡e? MvwYwZK e ̈vL ̈v `vI| mgvavb: POQ G, sin35  QO PQ  QO  5sin35 Avevi, QOR G, sin55  QO QR Q P O 35 5m 55 R  QR  QO sin55  5sin35 sin55  3.5 m awi, PQ I QR c_ e ̈env‡i h_vμ‡g t1 I t2 mgq jv‡M| PQ      u + 0 2 t1 .....(i) QR      u + 0 2 t2 .....(ii) GLb, (ii)  (i) K‡i, t2 t1  QR PQ  3.5 5  0.7 Ges PQ c‡_ e ̈wqZ ÿgZv, P1  mg  QO t1 .....(iii) RQ c‡_ e ̈wqZ ÿgZv, P2  mg  QO t2 .....(iv) Avevi, (iii)  (iv) K‡i, P1 P2  t2 t1  0.7      t2 t1  0.7  P1 P2 < 1  P1 < P2 myZivs, PQ c‡_ †m Kg ÿgZv e ̈‡q Q we›`y‡Z †cuŠQv‡e| (Ans.) 8| GKwU cvwbc~Y© Kzqvi MfxiZv 15 m I e ̈vmva© 1 m| KzqvwU cvwbk~b ̈ Kivi Rb ̈ 6 HP ÿgZvi GKwU cv¤ú jvMv‡bv n‡jv| A‡a©K cvwb DVv‡bvi ci cv¤úwU bó n‡q †Mj| evwK cvwb †Zvjvi Rb ̈ GKB ÿgZvm¤úbœ Av‡iv GKwU cv¤ú jvMv‡bv nj| [Xv. †ev. 23] (K) RoZvi åvgK Kv‡K e‡j? (L) †Kv‡bv e ̄‘i MwZkw3i mv‡_ fi‡e‡Mi m¤úK© †jLwP‡Îi mvnv‡h ̈ e ̈vL ̈v K‡iv| (M) cÖ_g cv‡¤úi Øviv K...ZKvR wbY©q K‡iv| mgvavb: cÖ_g cv‡¤úi Øviv K...ZKvR, W1 = mgh h = fi‡K‡›`ai miY = r 2h 2   g  h 4 = 3.1416  1  15 2  9.8  15 4  1000 = 865903.5 J (Ans.) (N) cv¤ú `ywU Øviv cvwb Zzj‡j mgq GKB jvM‡e wK? MvwYwZK we‡kølY Ki| mgvavb: 1g cv¤úwUi †ÿ‡Î, P = mgh t1  t1 = 86590.5 6  746  t1 = 193.45 s 2q cv¤úwUi †ÿ‡Î K...ZKvR, W2 = mgh = r 2 h 4  g      h 2 + h 4 = 2597710.5  t2 = 2597710.5 6  746 = 580.36 s h 2 h 2  cv¤ú 2wU Øviv cvwb Zzj‡Z GKB mgq jvM‡e bv| (Ans.) 9| [iv. †ev. 23] Aa = 4ms –2 m = 20 kg a = 4ms–2 C B m = 20 kg 45 20 kg f‡ii GKwU e ̄‘‡K wPÎvbyhvqx A we›`y †_‡K B we›`y‡Z DVv‡bv n‡jv| GKB f‡ii Aci GKwU e ̄‘‡K C †_‡K B we›`y‡Z †bqv n‡jv| (K) msiÿYkxj ej Kv‡K e‡j? (L) miY ebvg MwZkw3i †jLwP‡Îi XvjwU ej wb‡`©k K‡iÑ e ̈vL ̈v Ki| (M) cÖ_g †ÿ‡Î Kv‡Ri cwigvY wbY©q Ki| mgvavb: WAB = Fh = m  (g + a)  h = 20  (9.8 + 4) h = 276 h (Ans.) (N) cÖ_g I wØZxq †Kvb †ÿ‡Îi e ̄‘wU‡K wb‡q hvIqv mnR n‡q‡Q? MvwYwZKfv‡e †`LvI| mgvavb: A gsin45 C B 45 h gcos45 45 g C n‡Z B we›`y‡Z e ̄‘wU‡K Avbvi †ÿ‡Î, Kvh©Ki Z¡iY, g = gsin 45 + a = 10.93 ms–2 Avevi, CB = h sin45 = 1.41421 h  WCB = 20  10.93  1.41142 h = 309.1470 h  1g e ̄‘wU‡K wb‡q hvIqv mnR n‡q‡Q| (Ans.)