Title 6. P1C6. Phy. For FRB-2024_With Solve_Ridoy- 12.01.25 - OK.pdf ✅

gnvKl© I AwfKl©  Final Revision Batch 3 (N) Dfq e ̄‘ wbR MÖn c„ô n‡Z mgvb D”PZvq DV‡Z cvi‡e wK? MvwYwZKfv‡e we‡kølY Ki| mgvavb: Avgiv Rvwb, Lvov Dc‡ii w`‡K wbwÿß e ̄‘i m‡e©v”P D”PZv, h = u 2 2g  wbw`©ó †e‡M wbwÿß e ̄‘i †ÿ‡Î, h  1 g AZGe, h1 h2 = g2 g1 = M2 M1  R 2 1 R 2 2     g  M R 2 = 1 8      169 98 2 [ÔMÕ n‡Z cÖvß ] = 0.372  h1 = 0.372  h2 myZivs Dfq e ̄‘ wbR MÖn c„ô n‡Z mgvb D”PZvq DV‡Z cvi‡e bv| (Ans.) 5| GKwU DcMÖn c„w_ex‡K 12 NÈvq e„ËvKvi c‡_ cwiågY Ki‡Z cv‡i| c„w_exi e ̈vmva© 6400 km Ges g = 9.8 ms–2 | [w`. †ev. 24] (K) cvwK©s Kÿc_ Kv‡K e‡j? (L) B ̄úv‡Zi KvwV‡b ̈i ̧YvsK 7.8  1012 Nm–2 ej‡Z Kx eyS? (M) c„w_exi †K›`a n‡Z DcMÖnwU KZ D”PZvq Ae ̄’vb KiwQj wbY©q Ki| mgvavb: Avgiv Rvwb, c„w_exi †K›`a n‡Z K...wÎg DcMÖ‡ni D”PZv, r =     GMT2 4π2 1 3 =     gR2T 2 4π2 1 3 =      9.8  (6.4  10  6 ) 2  (12  3600) 2 4π2 1 3 = 2.667  107 m (Ans.) (N) D”PZvi cwieZ©b bv K‡i DcMÖnwU‡K KZ †eM cÖ`vb Ki‡j GwU f‚-w ̄’i DcMÖ‡n cwiYZ n‡eÑ MvwYwZKfv‡e we‡kølY Ki| mgvavb: Avgiv Rvwb, f~-w ̄’i DcMÖ‡ni chv©qKvj 24 NÈv Ges K...wÎg DcMÖ‡ni †eM, v = 2πr T DcMÖnwUi cÖv_wgK †eM, v1 = 2πr T1 = 2π  2.667  107 12  3600 ms–1 = 3878.99 ms–1 H D”PZvq f~-w ̄’i DcMÖ‡ni †eM, v2 = 2πr T = 2π  2.667  107 24  3600 ms–1 = 1939.497 ms–1 myZivs DcMÖnwU †eM n«vm K‡i 1939.497 ms–1 Kiv n‡j GwU f~-w ̄’i DcMÖ‡n cwiYZ n‡e| (Ans.) 6| A B d = 1.5  106 km M = 6  1024 kg R = 6400 km M = 7.4  1022 kg R = 1400 km A I B `ywU KvíwbK MÖn ci ̄úi n‡Z 1.5  106 km `~‡i Aew ̄’Z| Zv‡`i ms‡hvRK †iLvi ga ̈we›`y P| [h. †ev. 24] (K) gnvKl©xq wefe Kx? (L) †Kv‡bv ̄’v‡bi AwfKl©xq Z¡i‡Yi gvb H ̄’v‡b LwbR m¤ú` cvIqvi m¤¢vebv wb‡`©k K‡i? e ̈vL ̈v Ki| (M) P we›`y‡Z jwä gnvKl©xq cÖvej ̈ †ei Ki| mgvavb: A P B  EA  EB A MÖ‡ni P we›`y‡Z cÖvej ̈, EA = GMA AP2 = 4GMA d 2     AP =  d 2 = 4  6.673  10–11  7.4  1022 (1.5  109 ) 2 = 7.118  10–4 Nkg–1 , PA eivei Avevi, B MÖ‡ni Rb ̈ P we›`y‡Z cÖvej ̈, EB = GM BP2 = 4GMB d 2     BP =  d 2 = 4  6.673  10–11  7.4  1022 (1.5  109 ) 2 = 8.779  10–6 Nkg–1 , PB eivei  Enet = EA – EB = 7.118  10–4 – 8.779  10–6 = 7.03  10–4 N kg–1 , PA eivei (Ans.) (N) A I B †Kvb MÖnc„ô n‡Z 100 kg f‡ii b‡fvhvb‡K gnvk~‡b ̈ cvVv‡Z †ewk MwZkw3 cÖ‡qvRb? MvwYwZK we‡kølYmn gšÍe ̈ Ki| mgvavb: Avgiv Rvwb, †Kv‡bv MÖ‡ni c„ô n‡Z †Kv‡bv e ̄‘‡K gnvk~‡b ̈ cvVv‡Z cÖ‡qvRbxq MwZkw3, Ek = 1 2 mv 2 e = 1 2 m  2 GM R = GMm R A MÖ‡ni †ÿ‡Î, EKA = GMAm RA = 6.673  10–11  6  1024  1000 6400  103 = 6.256  1010 J
4  HSC Physics 1st Paper Chapter-6 B MÖ‡ni †ÿ‡Î, EKB = 6.673  10–11  7.4  1022  1000 1600  103 = 3.086  109 J GLb, EkA EkB = 6.256  1010 3.086  109  EkA = 20.27  EkB myZivs, A MÖnc„ô n‡Z b‡fvhvb‡K gnvk~‡b ̈ cvVv‡Z B MÖ‡ni Zzjbvq cÖvq 20.27 ̧Y †ewk MwZkw3 cÖ‡qvRb| (Ans.) 7| c„w_exi fi I e ̈vmva© h_vμ‡g 6  1024 kg I 6400 km| c„w_ex c„ô n‡Z 1000 km `~‡i GKwU DcMÖn AveZ©bkxj Av‡Q| GKRb b‡fvPvix g‡b K‡i DcMÖnwU‡K Av‡iv 22200 km `~i‡Z¡ miv‡j Gi †eM A‡a©K n‡e| [gnvKl© aaæeK = 6.673  10–11 Nm2 kg–2 ] [iv. †ev. 24] (K) gyw3 †eM Kv‡K e‡j? (L) m~h© I c„w_exi ga ̈eZ©x `~iZ¡ K‡g †M‡j eQ‡i w`‡bi msL ̈v GKB _v‡K bvÑ e ̈vL ̈v Ki| (M) DÏxcK Abymv‡i DcMÖnwUi cÖv_wgK Ae ̄’v‡b c„w_exi Rb ̈ gnvKl©xq wefe wbY©q Ki| mgvavb: f~-c„ô n‡Z h D”PZvq gnvKl©xq wefe, V = – GM R + h = – 6.673  10–11  6  1024 (6400 + 1000)  103 J kg–1 myZivs, DcMÖnwUi cÖv_wgK Ae ̄’v‡b c„w_exi Rb ̈ gnvKlx©q wefe – 5.411  107 J kg–1 (Ans.) (N) b‡fvPvixi aviYv mwVK wK-bv? MvwYwZKfv‡e we‡kølY Ki| mgvavb: Avgiv Rvwb, f~-c„ô n‡Z h D”PZvq AveZ©bkxj DcMÖ‡ni †eM, v = GM R + h  cÖv_wgK Ae ̄’v‡b DcMÖnwUi †eM, v1 = GM R + h1 = 6.673  10–11  6  1024 (6400 + 1000)  103 = 7355.63 ms–1 DcMÖnwU‡K Av‡iv 22200 km `~i‡Z¡ miv‡j †eM, v2 = GM R + h1 + h2 = 6.673  10–11  6  1024 (6400 + 1000 + 22200)  103 = 3677.82 ms–1 GLb, V2 V1 = 3677.82 7355.63 = 0.5 A_©vr, DcMÖnwU‡K Av‡iv 22200 km `~i‡Z¡ miv‡j Gi †eM A‡a©K nq| myZivs, b‡fvPvixi aviYv mwVK (Ans.) 8| Q P M O N ON = 6.4  103 km PQ = 100 km PM = 50 km f‚-c„‡ô AwfKl©R Z¡iY = 9.8 ms–2 [Xv. †ev. 24] (K) f‚-w ̄’i DcMÖn Kx? (L) gyw3‡eM e ̄‘i f‡ii Dci wbf©ikxj bq †Kb? (M) wP‡Îi Q we›`y‡Z AwfKl©R Z¡i‡Yi gvb wbY©q Ki| mgvavb: Avgiv Rvwb, f~-c„ô n‡Z h D”PZvq AwfKl©R Z¡iY, gh = GM (R + h) 2 = gR2 (R + h) 2 [ GM = gR2 ]  f~-c„ô n‡Z PQ = 100 km D”PZvq Q we›`y‡Z AwfKl© Z¡iY, gQ =     R R + h 2  g =     6.4  106 6.4 106 + 100  103 2  9.8 ms–2 = 9.5007 ms–2 (Ans.) (N) 5 kg f‡ii e ̄‘i Rb ̈ h_vμ‡g P I Q we›`y‡Z IR‡bi Zzjbv MvwYwZKfv‡e hvPvB Ki| mgvavb: P we›`y‡Z (f~-c„ô) Awfl©R Z¡iY, gP = 9.8 ms–2 ÔMÕ n‡Z cvB, Q we›`y‡Z AwfKl©R Z¡iY, gQ = 9.5007 ms–2 5 kg f‡ii e ̄‘i Rb ̈ P I Q we›`y‡Z IRb h_vμ‡g, WP I WQ n‡j, WP WQ = mgP mgQ = 5  9.8 5  9.5007 = 1.032  WP = 1.032  WQ myZivs 5 kg f‡ii e ̄‘i IRb P we›`yi Zzjbvq Q we›`y‡Z 1.032 ̧Y n‡e| (Ans.) 9| c„w_exi e ̈vmva© 6400 km, c„w_exi wbR A‡ÿi mv‡c‡ÿ AveZ©bKvj 24 NÈv| f‚c„‡ô AwfKl©xq Z¡iY g = 9.8 ms–2 | [g. †ev. 24] (K) †m‡KÛ †`vjK Kx? (L) c„w_exi Af ̈šÍ‡i I Dc‡i mgvb `~i‡Z¡ ÔgÕ Gi gvb mgvb bq †Kb? (M) c„w_exi 60 Aÿvs‡k AwfKl©xq Z¡i‡Yi gvb KZ? mgvavb: c„w_exi 60 Aÿvs‡k AwfKl©xq Z¡iY, g = g –  2Rcos2  = g –     2π T 2 Rcos2  = 9.8 –     2π 24  3600 2  6.4  106  cos2 60 = 9.792 ms–2 (Ans.)