Tiêu đề 6. Phy-1st-Gravitation and Gravity__With Solve_Sha 5.10.23 PDF.pdf ✅

gnvKl© I AwfKl©  Engineering Practice Content 1 gnvKl© I AwfKl© Gravitation and Gravity lô Aa ̈vq ACS Physics Department Gi g‡bvbxZ cÖkœmg~n 1| `yBwU e ̄‘i fi h_vμ‡g 4 kg Ges 8 kg| e ̄‘ `yBwU ci ̄úi 2 m e ̈eav‡b Aew ̄’Z| gnvKl© e‡ji gvb wbY©q K‡iv| [G = 6.67  10–11 N – m 2 kg–2 ] [Easy] mgvavb: F = Gm1m2 d 2 = 6.67  10–11  8  4 2 2 = 5.34  10–10 N (Ans.) 2| 5 kg f‡ii `yBwU †MvjK‡K ci ̄úi n‡Z 2 m `~‡i ̄’vcb Ki‡j hw` AvKl©Y e‡ji gvb 41.67  10–11 N nq Z‡e gnvKl©xq aaæe‡Ki gvb KZ n‡e? [Easy] mgvavb: F = Gm1m2 d 2  G = Fd2 m1m2 = 41.67  10–11  2 2 5  5  G = 6.6672  10–11 Nm2 kg–2 (Ans.) 3| g1⁄2j MÖn I c„w_exi `~iZ¡ cÖvq 108 m| g1⁄2j MÖ‡ni fi n‡jv 6.5  1023 kg| f~-c„‡ôi Ici 50 kg f‡ii GKRb †jvK‡K g1⁄2j MÖn Kx cwigvY e‡j AvKl©Y Ki‡e? [Easy] mgvavb: F = GMm R 2 = 6.67  10–11  6.5  1023  50 (108 ) 2 = 0.217 N (Ans.) 4| gnvKl© m~Î e ̈envi K‡i c„w_exi fi I NbZ¡ wbY©q K‡iv| [Medium] mgvavb: g = GM R 2  M = gR 2 G = 9.8  (6.4  106 ) 2 6.673  10–11  M = 6.015  1024 kg Avevi,  = 3g 4GR = 3  9.8 4  3.1416  6.673  10–11  6.4  106   = 5.5  103 kgm–3 (Ans.) 5| e„n ̄úwZi e ̈vmva© c„w_exi e ̈vmv‡a©i 10.97 ̧Y Ges e„n ̄úwZi fi c„w_exi f‡ii 318.3 ̧Y| f~-c„‡ô AwfKl©R Z¡i‡Yi gvb 9.8 ms–2 | e„n ̄úwZi c„‡ô AwfKl©R Z¡i‡Yi gvb KZ n‡e? [Easy] mgvavb: c„w_ex c„‡ô AwfKl©R Z¡iY, ge = GMe Re 2 ... (i) e„n ̄úwZi c„‡ô AwfKl©R Z¡iY, gj = GMj Rj 2 ... (ii) (i)  (ii)  ge gj = Me Mj  Rj 2 Re 2 = Me 318.3  Me  (10.97 Re) 2 Re 2  gj = 25.92 ms–2 (Ans.) 6| GKwU e ̄‘i IRb c„w_ex‡Z 56.84 N Ges P‡›`a 9.8 N| c„w_exi AwfKl©xq Z¡iY P‡›`ai AwfKl©xq Z¡i‡Yi KZ ̧Y? [Easy] mgvavb: awi, e ̄‘wUi fi = m kg  c„w_exi IRb, We = mge ... (i) P‡›`ai IRb, Wm = mgm ... (ii) (i)  (ii)  We Wm = ge gm  56.84 9.8 = ge gm  ge = 5.8  gm A_©vr, c„w_exi AwfKl©R Z¡iY P‡›`ai AwfKl©R Z¡i‡Yi 5.8 ̧Y|  5.8 (Ans.) 7| c„w_exi fi 5.98  1024 kg| c„w_exi c„‡ô AwfKl©xq Z¡iY 9.8 ms–2 a‡i c„w_exi e ̈vm wbY©q K‡iv| [Easy] [G = 6.66  10–11 N m 2 kg–2 ] mgvavb: g = GM R 2  R = GM g = 6.66  10–11  5.98  1024 9.8  R = 6.375  106 m  c„w_exi e ̈vm, D = 2R = 2  6.375  106 m = 12.75  106 m (Ans.) 8| GKwU gnvk~b ̈hvb c„w_ex †_‡K Puv‡`i w`‡K hv‡”Q| c„w_ex †_‡K Ggb GKwU Ae ̄’vb †ei K‡iv †hLv‡b Gi Ici gnvKl©xq ej k~b ̈| †`Iqv Av‡Q, c„w_exi fi 6.0  1024 kg, Puv‡`i fi 7.4  1022 kg, c„w_exi †K›`a I Puv‡`i †K‡›`ai ga ̈eZ©x `~iZ¡ 3.8  108 m| [Medium] mgvavb: GLv‡b, awi, c„w_ex †_‡K x m `~‡i gnvKl©xq ej k~b ̈ nq| GMem x 2 = GMmm (3.8  108 – x) 2  3.8  108 – x x = 7.4  1022 6. 1024  3.8  108 – x = 0.111x  x = 3.42  108 m (Ans.)
2  Physics 1st Paper Chapter-6 9| Puv` c„w_ex †_‡K 3.9  105 km `~‡i Aew ̄’Z| Puv‡`i fi 7.3  1022 kg Ges c„w_exi fi 6  1024 kg| c„w_ex I Puv‡`i gvSLv‡b Ggb GKwU we›`y Av‡Q †hLv‡b GKwU KYvi Ici c„w_exi AvKl©Y ej I Puv‡`i AvKl©Y ej mgvb| c„w_ex n‡Z H ̄’v‡bi `~iZ¡ KZ? [Medium] mgvavb: awi, c„w_ex †_‡K x m `~‡i KYvwUi Ici c„w_exi AvKl©Y ej I Puv‡`i AvKl©Y ej mgvb nq|  GMem x 2 = GMmm (3.9  108 – x) 2  3.9  108 – x x = 7.3  1022 6  1024  3.9  108 – x = 0.110x  x = 3.51  108 m (Ans.) 10| c„w_ex‡K 6.37  106 m e ̈vmv‡a©i GKwU mgmË¡ †MvjKg‡b K‡i Ges Gi DcwiZj AwfKl©R Z¡i‡Yi gvb 9.81 ms–2 a‡i c„w_exi fi †ei K‡iv| [Easy] [G = 6.67  10–11 N m2 kg–2 ] mgvavb: 5.97  1024 kg g = GM R 2  M = gR 2 G = 9.81  (6.37  106 ) 2 6.67  10–11  M = 5.97  1024 kg (Ans.) 11| g = 9.8 ms–2 ̄’v‡b GKwU w ̄úas wbw3‡Z †Kv‡bv GKwU e ̄‘i IRb 9.8 N n‡j e ̄‘wUi fi KZ? †Kv‡bv ̄’v‡b H w ̄úas wbw3‡Z e ̄‘wUi IRb 9.4 N n‡j H ̄’v‡bi AwfKl©xq Z¡iY wbY©q Ki| [Easy] mgvavb: e ̄‘i fi = m kg n‡j, W = mg  m = 9.8 9.8  m = 1 kg Avevi, W = mg  g = 9.4 1  g = 9.4 ms–2 (Ans.) 12| c„w_exi fi I e ̈vmva© P‡›`ai fi I e ̈vmv‡a©i Zzjbvq h_vμ‡g 81 ̧Y Ges 4 ̧Y eo n‡j G‡`i c„‡ô AwfKl©R Z¡i‡Yi gv‡bi Zzjbv K‡iv| [Easy] mgvavb: c„w_ex c„‡ô AwfKl©R Z¡iY, ge = GMe Re 2 ... (i) P‡›`ai c„‡ô AwfKl©R Z¡iY, gm = GMm Rm 2 ... (ii) (i)  (ii)  ge gm = Me Mm  Rm 2 Re 2 = 81  Mm Mm  Rm 2 (4 Rm) 2 = 81 16  ge = 5.0625 gm  c„w_ex c„‡ôi AwfKl©R Z¡iY P‡›`ai c„‡ôi 5.0625 ̧Y| (Ans.) 13| P›`ac„‡ô AwfKl©R Z¡i‡Yi gvb f~-c„‡ô AwfKl©R Z¡i‡Yi gv‡bi 1 6 ̧Y| c„w_exi fi P‡›`ai f‡ii cÖvq 81 ̧Y n‡j c„w_exi e ̈vm P‡›`ai e ̈v‡mi KZ ̧Y? [Medium] mgvavb: c„w_ex c„‡ô AwfKl©R Z¡iY, ge = GMe Re 2 ... (i) P‡›`ai c„‡ô AwfKl©R Z¡iY, gm = GMm Rm 2 ... (ii) (i)  (ii)  ge gm = Me Mm  Rm 2 Re 2  ge ge  1 6 = 81  Mm Mm  Rm 2 Re 2  Rm Re = 6 81 = 0.272  Re = 3.67  Rm  3.67 (Ans.) 14| P‡›`ai fi c„w_exi f‡ii 1 80 fvM| P‡›`ai e ̈vmva© c„w_exi e ̈vmv‡a©i 1 4 fvM| c„w_ex-c„‡ô AwfKl©R Z¡i‡Yi gvb 9.8 ms–2 n‡j P‡›`ai c„‡ô AwfKl©R Z¡i‡Yi gvb †ei K‡iv? [Easy] mgvavb: c„w_ex c„‡ô AwfKl©R Z¡iY, ge = GMc Re 2 ... (i) P‡›`ai c„‡ô AwfKl©R Z¡iY, gm = GMm Rm 2 ... (ii) (i)  (ii)  ge gm = Me Mm  Rm 2 Re 2  ge gm = Me Me 80      Re 4 2 Re 2 = 80 16  9.8 gm = 5  gm = 1.96 ms–2 (Ans.) 15| c„w_exi c„‡ô GKwU †jv‡Ki IRb 40.5 †KwR n‡j P›`ac„‡ô Gi IRb KZ n‡e †ei K‡iv| g‡b K‡iv, c„w_exi fi I e ̈vmva© P‡›`ai fi I e ̈vmv‡a©i Zzjbvq h_vμ‡g 81 ̧Y Ges 4 ̧Y eo| [Easy] mgvavb: c„w_ex c„‡ô AwfKl©R Z¡iY, ge = GMe Re 2 ... (i) P‡›`ai c„‡ô AwfKl©R Z¡iY, gm = GMm Rm 2 ... (ii) (i)  (ii)  ge gm = Me Mm  Rm 2 Re 2 = 81  Mm Mm  Rm 2 (4Rm) 2 = 81 16  ge gm = 81 16 e ̄‘i fi = m kg n‡j, c„w_ex c„‡ô IRb P›`ac„‡ô IRb = mge mgm  40.5 Wm = 81 16  Wm = 8 kg-wt (Ans.)
gnvKl© I AwfKl©  Engineering Practice Content 3 16| f~-c„ô n‡Z KZ DuPz‡Z †M‡j †mLvbKvi AwfKl©xq Z¡i‡Yi gvb f~-c„‡ô AwfKl©xq Z¡i‡Yi gv‡bi GK Z...Zxqvsk n‡e? c„w_exi e ̈vmva© = 6.38  106 m [Easy] mgvavb: awi, f~-c„ô n‡Z h m D”PZvq †h‡Z n‡e| cÖkœg‡Z, g = 1 3 g  GM (R + h) 2 = 1 3  GM R 2  R R + h = 1 3  6.38  106 6.38  106 + h = 1 3  h = 4.67  106 m (Ans.) 17| Puv‡`i fi 7.35  1022 kg Ges e ̈vmva© 1.74  106 m [Easy] i. Puv‡`i c„‡ô g Gi gvb KZ? mgvavb: g = GM R 2 = 6.673  10–11  7.35  1022 (1.74  106 ) 2 = 1.62 ms–2 (Ans.) ii. Zv c„w_exi c„‡ôi g Gi Zzjbvq KZ ̧Y? mgvavb: gm ge = 1.62 9.8 = 0.16  gm = 0.165  ge (Ans.) 18| f~-c„ô n‡Z 400 km Af ̈šÍ‡i I f~-c„‡ô AwfKl©xq Z¡i‡Yi AbycvZ †ei K‡iv| c„w_exi e ̈vmva© = 6400 km| [Easy] mgvavb: f~-c„ô n‡Z 400 km Af ̈šÍ‡i I f~-c„‡ô AwfKl©R Z¡i‡Yi gvb h_vμ‡g g I g n‡j, g g =     1 – h R =     1 – 400 6400 = 15 16  g : g = 15 : 16 (Ans.) 19| c„w_exi e ̈vmva© 6.38  106 m Ges gnvKl©xq aaæe‡Ki gvb 6.67  10–11 Nm2 kg–2 a‡i Gi Mo NbZ¡ †ei K‡iv| [Easy] [g = 9.81 ms–2 ] mgvavb:  = 3g 4GR = 3  9.81 4  3.1416  6.67  10–11  6.38  106 = 5.503  103 kgm–3 (Ans.) 20| c„w_exi e ̈vmva© R = 6.4  106 m Ges Gi c„‡ô AwfKl©R Z¡iY 9.8 ms–2 | f~-c„ô †_‡K 6.4  105 m D”PZvq AwfKl©R Z¡i‡Yi gvb †ei K‡iv| [Easy] [h. †ev. 01] mgvavb: g =     R R + h 2  g =     6.4  106 6.4  106 + 6.4  105 2  9.8 = 8.1 ms–2 (Ans.) 21| c„w_exi 6400 km e ̈vmv‡a©i GKwU †MvjK ai‡j f~-c„ô n‡Z KZ D”PZvq AwfKl©xq Z¡i‡Yi gvb f~-c„‡ôi AwfKl©xq Z¡i‡Yi gv‡bi 1 64 Ask n‡e? [Easy] [wm. †ev. 06; h. †ev. 03; P. †ev. 10] mgvavb: awi, wb‡Y©q D”PZv = h km Avgiv Rvwb, g =     R R + h 2  g  g g = R R + h  1 64 = R R + h  8R = R + h  h = 7R  h = 7  6400 km  h = 44800 km (Ans.) 22| c„w_ex‡K 6.4  106 m e ̈vmv‡a©i GKwU mgmË¡ †MvjK g‡b K‡i Ges Gi DcwiZj AwfKl©R Z¡i‡Yi gvb 9.8 ms–2 a‡i c„w_exi fi †ei K‡iv| [G = 6.67  10–11 N–m 2 kg–2 ] [Easy] mgvavb: g = GM R 2  M = gR2 G = 9.8  (6.4  106 ) 2 6.67  10–11  M = 6.018  1024 kg (Ans.) 23| GKwU e ̄Íi fi 12 wgwjMÖvg| c„w_exi †K‡›`ai w`‡K e ̄‘wU KZ e‡j AvKwl©Z n‡e? [AwfKl©xq Z¡iY g = 9.8 ms–2 ] [Easy] mgvavb: F = mg = 12  10–6  9.8 = 1.176  10–4 N (Ans.) 24| g1⁄2j MÖ‡ni e ̈vm 6000 km Ges Gi c„‡ô AwfKl©xq Z¡iY 3.8 ms–2 | g1⁄2j MÖ‡ni c„ô n‡Z GKwU e ̄‘i gyw3‡eM wbY©q K‡iv| [Easy] [Xv. †ev. 06; w`. †ev. 10; e. †ev. 08] mgvavb: GLv‡b, R = 6000  103 2 = 3  106 m gyw3‡eM, ve = 2gR = 2  3.8  3  106 = 4774.93 ms–1 (Ans.) 25| f‚-c„‡ô †Kv‡bv †jv‡Ki IRb 684 N n‡j wZwb P›`ac„‡ô wM‡q KZUzKz IRb nviv‡eb? c„w_exi fi I e ̈vmva© h_vμ‡g P‡›`ai fi I e ̈vmv‡a©i Zzjbvq 81 ̧Y Ges 4 ̧Y| [Medium] [P. †ev. 07; wm. †ev. 09] mgvavb: c„w_ex c„‡ô AwfKl©R Z¡iY, ge = GMe Re 2 ... (i) P‡›`ai c„‡ô AwfKl©R Z¡iY, gm = GMm m 2 ... (ii)
4  Physics 1st Paper Chapter-6 (i)  (ii)  ge gm = Me Mm  Rm 2 Re 2 = 81  Mm Mm  Rm 2 (4Rm) 2 = 81 16 Avevi, We Wm = mge mgm  684 Wm = 81 16  Wm = 135.11 N  IRb nviv‡e = (684 – 135.11) N = 548.88 N (Ans.) 26| g‡b Ki, c„waexi Kÿ-c_ e„ËvKvi hvi e ̈vmva© 1.5  108 km| m~‡h©i fi wbY©q Ki| †`Iqv Av‡Q 1 eQi = 365 w`b Ges gnvKl©xq aaæeK G = 6.7  10–11 Nm2 kg–2 [Medium] mgvavb: gnvKl© ej = †K›`agyLx ej  GMm r 2 = m 2 r  M =     2 T 2  r 3  1 G = 4 2  (1.5  1011) 3 (365  24  3600) 2  6.7  10–11  M = 2  1030 kg (Ans.) 27| f~-†K‡›`a AwfKl©R Z¡i‡Yi gvb †ei K‡i| [Easy] mgvavb: h m MfxiZvq AwfKl©R Z¡iY, g = g    1 – h R  f~-†K‡›`a AwfKl©R Z¡iY, g = g    1 – R R = g  0 = 0 ms–2 (Ans.) 28| mgvb f‡ii `ywU e ̄‘ ci ̄úi †_‡K 0.5 m `~i‡Z¡ †_‡K 6.67  10–5 N e‡j AvKl©Y K‡i| e ̄‘؇qi fi wbY©q K‡iv| [Easy] [Xv. †ev. 09] mgvavb: F = G m  m d 2  m 2 = 6.67  10–5  (0.5) 2 6.67  10–11  m = 500 kg (Ans.) 29| c„w_exi fi P‡›`ai 81 ̧Y Ges Zv‡`i ga ̈eZ©x `~iZ¡ 3.6  105 km| P›`a I c„w_exi ms‡hvMKvix †iLvi †Kv_vq †Kv‡bv e ̄‘i Ici Df‡qi Uvb mgvb n‡e? [Medium] mgvavb: awi, c„w_ex n‡Z x m `~‡i e ̄‘i Ici Uvb mgvb n‡e|  Fe = Fm  GMe  m x 2 = GMm  m (3.6  108 – x) 2  3.6  108 – x x = Mm Me = Mm 81  Mm  3.6  108 – x x = 1 9  3.24  109 – 9x = x  x = 3.24  108 m (Ans.) 30| GKwU MÖ‡ni fi I e ̈vmva© DfqB c„w_exi fi I e ̈vmv‡a©i wØ ̧Y| c„w_exi c„‡ô g Gi 9.8 ms–2 n‡j H MÖ‡ni c„‡ô g Gi gvb KZ n‡e? [Easy] mgvavb: c„w_ex c„‡ô AwZKl©R Z¡iY, ge = GMe Re 2 ... (i) MÖnwUi c„‡ô AwZKl©R Z¡iY, g = GM R 2 ... (ii) (i)  (ii)  g gm = M Me  Re 2 R 2  g = 2  Me Me  Re 2 (2  Re) 2  9.8  g = 4.9 ms–2 (Ans.) 31| c„w_exi fi I e ̈vmva© h_vμ‡g P‡›`ai fi I e ̈vmv‡a©i 81 I 4 ̧Y| c„w_ex c„‡ô GKRb †L‡jvqvo D”P jv‡d m‡e©v”P 1.8 m D‡”P DV‡Z cv‡i| P›`ac„ô n‡Z †m m‡e©v”P KZ D”PZvq DV‡Z cvi‡e? [Medium] mgvavb: c„w_ex‡Z wefekw3, Pe = mgehe ... (i) P‡›`a wefekw3, Pm = mgmhm ... (ii) (i)  (ii)  Pm Pe = gmhm gehe  1 = GMm Rm 2  hm GMe Re 2  he [GKB KvR K‡i e‡j Pe = Pm]  1 = Mm Me  Re 2 Rm 2  hm he  1 = 1 81  16  hm 1.8  hm = 9.11 m (Ans.) 32| c„w_exi Mo NbZ¡ 5.5  103 kgm–3 Ges e ̈vmva© 6.37  106 m n‡j c„w_ex c„‡ô AwfKl©R Z¡iY KZ n‡e? [G = 6.67  10–11 Nm2 kg–2 ] [Easy] mgvavb: g = 4 3 GR = 4 3  6.67  10–11  3.1416  6.37  106  5.5  103 = 9.79 ms–2 (Ans.) 33| c„w_ex-c„ô n‡Z KZ D”PZvq AwfKl©R Z¡i‡Yi gvb 4.9 ms–2 n‡e? [c„w_exi e ̈vmva© = 6.4  106 m, AwfKl©R Z¡iY c„w_ex-c„‡ô 9.8 ms–2 ] [Easy] mgvavb: awi, wb‡Y©q D”PZv = h m  g = R 2 (R + h) 2  g  4.9 9.8 = R R + h  R R + h = 0.707  R = 0.707R + 0.707 h  h = 2.651  106 m (Ans.)