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.)