Title 6. P1C6.-Gravitation and Gravity-Engg.(With Solve).pdf ✅

gnvKl© I AwfKl©  Engineering Question Bank & Practice Book .................................................................................... 1 WRITTEN weMZ mv‡j BUET-G Avmv cÖkœvejx 1. f‚c„ô †_‡K 600 km Dc‡i 500 kg f‡ii GKwU m ̈v‡UjvB‡Ui †eM 8 km/s †mvRv Dc‡ii w`‡K| m ̈v‡UjvBUwU‡K H Kÿc‡_ ̄’vcb Ki‡Z cÖ‡qvRbxq e‡ji NvZ wbY©q K‡iv| [BUET 23-24 cÖ‡kœi Abyiƒc] mgvavb: Avbyf~wgK †eM, vx = GM R + h  vx = 6.673  10–11  6  1024 6.4  106 + 600  103  vx = 7.562 km/s  cÖ‡qvRbxq e‡ji NvZ, J  = Pf  – Pi   J  = m (vf )  – vi   |J|  = m v 2 f + v2 i  J = 500 80002 + 75622  J = 5.504  106 kgms–1 (Ans.) 2. GKwU e ̄‘‡K 2000 m/s †e‡M wb‡ÿc Ki‡j hw` Gi kw3i 20% bó nq Zvn‡j e ̄‘wU KZ D”PZvq DV‡e? g1⁄2j MÖ‡ni fi 6.4 × 1023 kg Ges e ̈vmva© 3400 km| [BUET 22-23] mgvavb: Epf – Epi = 0.8 Ek  – GMm R + h + GMm R = 0.8 × 1 2 mv2  0.8 × 1 2 v 2 = 6.673 × 10–11 × 6.4 × 1023 ×     1 3.4 × 106 – 1 3.4 × 106 + h  h = 4.96 × 105 m (Ans.) 3. 200 kg f‡ii GKwU K...wÎg DcMÖn‡K f~-c„ô †_‡K GKU wbw`©ó D”PZvq Zz‡j Zvi g‡a ̈ 6000 MJ MwZkw3 †`qv n‡jv| DcMÖnwU KZ D”PZvq c„w_ex‡K cwiågY Ki‡e? c„w_exi fi 6 × 1024 kg, e ̈vmva© 6400 km Ges G = 6.6 × 10–11 Nm2 kg–2 | [BUET 20-21] mgvavb: GMm r 2 = mv2 r  GMm 2r = 1 2 mv2  G × 6 × 1024 × 200 R + h = 6 × 109 × 2  h = 273 × 103 m = 273 km (Ans.) 4. c„w_exi c„‡ô GKwU bvB‡Uav‡Rb AYyi †eM 0C ZvcgvÎvq D3 M ̈v‡mi r.m.s †e‡Mi mgvb| hw` bvB‡Uav‡Rb AYywU Ab ̈vb ̈ AYyi mv‡_ msNl© Qvov †mvRv Dc‡ii w`‡K D‡V, Zvn‡j AYywU KZ D”PZvq DV‡e? [†`Iqv Av‡Q, bvB‡Uav‡Rb AYyi fi m = 4.65 × 10–26 kg Ges Boltzmann aaæeK, k = 1.38 × 10–23 JK–1 ] [BUET 19-20] mgvavb: v = crms = 3kT m Einitial = Efinal  1 2 mv2 – GMm R = – GMm R + h  1 2 × 3kT m – GM R = – GM R + h  3 2 × 1.38 × 10–23 × 273 4.65 × 10–26 = 6.673 × 10–11 × 6 × 1024     1 6.4 × 106 – 1 6.4 × 106 + h  h = 1.2456 × 104 m (Ans.) 5. cÖwZwU 2 × 1030 kg f‡ii `ywU Zviv gy‡LvgywL msN‡l©i Rb ̈ G‡K Ac‡ii w`‡K avegvb| wbKUeZ©x nIqvi c~‡e© Zviv `ywUi ga ̈eZ©x `~iZ¡ wQj 109 km Ges Zv‡`i MwZ wQj bMY ̈| msN‡l©i mg‡q Zv‡`i †eM KZ n‡e? cÖwZwU Zvivi e ̈vmva© 104 km| a‡i bvI †h, msNl© bv nIqv ch©šÍ Zviv `ywU AweK...Z _vK‡e| [G = 6.67 × 10–11 Nm2 kg–2 ] [BUET 19-20] mgvavb: msN‡l©i c~‡e©, M M u1 = 0 ms–1 u2 = 0 ms–1 R1 = 109 km msN‡l©i ci, R2 = 2 × 104 km kw3i msiÿYkxjZv Abyhvqx, msN‡l©i c~‡e© †gvU kw3 = msN‡l©i ci †gvU kw3  (Ek)initial + (Ep)initial = (Ek)final + (Ep)final  1 2 × 2 × M × 02 – GM2 R1 = 1 2 (2M)v2 – GM2 R2  v 2 = GM     1 R2 – 1 R1  v = G × 2 × 1030     1 2 × 107 – 1 1012 ms–1 = 2.58 × 106 ms–1 (Ans.)
2 .........................................................................................................................................  Physics 1st Paper Chapter-6 6. 80 kg IR‡bi GKwU K...wÎg DcMÖn f~-c„ô †_‡K KZ D”PZvq ̄’vcb Ki‡j Zv cÖwZ 24 N›Uvq 2 evi GKB ̄’vb ch©‡eÿY Ki‡Z cvi‡e? [c„w_exi e ̈vmva© 6400 km I Zvi fi 6 × 1021 Ton] [BUET 17-18] mgvavb: h =     T 2GM 4 2 1 3 – R =      (12 × 3600)  2 × 6.673 × 10–11 × 6 × 1024 4 2 1 3 – 6.4 × 106 m  h = 20.25 × 106 m (Ans.) 7. Kíbv Ki †h, c„w_exi e ̈vm eivei GKwU myo1⁄2 Lbb Kiv nj| GKwU e ̄‘‡K myo‡1⁄2i GK cÖvšÍ †_‡K †Q‡o †`qv nj Ges e ̄‘wU mij Qw›`Z ̄ú›`‡b ̄úw›`Z n‡Z jvM‡jv| c„w_ex‡K GKwU mylg †MvjK g‡b K‡i Ges evav`vbKvix mKj ej D‡cÿv K‡i c„w_exi †K›`a †_‡K 5 × 105 m `~i‡Z¡ e ̄‘wUi Z¡iY I †`vj‡bi ch©vqKvj wbY©q Ki| [†`Iqv Av‡Q, c„w_exi e ̈vmva© R = 6.4 × 106 m Ges g = 9.8 ms–2 ] [BUET 16-17] mgvavb: c„ô †_‡K h MfxiZvq A_©vr †K›`a †_‡K x `~i‡Z¡ cv_‡ii Dci Z¡iY, a = – 4 3 Gx    ∵  g = 4 3 GR  a g = – x R  a = – g x R = – 9.8 × 5 × 105 6.4 × 106 ms–2 = – 0.765 ms–2 (Ans.) a = – 4 3 Gx  –  2 x = – 4 3 Gx   = 4G 3  2 T = 4G 3  T = 3 G = 3 5.5 × 103 × 6.673 × 10–11  T = 5067.5 s (Ans.) 8. GKwU mylg †Mvj‡Ki fi 1 × 104 kg Ges e ̈vmva© 1 m| †MvjK KZ...©K †Mvj‡Ki †K›`a n‡Z 0.5 m `~i‡Z¡ Aew ̄’Z m1 f‡ii GKwU KYvi Dci gnvKl© e‡ji gvb KZ? [G = 6.673 × 10–11 Nm2 kg–2 ] [BUET 16-17] mgvavb: F = GMm1 R 3 r = 6.673 × 10–11 × 104 × 0.5 m1 1 3 N  F = 3.3365 × 10–7m1 N (Ans.) 9. GKwU 20 kg f‡ii K...wÎg DcMÖn ARvbv f‡ii GKwU MÖ‡ni Pviw`‡K 8.0 × 106 m e ̈vmv‡a©i e„ËvKvi c‡_ AvewZ©Z n‡j Zvi ch©vqKvj 2.4 h nq| MÖnc„‡ôi AwfKl©R Z¡i‡Yi gvb 8.0 ms–2 n‡j MÖnwUi e ̈vmva© KZ? [BUET 14-15] mgvavb: r =     T 2GM 4 2 1 3  r =     (2.4 × 3600) 2 × gR2 4 2 1 3  (8 × 106 ) 3 = (2.4 × 3600) 2 × 8 × R2 4 2  R = 5.82 × 106 m (Ans.) 10. GKwU wi‡gvU †mwÝs m ̈v‡UjvBU c„w_exi Pvwiw`‡K f~-c„ô n‡Z 250 km Dc‡i e„ËvKvi c‡_ Nyi‡Q| GB c‡_ m ̈v‡UjvBUwUi MwZ‡eM Ges N~Y©bKvj wbY©q Ki| [Re = 6400 km, g = 9.8 ms–2 ] [BUET 10-11] mgvavb: v = GM R + h = gR2 R + h = 6.4 × 106 9.8 6.4 × 106 + 250 × 103 ms–1  v = 7769.3 ms–1 (Ans.) T = 2 (R + h) v = 2 (6400 × 103 + 250 × 103 ) 7769.3 s  T = 5377.98 s (Ans.) 11. f~-c„ô n‡Z Lvov Dc‡ii w`‡K GKwU i‡KU‡K 5 kms–1 `aæwZ‡Z Dr‡ÿcY Kiv nj| i‡KUwU wVK wdievi g~û‡Z© f~-c„ô †_‡K KZ D”PZvq †cuŠQv‡e Zv †ei Ki| [c„w_exi fi = 6.0 × 1024 kg, c„w_exi e ̈vmva© = 6.4 × 106 m, G = 6.67 × 10–11 Nm2 kg–2 ] [BUET 05-06] mgvavb: kw3i msiÿYkxjZv Abyhvqx, Einitial = Efinal  – GMm R + 1 2 mv2 = – GMm R + h  – G × 6 × 1024 6.4 × 106 + 1 2 × (5 × 103 ) 2 = – G × 6 × 1024 6.4 × 106 + h  h = 1.598 × 106 m (Ans.) 12. g1⁄2j MÖ‡ni fi c„w_exi f‡ii 0.11 ̧Y Ges Gi e ̈vmva© c„w_exi e ̈vmv‡a©i 0.532 ̧Y| g1⁄2j MÖ‡ni f~-c„ô †_‡K GKwU gnvk~b ̈hvb‡K b~ ̈bZg KZ †e‡M Dr‡ÿcY Ki‡j gnvk~b ̈hvbwU g1⁄2j MÖ‡ni ga ̈vKl©Y e‡ji evB‡i P‡j †h‡Z cvi‡e? [c„w_exi fi 5.975 × 1024 kg, c„w_exi e ̈vmva© = 6.371 × 106 m, G = 6.673 × 10–11 Nm2 kg–2 ] [BUET 03-04] mgvavb: g1⁄2j MÖ‡n gyw3‡eM, ve = 2GMm Rm = 2 × G × 0.11 × 5.975 × 1024 6.371 × 106 × 0.532 ms–1  v = 5087.23 ms–1 (Ans.) 13. f~-c„‡ôi PZzw`©‡K wbiÿe„Ë eivei e„ËvKvi c‡_ AveZ©bkxj GKwU f~-w ̄’i †hvMv‡hvM DcMÖ‡ni e„ËvKvi c‡_i e ̈vmva© KZ? DcMÖnwU f~-c„ô n‡Z KZ D”PZvq Nyi‡Q? [BUET 01-02] mgvavb: h =     T 2GM 4 2 1 3 – R =     (24 × 3600) 2 × 6.673 × 10–11 × 6 × 1024 4 2 1 3 – 6.4 × 106 = 35.9 × 106 m (Ans.)  e„ËvKvi c‡_i e ̈vmva© = h + R = 42.3 × 106 m (Ans.)
gnvKl© I AwfKl©  Engineering Question Bank & Practice Book ................................................................................... 3 weMZ mv‡j KUET-G Avmv cÖkœvejx 1. c„w_ex †_‡K 2600 wK‡jvwgUvi D”PZvq GKwU K...wÎg DcMÖn c„w_ex‡K †K›`a K‡i e„ËvKvi c‡_ cÖ`wÿY Ki‡Q| Gi †eM N›Uvq KZ n‡e? [c„w_exi e ̈vmva© = 6400 wK‡jvwgUvi, fi = 6 × 1024 †KwR Ges G = 6.67 × 10–11 wbDUb-wg2 /†KwR2 ] [KUET 19-20] mgvavb: K...wÎg DcMÖ‡ni †eM, v = GM R + h = 6.67 × 10–11 × 6 × 1024 6400 × 103 + 2600 × 103 = 6668.33 ms–1  v = 24005.98 kmh–1 (Ans.) 2. c„w_exi e ̈vmva© R = 6.4 × 106 m Ges AwfKl©R Z¡iY 9.8 ms–2 n‡j c„w_exi c„ô n‡Z †Kvb e ̄‘i gyw3‡eM KZ n‡e? [RUET 13-14, 09-10; CUET 13-14; KUET 05-06] mgvavb: gyw3‡eM, ve = 2gR = 2 × 9.8 × 6.4 × 106 = 1.12 × 104 ms–1 (Ans.) 3. c„w_ex c„‡ô GKRb †jv‡Ki IRb 80 kg-wt| c„w_exi fi P‡›`ai f‡ii 81 ̧Y n‡j P‡›`a †jvKwUi IRb KZ n‡e? (c„w_ex Ges P‡›`ai e ̈vmv‡a©i AbycvZ 4:1) [KUET 04-05] mgvavb: Wm We = gm ge = Mm Me ×     Re Rm 2 = Mm 81Mm ×     4 1 2 = 1 81 × 42 = 16 81  Wm = 16 81 × 80 kg-wt = 15.8 kg-wt (Ans.) weMZ mv‡j RUET-G Avmv cÖkœvejx 1. g‡b Ki, c„w_exi †K›`a w`‡q Gi e ̈v‡mi GK cÖvšÍ †_‡K Aci cÖvšÍ ch©šÍ GKwU Uv‡bj Lbb Kiv n‡jv| †`LvI †h, GB Uv‡b‡j GKwU cv_i †dj‡j Gi MwZ mij †`vjb MwZ n‡e| cv_iwUi mij †`vjbMwZi ch©vqKvj wbY©q Ki| (c„w_exi NbZ¡ = 5.5 × 103 kgm–3 ) [RUET 19-20] mgvavb: c„w_exi c„ô †_‡K h MfxiZvq A_©vr †K›`a †_‡K x `~i‡Z¡ cv_‡ii Dci wμqvkxj gnvKl©xq ej, F = ma = – 4 3 Gxm [∵ ej I mi‡Yi w`K wecixZ]  a  – x hv mij †`vjb MwZi kZ©|  cv_iwUi MwZ mij †`vjb MwZ n‡e| a = – 4 3 Gx  –  2 x = – 4 3 Gx   = 4G 3  2 T = 4G 3  T = 3 G = 3 5.5 × 103 × 6.673 × 10–11  T = 5068.64 s (Ans.) 2. †`LvI †h, †Kvb e ̄‘‡K b~ ̈bZg 11.2 kms–1 †e‡M gnvk~‡b ̈i w`‡K Qz‡o gvi‡j e ̄‘wU c„w_exi AwfKl©R e‡ji AvKl©Y KvwU‡q DV‡Z cv‡i| c„w_exi e ̈vmva© = 6.4 × 106 m| [RUET 17-18] mgvavb: c„w_exi AwfKl©R e‡ji AvKl©Y KvwU‡q gnvk~‡b ̈ e ̄‘wUi †gvU kw3 k~b ̈ n‡e| Einitial = Efinal  – GMm R + 1 2 mv2 = 0  v = 2GM R  v = 2 × 6.673 × 10–11 × 6 × 1024 6.4 × 106 ms–1 = 11185 ms–1  v = 11.185 kms–1 (Ans.) 3. GKwU K...wÎg DcMÖn c„w_ex c„ô †_‡K 700 km D”PZvq e„ËvKvi c‡_ Nyi‡Q| Gi Avbyf~wgK †eM wbY©q Ki| [c„w_exi e ̈vmva© = 6300 km Ges c„w_ex c„‡ô g = 9.8 ms–2 ] [RUET 17-18] mgvavb: Avbyf~wgK †eM, v = GM R + h = gR2 R + h = R g R + h = 6.3 × 106 × 9.8 6.3 × 106 + 7 × 105  v = 7454.26 ms–1 (Ans.) 4. c„w_exi fi P‡›`ai f‡ii 81 ̧Y Ges Zv‡`i †K‡›`ai ga ̈eZ©x `~iZ¡ 38.6 × 104 km| P›`a I c„w_exi ms‡hvMKvix †iLvi †Kv_vq †Kvb e ̄‘i Dci Df‡qi Uvb mgvb n‡e? [RUET 08-09] mgvavb: F1 = F2  GMm x 2 = GMm 81 × (38.6 × 107 – x) 2 [†hLv‡b x = c„w_ex †_‡K `~iZ¡]  x = 9  (38.6 × 107 – x)  x = 34.74 × 107 m (Ans.)
4 .........................................................................................................................................  Physics 1st Paper Chapter-6 5. c„w_ex I m~h© mgvb e‡j G‡K Aci‡K AvKl©Y K‡i| ZeyI c„w_ex m~‡h©i Pvwiw`‡K †Nv‡i †Kb? [RUET 06-07] mgvavb: c„w_ex I m~h© mgvb e‡j G‡K Aci‡K AvKl©Y K‡i| wKš‘ c„w_exi Zzjbvq m~‡h©i fi A‡bK †ewk nIqvq c„w_ex m~‡h©i Pviw`‡K †Nv‡i| c„w_ex I m~‡h©i ga ̈eZ©x AvKl©Y ej G‡ÿ‡Î c„w_ex‡K †K›`agyLx e‡ji †RvMvb †`q| (Ans.) 6. c„w_exi fi I G Gi gvb h_vμ‡g 6 × 1024 kg I 6.7 × 10–11 Nm2 kg–2 Ges e ̈vmva© 6.4 × 106 m n‡j, f~-w ̄’i DcMÖ‡ni D”PZv I †eM KZ? [RUET 03-04] mgvavb: h =     GMT2 4 2 1 3 – R =     6.7 × 10–11 × 6 × 1024 × 864002 4 2 1 3 – 6.4 × 106  h = 3.596 × 107 m (Ans.) v = GM R + h = 6.7 × 10–11 × 6 × 1024 6.4 × 106 + 35.96 × 106  v = 3080 ms–1 (Ans.) weMZ mv‡j CUET-G Avmv cÖkœvejx 1. Avgv‡`i c„w_exi e ̈vm 12800 km| GKwU DcMÖn e„ËvKvi K‡ÿ 7.8 kms–1 MwZ †e‡M Ny‡i| e„ËvKvi K‡ÿ AwfKl©R Z¡iY 9.0 ms–2 n‡jÑ [CUET 04-05] (K) e„ËvKvi K‡ÿi D”PZv (L) GKevi c~Y© N~Y©‡bi mgqKvj wbY©q Ki| mgvavb: (K) mg = mv2 (R + h)  9 = (7800) 2 6.4 × 106 + h  h = 360 km (Ans.) (L) T = 2 (R + h) v = 2 (6.4 × 106 + 360 × 103 ) 7800  T = 5445.42 s (Ans.) 2. c„w_exc„‡ô GKwU †jv‡Ki IRb 90 kg n‡j g1⁄2j c„‡ô Zvi IRb KZ n‡e? g1⁄2j Gi fi c„w_exi f‡ii 1 9 Ask Ges g1⁄2‡ji e ̈vmva© c„w_exi e ̈vmv‡a©i A‡a©K| [CUET 03-04] mgvavb: Wm We = gm ge = Mm Me ×     Re Rm 2 = 1 9 × 22 = 4 9  Wm = 4 9 × 90 × 9.8 N = 392 N (Ans.) weMZ mv‡j BUTex-G Avmv cÖkœvejx 1. GKwU e ̄‘‡K f~-c„ô n‡Z Dc‡i DVv‡bv nj| m‡e©v”P Ae ̄’v‡b AwfKl©R Z¡i‡Yi gvb f~-c„‡ôi AwfKl©R Z¡i‡Yi gv‡bi 64 fv‡Mi 1 fvM| e ̄‘wU‡K f~-c„ô †_‡K KZ D”PZvq DVv‡bv n‡qwQj? (c„w_exi e ̈vmva© R = 6.4 × 106 m) [BUTex 22-23] mgvavb: gh =     R R + h 2 g  1 64 = R R + h  R + h R = 8  h = 7R = 4.48 × 107 m (Ans.) 2. c„w_exi N~Y©b †eM eZ©gvb N~Y©b †e‡Mi KZ ̧Y n‡j wbiÿxq A‡j †Kv‡bv e ̄‘ fvinxb n‡e? [BUTex 20-21] mgvavb: eZ©gvb N~Y©b †eM, 1 = 2 24 × 3600 rad/s = 7.27 × 10–5 rad/s wbiÿxq A‡j †Kv‡bv e ̄‘ fvinxb n‡j, 0 = g – 2 2 R  2 = g R = 9.8 6.4 × 106 = 1.23 × 10–3 rad/s  2 1 = 1.23 × 10–3 7.27 × 10–5 = 17.02 (Ans.) 3. gnvKl© aaæeK ‘G’ Gi gvÎv wjL| [BUTex 10-11] mgvavb: G = Fr2 m1m2 = [MLT–2 ] [L2 ] [M2 ] = [L3M –1T –2 ] (Ans.) 4. c„w_ex †_‡K 1600 km D”PZvq K...wÎg DcMÖn c„w_ex‡K †K›`a K‡i e„ËvKvi c‡_ cÖ`wÿY Ki‡Q| DcMÖnwUi cÖwZ N›Uvq †eM KZ? [ME = 6 × 1024 kg, RE = 6.4 × 106 m, G = 6.67 × 10–11 Nm2 kg–2 ] [BUTex 07-08] mgvavb: Avgiv Rvwb, v = GME RE + h = 6.67 × 10–11 × 6 × 1024 6.4 × 106 + 1600 × 103 = 7072.84 ms–1  v = 25462.2 kmh–1 (Ans.) 5. ZvcgvÎv evo‡j gnvKl©xq aaæe‡Ki gvb wK n‡e? [BUTex 06-07] mgvavb: †Kvb cwieZ©b n‡e bv| †Kbbv gnvKl©xq aaæeK ZvcgvÎvi Dci wbf©i K‡i bv| (Ans.)