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

gnvKl© I AwfKl©  Varsity Practice Sheet ........................................................................................................................ 1 weMZ mv‡j DU-G Avmv cÖkœvejx 1. Puv‡`i AwfKl©R Z¡iY c„w_exi AwfKl©R Z¡i‡Yi Qq fv‡Mi GK fvM| Puv‡`i e ̈vmva© c„w_exi e ̈vmv‡a©i GK-PZz_©vsk| c„w_exi fi M-Gi Zzjbvq Puv‡`i fi KZ? [DU 23-24] M 6 M 16 M 24 M 96 DËi: M 96 e ̈vL ̈v: g  M R 2  gm ge = Mm Me      Re Rm 2  Mm = 1 6      1 4 2  Me = M 96 2. ai, c„w_exi e ̈vm eivei GKwU myo1⁄2 Lbb Kiv n‡jv Ges c„w_ex c„ô †_‡K GKwU ÿz`a e ̄‘‡K myo‡1⁄2i g‡a ̈ †Q‡o †`Iqv n‡jv| e ̄‘wU hLb c„w_exi †K‡›`a †cuŠQv‡e ZLb gyw3‡eM ve-Gi mv‡c‡ÿ e ̄‘wUi †eM KZ n‡e? [DU 23-24] 3 2 ve 1 2 ve 1 2 ve 0 DËi: 1 2 ve e ̈vL ̈v: vmax = A = k m  R  vmax = g R  R = gR  vmax = 1 2  2gR = ve 2 3. m f‡ii GKwU DcMÖn R e ̈vmv‡a©i GKwU e„ËvKvi Kÿc‡_ M f‡ii GKwU MÖn‡K cÖ`wÿY K‡i| GKwU c~Y© N~Y©‡bi Rb ̈ cÖ‡qvRbxq mgq wb‡Pi †KvbwUi mgvbycvwZK? [DU 22-23] M m R 3 2 R 2 DËi: R 3 2 e ̈vL ̈v: T = 2 R 3 GM  T  R 3 2 4. AwfKl©xq Z¡iY g ebvg c„w_ex c„ô n‡Z MfxiZv h Gi †jLwPÎ †KvbwU? [DU 20-21] g h g h g h g h DËi: g h e ̈vL ̈v: g =     1 – h R g  g = g – g R h y = mx + c AvKv‡i cÖKvk K‡i, g = – g R h + g g h m = – g R 5. MÖ‡ni MwZi †ÿ‡Î, ÒGKwU bÿÎ †_‡K MÖn‡K ms‡hvMKvix mij‡iLv mgvb mg‡q mgvb †ÿÎdj AwZμg K‡iÓÑ GwU †Kvb bxwZi mivmwi djvdj? [DU 18-19] kw3i msiÿY bxwZ fi‡e‡Mi msiÿY bxwZ †K.wYK fi‡e‡Mi msiÿY bxwZ f‡ii msiÿY bxwZ DËi: †K.wYK fi‡e‡Mi msiÿY bxwZ 6. GKwU K...wÎg DcMÖn 7000 km e ̈vmva©wewkó e„ËvKvi Kÿc‡_ c„w_ex‡K cÖ`wÿY Ki‡Q| DcMÖnwUi ch©vqKvj 2 h n‡j †K›`agyLx Z¡iY KZ? [DU 16-17] 1.331 ms–2 2.663 ms–2 5.325 ms–2 10.650 ms–2 DËi: 5.325 ms–2 e ̈vL ̈v: K...wÎg DcMÖ‡ni †K›`agyLx Z¡iY a n‡j, a =  2R  a =     2 T 2 R  a =     2 2  3600 2  7  106  a = 5.3308 ms–2 Option Abyhvqx me‡P‡q KvQvKvwQ DËi 5.325 ms–2 |
2 .........................................................................................................................................  Physics 1st Paper Chapter-6 7. `yBwU KYvi g‡a ̈ gnvKl© e‡ji gvb †Kgb cwieZ©b n‡e hw` GKwU KYvi fi c~‡e©i wØ ̧Y, Ab ̈ KYvi fi wZb ̧Y Kiv nq Ges GKB mv‡_ Zv‡`i gv‡Si `~iZ¡ wØ ̧Y Kiv nq? [DU 15-16] c~‡e©i mgvb _vK‡e c~‡e©i wZb ̧Y n‡e c~‡e©i wØ ̧Y n‡e c~‡e©i †`o ̧Y n‡e DËi: c~‡e©i †`o ̧Y n‡e e ̈vL ̈v: F = GM1M2 d 2 ......... (i) cieZ©x †ÿ‡Î, F = G (2M1) (3M2) (2d) 2  F = 6 4  GM1M2 d 2  F = 1.5F [(i) n‡Z]  cieZ©x †ÿ‡Î ej c~‡e©i †`o ̧Y n‡e| 8. me©wb¤œ KZ †e‡M f‚-c„ô n‡Z m f‡ii GKwU e ̄‘‡K Dc‡ii w`‡K wb‡ÿc Ki‡j Zv Avi KL‡bv wd‡i Avm‡e bv? [DU 15-16] 2gR 2 gR gR 2 gR DËi: 2gR e ̈vL ̈v: gyw3‡e‡Mi mgvb †e‡M f‚-c„ô n‡Z †Kv‡bv e ̄‘‡K wb‡ÿc Ki‡j Zv Avi c„w_ex‡Z wd‡i Avm‡e bv|  ve = 2GM R  ve = 2GMR R 2  ve = 2gR [g Gi gvb ewm‡q] 9. r `~i‡Z¡ ivLv `ywU ÿz`a KYvi g‡a ̈ ci ̄úi gva ̈vKl©xq AvKl©Y ej F| KYv `ywUi gvSLv‡b GKwU fvix †jvnvi cvZ ivLv n‡j GLb Zv‡`i g‡a ̈ ci ̄úi AvKl©Y ej KZ? [DU 13-14] 0 F F 2 F 4 DËi: F e ̈vL ̈v: F = GMm r 2 GLv‡b, gnvKl©xq aaæeK G, gva ̈‡gi †Kv‡bv ag© †hgb cÖ‡ek ̈Zv, cÖeYZv ev w`K`wk©Zvi Dci wbf©i K‡i bv| A_©vr, gnvKl©xq aaæeK gva ̈‡gi Dci wbf©i K‡i bv| d‡j gnvKl© ej gva ̈‡gi Dci wbf©i K‡i bv| weMZ mv‡j GST-G Avmv cÖkœvejx 1. GKwU DcMÖn wbR A‡ÿ 10 NÈvq AveZ©b K‡i| Gi e ̈vm 14  104 m| 104 kg fiwewkó GKwU b‡fvhvb DcMÖnwU‡Z AeZiY Ki‡j DcMÖ‡ni wbR A‡ÿi N~Y©‡bi Kvi‡Y b‡fvhv‡bi IRb KZ n«vm cv‡e? [GST 23-24] 21.44 N 24.21 N 21.24 N 24.44 N DËi: Blank e ̈vL ̈v: W = m 2 r = m     2 T 2  = 104 ×     2 × 3.1416 10 × 3600 2 × 7 × 104 N = 7 × 108     2 × 3.1416 36000 2 N  7  108 106      6 36 2  7  102  1 36  7 35 102  20 N  W  21.323 N 2. f‚-c„ô †_‡K R 2 (R = c„w_exi e ̈vmva©) D”PZvq I GKB MfxiZvq AwfKl©R Z¡i‡Yi AbycvZÑ [GST 22-23] 1 : 9 2 : 9 4 : 9 8 : 9 DËi: 8 : 9 e ̈vL ̈v: gup =     R R + h 2  g ...... (i) gdown =     1 – h R  g ....... (ii) (i)  (ii) K‡i cvB, gup gdown =       R R + R 2 2       1 – R 2 R  gup gdown = 4 9 1 2  gup gdown = 8 : 9
gnvKl© I AwfKl©  Varsity Practice Sheet ....................................................................................................................... 3 3. A I B MÖn؇qi fi h_vμ‡g M I 2M Ges e ̈vmva© h_vμ‡g R I 2R n‡j Zv‡`i AwfKl©R Z¡i‡Yi AbycvZ gA : gB KZ? [GST 20-21] 1 : 1 1 : 2 2 : 1 4 : 1 DËi: 2 : 1 e ̈vL ̈v: g = GM R 2  g  M R 2  gA gB = MAR 2 B MBR 2 A  gA gB = M (2R) 2 2MR2  gA gB = 2  gA : gB = 2 : 1 weMZ mv‡j JU-G Avmv cÖkœvejx 1. hw` c„w_exi e ̈vmva© 1% Kgv‡bv nq wKš‘ fi mgvb _v‡K, Zvn‡j f‚-c„‡ôi AwfKl©R Z¡iY g Gi gvbÑ [JU 22-23] 0.5% e„w× cv‡e 0.5% Kg‡e 2% e„w× cv‡e 2% Kg‡e DËi: 2% e„w× cv‡e e ̈vL ̈v: g = GM R1 2 ........ (i) cieZ©x †ÿ‡Î, R2 = 99 100 R1  g = GM R2 2  g = GM     99 100  R1 2  g =     100 99 2  g [(i) n‡Z] = 1.02g g – g g  100% = 1.02g – g g  100% = 2%  2% e„w× cv‡e| 2. c„w_exi †K‡›`a gnvKl©xq Z¡iY KZ? [JU 22-23; CU 14-15; SUST 05-06] k~b ̈ Amxg c„w_ex c„‡ôi mgvb †KvbwU bq DËi: k~b ̈ e ̈vL ̈v: †K›`a n‡Z x `~i‡Z¡, g = 4 3 Gx †K‡›`a x = 0 nIqvq, g = 0 3. c„w_exi gyw3‡eM KZ? [JU 22-23; CU 18-19, 16-17, 13-14] 5.6 kms–1 11.2 kms–1 22.4 kms–1 28 kms–1 DËi: 11.2 kms–1 e ̈vL ̈v: c„w_exi gyw3‡eM v n‡j, v = 2GM R = 2  6.673  10–11  6  1024 6.4  106 = 11.185 kms–1  11.2 kms–1 4. mgvb f‡ii `ywU DcMÖ‡ni e ̈vmva© h_vμ‡g R Ges 4R n‡j DcMÖn `ywUi ch©vqKv‡ji AbycvZÑ [JU 22-23] 1 : 16 1 : 8 1 : 64 16 : 1 DËi: 1 : 8 e ̈vL ̈v: †Kcjv‡ii 3q m~Î Abymv‡i, T 2  R 3      T1 T2 2 =     R1 R2 3      T1 T2 2 =     R 4R 3  T1 T2 =     1 4 3 2  T1 T2 = 1 8  T1 : T2 = 1 : 8 5. wb‡Pi †KvbwUi c„‡ô gnvKl© cÖvej ̈ me‡P‡q †ewk? [JU 19-20] P›`a eya c„w_ex e„n ̄úwZ DËi: e„n ̄úwZ e ̈vL ̈v: Option ̧‡jvi g‡a ̈ e„n ̄úwZi M R 2 AbycvZ me©vwaK| 6. c„w_ex c„‡ô gyw3‡eM P›`a c„‡ôi gyw3‡eMÑ [JU 19-20] A‡cÿv †ewk A‡cÿv Kg Gi mgvb Gi mv‡_ AcwiewZ©Z DËi: A‡cÿv †ewk e ̈vL ̈v: gyw3‡eM, v = 2GM R  v  M R Puv‡`i †ÿ‡Î M R Gi gvb c„w_exi Gi †P‡q Kg nIqvq    Me  Re > Mm Rm c„w_exi gyw3‡eM Puv‡`i gyw3‡eM A‡cÿv †ewk|
4 .........................................................................................................................................  Physics 1st Paper Chapter-6 7. M f‡ii e ̄‘‡K †K‡U m I (M – m) f‡ii e ̄‘‡Z iƒcvšÍwiZ Kiv n‡jv| M m KZ n‡j G‡`i g‡a ̈ gnvKl© ej m‡e©v”P n‡e? [JU 19-20] 2 4 3 5 DËi: 2 e ̈vL ̈v: GKwU As‡ki fi m  Aci As‡ki fi (M – m) m I (M – m) fi؇qi g‡a ̈ Kvh©Ki ej F n‡j, F = Gm (M – m) d 2  F = G d 2 (mM – m 2 ) gnvKl©xq ej m‡e©v”P n‡j dF dm = 0 n‡e|  d dm      G  d 2 (mM – m 2 ) = 0  G d 2 d dm (mM – m 2 ) = 0  M – 2m = 0  M m = 2 8. welyexq AÂj n‡Z †giæ A‡ji w`‡K AwfKl©xq Z¡iYÑ[JU 18-19] n«vm cvq e„w× cvq GKB n‡e 45 Aÿvs‡k m‡e©v”P DËi: e„w× cvq e ̈vL ̈v: g = g –  2R cos2  welyexq A‡j, g1 = g –  2R [ = 0] †giæ A‡j, g2 = g [ = 90]  g2 > g1 9. gnvKl©xq cÖvej ̈ E-Gi ivwkgvjv †KvbwU? [JU 18-19] E = GM r E = GM r 2 E = GM r 3 E = GMm2 r DËi: E = GM r 2 10. BTRC e1⁄2eÜz-1 K...wÎg DcMÖn XvKvi f‚-c„ô n‡Z 36000 km E‡aŸ© ̄’vcb Kiv n‡j DcMÖ‡ni ch©vqKvj KZ? [JU 18-19] 24.02 h 22.08 h 23.02 h 25.08 h DËi: 24.02 h e ̈vL ̈v: K...wÎg DcMÖ‡ni ch©vqKvj T n‡j, T 2 = 4 2 (R + h) 3 GM T = 2  (6.4  106 + 3.6  107 ) 3 6.673  10–11  6  1024 = 24.08 h Option Abyhvqx me‡P‡q KvQvKvwQ DËi 24.02 h| 11. GKwU MÖ‡ni e ̈vm 4  108 m Ges fi 22  1028 kg| D3 MÖ‡n gyw3‡eM KZ? [JU 17-18] 121.4 kms–1 122.5 kms–1 130.6 kms–1 110.6 kms–1 DËi: Blank e ̈vL ̈v: †Kv‡bv MÖ‡ni gyw3‡eM v n‡j, v = 2GM R v = 2  6.673  10–11  22  1028 2  108 = 383152.71 ms–1 = 383.15271 kms–1 mwVK DËi †bB| 12. c„w_exi NbZ¡Ñ [JU 17-18; KU 14-15] 5.5  103 kgm–3 5.96  1024 kgm–3 6.673  10–11 kgm–3 †KvbwUB bq DËi: 5.5  103 kgm–3 13. c„w_exi `y‡h©vM e ̈e ̄’vcbv ch©‡eÿ‡Yi Rb ̈ ̄’vwcZ K...wÎg DcMÖn‡K ejv nqÑ [JU 16-17] mvgwiK DcMÖn ch©‡eÿK DcMÖn gnvKvk †K›`a AvenvIqv DcMÖn DËi: ch©‡eÿK DcMÖn 14. †Kvb GKwU MÖ‡ni e ̈vmva© c„w_exi e ̈vmv‡a©i A‡a©K| wKš‘ MÖ‡ni c„‡ôi AwfKl©R Z¡iY c„w_exi AwfKl©R Z¡i‡Yi Pvi ̧Y| D3 MÖ‡ni gyw3‡eM c„w_exi gyw3‡e‡MiÑ [JU 15-16] wØ- ̧Y Pvi ̧Y AvU ̧Y †KvbwUB bq DËi: †KvbwUB bq e ̈vL ̈v: c„w_exi gyw3‡eM, ve = 2geRe .......... (i) Aci MÖ‡ni gyw3‡eM, v = 2gR ....... (ii)  v = 2  4ge  1 2 Re = 2  2geRe  v = 2 ve 15. 3  106 m MfxiZv wewkó GKwU Lwbi Zj‡`‡k AwfKl©R Z¡i‡Yi gvb KZ n‡e? f‚-c„‡ô AwfKl©R Z¡iY 10 ms–2 Ges c„w_exi e ̈vmva© 6  106 m| [JU 15-16] 8 ms–2 6 ms–2 5 ms–2 †Kv‡bvwUB bq DËi: 5 ms–2 e ̈vL ̈v: Lwbi wb‡P (h MfxiZvq) AwfKl©R Z¡iY, g =     1 – h R g  g =     1 – 3  106 6  106  10 = 5 ms–2