Title 6. P1C6. HSC PREP Papers 26_With Solve.pdf ✅

gnvKl© I AwfKl©  HSC Prep Papers 1 lô Aa ̈vq gnvKl© I AwfKl© Gravitation and Gravity Topicwise CQ Trend Analysis UwcK 2016 2017 2018 2019 2022 2023 †gvU gnvKl© ej Ñ 1 Ñ Ñ 1 Ñ 2 MÖn-DcMÖn-bÿ‡Îi fi Ñ 1 Ñ Ñ Ñ Ñ 1 AwfKl© ej 1 Ñ 1 Ñ Ñ Ñ 2 AwfKl©R Z¡iY wbY©q/gnvKl©xq cÖvej ̈ Ñ 1 1 1 1 1 5 f~-c„ô n‡Z D”PZi ̄’v‡b AwfKl©xq Z¡iY 1 1 Ñ 3 3 1 9 wfbœ Aÿvs‡k (N~Y©b RwbZ Kvi‡Y g Gi gv‡bi ZviZg ̈) Ñ 1 Ñ Ñ 1 2 4 c„w_exi †KŠwYK †eM Ñ 1 Ñ Ñ Ñ Ñ 1 gnvKl© wefe Ñ 2 Ñ Ñ 2 1 5 gyw3‡eM Ñ 2 1 1 1 2 7 K...wÎg DcMÖn 3 2 1 3 2 2 13 f~w ̄’i DcMÖn 2 Ñ Ñ 2 3 1 9 * we.`a.: 2020 mv‡j GBPGmwm cixÿv AbywôZ nqwb, 2021 mv‡j kU© wm‡jev‡m Aa ̈vqwU AšÍfz©3 wQjbv| weMZ mv‡j †ev‡W© Avmv m„Rbkxj cÖkœ 1| 10 kg f‡ii GKwU e ̄‘‡K welyexq AÂj n‡Z †giæ A‡j ̄’vbvšÍi Kiv n‡jv| c„w_exi evwl©K MwZ Ges AvwýK MwZ h_vμ‡g 365 days Ges 24 hours| c„w_ex I m~‡h©i ga ̈Kvi `~iZ¡ 1.5 × 1011 m, c„w_exi e ̈vmva© 6.4 × 106 m, AwfKl©R Z¡iY 9.81 ms–2 | [iv. †ev. 23] (K) gnvKl©xq aaæe‡Ki msÁv `vI| (L) m~‡h©i mKj MÖ‡n gyw3‡e‡Mi gvb mgvb wK-bv? e ̈vL ̈v Ki| (M) m~‡h©i Pvicv‡k c„w_exi •iwLK `aæwZ †ei Ki| mgvavb: V = s t = 2r t = 2    1.5  1011 365  86400 = 29885.847 ms–1 (Ans.) (N) hw` AvwýK MwZ bv _vK‡Zv Z‡e welyexq AÂj n‡Z †giæ A‡j e ̄‘wU ̄’vbvšÍ‡ii d‡j IR‡bi cwieZ©b n‡e wK? MvwYwZKfv‡e †`LvI| mgvavb: AvwýK MwZ bv _vK‡j c„w_exi  = 0 rads–1 G‡ÿ‡Î, welyexq A‡j, ge = g –  2Rcos2 (0) = g †giæ A‡j, gp = g –  2Rcos2 (90) = g A_©vr AvwýK MwZ bv _vK‡j c„w_exi N~Y©bRwbZ Kvi‡Y g Gi †Kv‡bv ZviZg ̈ n‡e bv| Z‡e c„w_exi AvK...wZRwbZ Kvi‡Y g Gi wKQz ZviZg ̈ nq| Avgiv Rvwb, g = GM R 2  g  1 R 2 Avevi, †giæ‡Z c„w_exi e ̈vmva© (Rp) < welyexq A‡j c„w_exi e ̈vmva© (Re)  gp > ge ; Wp > We A_©vr c„w_exi AvK...wZRwbZ Kvi‡Y welyexq AÂj n‡Z †giæ A‡j †Kv‡bv e ̄‘ ̄’vbvšÍi Kiv n‡j Zvi IRb e„w× cv‡e| (Ans.) 2| Puv`‡K GKwU mylg †MvjK we‡ePbv Kiv n‡jv| aiv hvK Puv‡`i †K›`a n‡Z 2  106 m D”PZvq GKwU K...wÎg DcMÖn N~Y©biZ Av‡Q| Puv‡`i cwiwa = 10.048  106 m Ges NbZ¡ = 1742.3 kgm–3 | [Kz. †ev. 23] (K) cvwK©s Kÿc_ Kx? (L) c„w_ex c„ô †_‡K Dc‡ii w`‡K AwfKl©R Z¡i‡Yi gv‡bi cwieZ©b †h m~Î †g‡b P‡j Zv e ̈vL ̈v K‡iv| (M) K...wÎg DcMÖnwUi •iwLK †e‡Mi gvb wbY©q K‡iv| mgvavb: Rm = 10.048  106 2 = 1599188.86 m gm = 4 3 GRm = 4 3    1742.3  6.673  10–11  1599188.86 = 0.778 ms–2 v = gR2 m Rm + h = 0.778  (1599185.12) 2 2  106 = 997.412 ms–1 (Ans.) (N) K...wÎg DcMÖnwU‡K hw` 1.7538 kms–1 †e‡M Puv‡`i c„ô †_‡K Dr‡ÿcY Kiv nq Zvn‡j Zvi P‚ovšÍ cwiYwZ MvwYwZK we‡kølYmn Dc ̄’vcb K‡iv| mgvavb: Puv‡`i gyw3‡eM, ve = 2gmRm = 2  0.788  1599188.86 = 1587.56 ms–1 = 1.5875 kms–1 1.7538 kms–1 > ve  e ̄‘wU cive„Ë c‡_ Puv` †Q‡o P‡j hv‡e| (Ans.)
2  HSC Physics 1st Paper Chapter-6 3| c„w_exi c„ô †_‡K 3 × 104 km D”PZvq GKwU K...wÎg DcMÖn 3 kms–1 †e‡M c„w_ex‡K AveZ©b Ki‡Q| c„w_exi fi, 6 × 1024 kg c„w_exi e ̈vmva©, 6.4 × 103 km DcMÖnwUi fi, 1 × 103 kg Ges G = 6.673 × 10–11 Nm2 kg–2 [h. †ev. 23] (K) w ̄úas aaæeK Kx? (L) ej Øviv K...ZKvR e ̄‘i MwZkw3i cwieZ©‡bi mgvbÑ e ̈vL ̈v Ki| (M) K...wÎg DcMÖnwU‡K DwjøwLZ D”PZvq Zzj‡Z KZ KvR Ki‡Z n‡q‡Q? mgvavb: W = GMm     1 ri – 1 rf W=6.67310–1161024103      1 6.4106 – 1 6.4106 +3107  W = 5.155  1010 J (Ans.) (N) DÏxc‡K DwjøwLZ D”PZvq K...wÎg DcMÖnwU ̄’vqx n‡e wK? we‡kølY Ki| mgvavb: v = GM R + h = 6.673  10–11  6  1024 (6.4  106 ) + (3  104  1000) = 3316.54 ms–1 < ve  DcMÖnwU ̄’vqx n‡e| (Ans.) 4| 24 NÈvq wbR A‡ÿ AveZ©biZ G c„w_ex‡Z GKwU e ̄‘i IRb me©Î mgvb nIqv m¤¢e bq| c„w_exi e ̈vmva©, 6.4 × 103 km AwfKl©R Z¡iY, 9.8 ms–2 [h. †ev. 23] (K) fvi‡K›`a Kx? (L) f~-c„ô †_‡K hZB wb‡P hvIqv hvq AwfKl©R Z¡i‡Yi gvb ZZB Kg‡Z _v‡KÑ e ̈vL ̈v Ki| (M) c„w_exi †giæ we›`y‡Z AwfKl©R Z¡i‡Yi gvb wbY©q Ki| mgvavb: gp = g –  2Rcos2  = 9.8 –     2 86400 2  6.4  106  {cos (90)} 2 = 9.8 ms–2 (Ans.) (N) DÏxc‡K c„w_exi welyexq A‡j GKwU e ̄‘i IRb k~b ̈ n‡Z n‡j †KŠwYK †e‡Mi gvb e„w× Ki‡Z n‡e|Ñ MvwYwZKfv‡e we‡kølY Ki| mgvavb:  = 2 T = 2 86400 = 0.0000727 rads –1 g = g –  2R cos2   0 = 9.8 –  2  6.4  106  cos2 (0)   = 0.001237 rads –1   = 0.001237 0.0000727 = 17.015  †KŠwYK †eM c~‡e©i 17.015 ̧Y Ki‡j welyexq A‡j GKwU e ̄‘i IRb k~b ̈ n‡e| (Ans.) 5| m~h© I c„w_exi fi h_vμ‡g 2  1030 kg I 6  1024 kg c„w_ex n‡Z m~‡h©i `~iZ¡ 1.5  1011 m| [h. †ev. 23] (K) gyw3‡eM Kv‡K e‡j? (L) cwi‡e‡ki ZvcgvÎvi n«vm e„w×i mv‡_ †`vjK Nwo `aæZ wKsev ax‡i P‡jÑ e ̈vL ̈v K‡iv| (M) m~h© I c„w_exi ms‡hvM‡iLvi ga ̈we›`y‡Z gnvKl©xq wef‡ei gvb †ei K‡iv| mgvavb: V = VS + VE = – GMS d 2 – GME d 2 = – 6.673  10–11 1.5  1011 2 (2  1030 + 6  1024) = –1.779  109 J (Ans.) (N) c„w_ex I m~‡h©i ms‡hvMKvix mij‡iLvi Dci GKvwaK we›`y‡Z cÖve‡j ̈i gvb k~b ̈ nIqv m¤¢e wKbv MvwYwZKfv‡e we‡kølY K‡iv| mgvavb: x r – x awi, m~h© n‡Z x `~i‡Z¡ jwä cÖve‡j ̈i gvb k~b ̈|  E1 = E2  GM x 2 = GM (r – x) 2  r – x x = m M  r x = m M + 1  x = r m M + 1 = 1.5  1011 6  1024 2  1030 + 1  x = 1.4974  1011 m (Ans.) 6| c„w_exi fi Ges e ̈vmva© h_vμ‡g M = 6 × 1024 kg Ges R = 6.4 × 106 m| c„w_exi c„ô †_‡K 700 km D”PZvq GKwU K...wÎg DcMÖn AveZ©b Ki‡Q| [G = 6.673 × 10–11 Nm2 kg–2 ] [e. †ev. 23] (K) †Ubmb ej Kv‡K e‡j? (L) Puv‡` gvbyl emevm Ki‡Z cv‡i wK bv? e ̈vL ̈v Ki| (M) K...wÎg DcMÖnwUi †K›`agyLx Z¡iY wbY©q Ki| mgvavb: v = GM R + h = 6.673  10–11  6  1024 6.4  106 + 700  103 = 7509.43 ms–1 a = v 2 r = (7509.43) 2 (6.4  106 + 700 + 103 ) = 7.94 ms–2 (Ans.)

4  HSC Physics 1st Paper Chapter-6 f‚c„ô n‡Z h D”PZvq, gh = R 2 (R + h) 2 g  y = c (R + x) 2 = c X 2 [†hLv‡b, X = R + x] h gh g O GwU GKwU Awae„ËKvi †jLwPÎ| (Ans.) 10| †Kv‡bv GKwU KvíwbK MÖ‡ni fi c„w_exi f‡ii mgvb wKš‘ e ̈vmva© c„w_exi e ̈vmv‡a©i wØ ̧Y| 3 kg f‡ii GKwU e ̄‘ Dfq MÖ‡ni c„ô n‡Z 9 kms–1 †e‡M Lvov Dc‡ii w`‡K wb‡ÿc Kiv n‡jv| c„w_exi fi 5.97 × 1024 kg Ges e ̈vmva© 6.4 × 106 m| [Xv. †ev. 22] (K) w ̄’wZ ̄’vcK msNl© Kv‡K e‡j? [Aa ̈vq-4] (L) †KŠwYK fi‡e‡Mi w`K Kxfv‡e cvIqv hvq, e ̈vL ̈v Ki| [Aa ̈vq-4] (M) c„w_exi gyw3 †eM wbY©q Ki| DËi: ve = 2GM R = 2  6.673  10–11  5.97  1024 6.4  106 = 11155 ms–1 (Ans.) (N) DÏxc‡Ki wbwÿß e ̄‘wU Dfq MÖ‡n wd‡i Avm‡e wK bvÑ MvwYwZKfv‡e we‡kølY Ki| DËi: MP = Me RP = 2Re c„w_exi †ÿ‡Î: ve = 11.155 kms–1 [M n‡Z] v < ve c„w_ex‡Z †diZ Avm‡e| KvíwbK MÖ‡ni †ÿ‡Î : ge gp =     Rp Re 2  ge gp = 4  gp = GMe R 2  1 4 = 2.431 ms–2 ve = 2gPRP = 2.4315  2  6.4  106 = 5.5788 kms–1 < v †diZ Avm‡e bv| (Ans.) 11| XvKvi f~-c„ô n‡Z Lvov 26000 km Dc‡i GKwU K...wÎg DcMÖn ̄’vcb Kiv n‡jv| c„w_exi e ̈vmva© 6400 km Ges fi 6 × 1024 kg. [P. †ev. 22] (K) gyw3 †e‡Mi msÁv `vI| (L) GKB Kÿc‡_ ̄’vwcZ `ywU wfbœ f‡ii m ̈v‡UjvB‡Ui †eM wK GKB n‡e, bv wfbœ n‡e? e ̈vL ̈v Ki| (M) K...wÎg DcMÖnwUi Kÿxq †eM wbY©q Ki| mgvavb: Kÿxq †eM, v = GM R + h  v = 6.673  10–11  6  1024 6.4  106 + 26000  103  v = 3515.31 ms–1  v = 3.515 kms –1 (Ans.) (N) DcMÖnwU‡K me mgq XvKvi Dci †`Lv hv‡e Kx? MvwYwZK we‡kølYc~e©K gZ `vI| DËi: T = 2 (R + h) 3 GM = 2 (6.4  106 + 26000  103 ) 3 6.673  10–11  6  1024 = 57911.01 s  T = 16.086 hr †h‡nZz, T  24 hr, †`Lv hv‡e bv| (Ans.) 12| c„w_exi c„ô n‡Z 500 km D”PZvq GKwU K...wÎg DcMÖn ̄’vcb Kiv n‡jv| c„w_exi e ̈vmva© 6400 km Ges c„w_exi c„‡ô AwfKl©R Z¡iY 9.81 ms–2 | [iv. †ev. 22] (K) `kv Kx? (L) c„w_exi Nb‡Z¡i cwieZ©‡b AwfKl©R Z¡i‡Yi cwieZ©b n‡e Kx? (M) DÏxc‡Ki D”PZvq AwfKl©R Z¡i‡Yi gvb wbY©q Ki| DËi: gup = g     R R + h 2 = 9.81      6.4  106 6.4  106 + 500  1000 2 = 8.44 ms–2 (Ans.) (N) DÏxc‡Ki DcMÖnwU f~w ̄’i DcMÖ‡n iƒcvšÍi m¤¢e wKbv? MvwYwZK we‡kølYmn †Zvgvi gZvgZ `vI| DËi: T = 2 (R + h) 3 GM = 2 (6.4  106 + 500  103 ) 3 6.673  10–11  6  1024 = 5681.18s = 1.57 hr  24 hrs f‚w ̄’i DcMÖ‡ni †ÿ‡Î, T = 2 (R + h) 3 GM  24  3600 = 2 (6.4  106 + h) 3 6.673  10–11  6  1024  h  36000 km  DcMÖnwU‡K Av‡iv (36000 – 500) = 35500 km Dc‡i DVv‡j DcMÖnwU f‚w ̄’i DcMÖ‡n cwiYZ n‡e| (Ans.)