Title 7. P1C7. Phy. For FRB-2024_With Solve_Ridoy 20.01.25.pdf ✅

c`v‡_©i MvVwbK ag©  Final Revision Batch 1 mßg Aa ̈vq c`v‡_©i MvVwbK ag© Structural Properties of Matter Topicwise CQ Trend Analysis UwcK 2016 2017 2018 2019 2022 2023 2024 †gvU weK...wZ 1 3 2 2 2 Ñ Ñ 10 cxob Ñ 1 1 2 4 Ñ 1 9 Amn ej 1 Ñ Ñ 1 Ñ Ñ Ñ 2 Bqs Gi ̧Yv1⁄4 Ges w ̄’wZ ̄’vcK mxgv msμvšÍ 1 3 Ñ 3 6 6 7 26 cxob-weK...wZ †jL Ñ Ñ Ñ Ñ 2 1 Ñ 3 AvqZb w ̄’wZ ̄’vcK ̧Yv1⁄4 I K...šÍb weK...wZ Ñ 1 Ñ Ñ 3 Ñ 1 5 GKK AvqZ‡b mwÂZ kw3 1 1 1 2 1 1 2 9 cqm‡bi AbycvZ Ñ 2 Ñ 1 3 3 6 15 * 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| GKwU cixÿ‡Y 1 cm Ges 3 cm e ̈mv‡a©i wfbœ Dcv`v‡bi `ywU Zvi GKwU `„p Aej¤^b †_‡K Szjv‡bv n‡jv| Zvi `ywUi •`N© ̈ Awfbœ| Zvi `ywU‡Z GKB fi Szjv‡bv‡Z wØZxq ZviwUi •`N© ̈ e„w× cÖ_g ZviwUi •`N© ̈ e„w×i A‡a©K n‡jv| cÖ_g ZviwUi cqm‡bi AbycvZ 0.3| [Xv. †ev. 24] (K) cxob Kx? (L) ZvcgvÎv evov‡j w ̄’wZ ̄’vcK ̧Yvs‡Ki gvb K‡g †Kb? e ̈vL ̈v Ki| (M) cÖ_g ZviwUi •`N© ̈ 10% evov‡j Gi e ̈vmva ̈ KZUzKz n«vm cv‡e? mgvavb: 1g Zv‡ii e ̈vmva©, r  1 cm •`N© ̈ e„w×, L L  10%  10 100  0.1 e ̈vmva© n«vm, r  ? Avgiv Rvwb, cqm‡bi AbycvZ   – r r L L ev, r  – r L L ev, r  – 0.3  1  0.1  r  – 0.03 cm GLv‡b FYvZ¥K wPý wb‡`©k K‡i †h Zv‡ii e ̈vmva© n«vm †c‡q‡Q| AZGZ, e ̈vmva© n«vm 0.03 cm| (Ans.) (N) DÏxc‡Ki †Kvb ZviwUi fvi en‡bi mÿgZv †ewk n‡e? MvwYwZKfv‡e hvPvB Ki| mgvavb: 1g Zv‡ii †ÿ‡Î, Y1  F1L1 A1 l1 Ges 2q Zv‡ii †ÿ‡Î, Y2  F2L2 A2 l2 †h‡nZz Dfq Zv‡ii cÖv_wgK •`N© ̈ Awfbœ GRb ̈ L1 = L2 Ges GKB fi Szjv‡j, F1 = F2  Y1 Y2  F1L1 A1 l1 F2L2 A2 l2  A2 l2 A1 l2  r 2 2 l1 2 r 2 1 l1  r 2 2 2r2 1  3 2 2  1 2  9 2    †h‡nZz 2q Zv‡ii •`N© ̈ e„w× cÖ_gwUi A‡a©K GRb ̈ l2   l1 2 ev, Y1  9 2 Y2  Y1 > Y2 AZGe, 1g ZviwUi Bqs Gi ̧YvsK 2q Zvi A‡cÿv †ewk| myZivs 1g ZviwU †ewk w ̄’wZ ̄’vcK| GRb ̈ 1g Zv‡ii fi en‡bi mÿgZv †ewk| (Ans.) 2| P, Q I R Zv‡ii wewfbœ ivwki gvb wb¤œiƒc: Zvi Avw` •`N© ̈ L e ̈vm D •`N© ̈ e„w× l •`N© ̈ n«vm d cÖhy3 ej F (m) (X10–3m) (X10–3m) (X10 –6 m) (N) P 1 2 0.14 0.0418 10 Q 1 2 0.18 0.0593 12 R 1 2 0.22 0.0912 13 [P. †ev. 24] (K) Av‡cwÿK Av`a©Zv Kv‡K e‡j? (L) c„w_exi †K‡›`a AwfKl©R Z¡i‡Yi gvb k~b ̈ †Kb? e ̈vL ̈v Ki| (M) ÔRÕ ZviwUi cqm‡bi AbycvZ KZ? mgvavb: †`Iqv Av‡Q, R Zv‡ii Avw` •`N© ̈, L  1m •`N© ̈ e„w×, l  0.22  10–3 m Avw` e ̈vm, D  2  10–3 m e ̈‡mi cwieZ©b, d  0.0912  10–6 m
2  HSC Physics 1st Paper Chapter-7 Avgiv Rvwb, cqm‡bi AbycvZ,   cvk¦© weK...wZ •`N© ̈ weK...wZ  d D l L  dL Dl  0.0912  10–6  1 2  10–3  0.22  10–3  0.207 (Ans.) (N) P I Q Zvi `ywUi g‡a ̈ †KvbwU †ewk w ̄’wZ ̄’vcK? †Zvgvi Dˇii mc‡ÿ MvwYwZK hyw3 `vI| [Abyiƒc Xv. †ev., Kz. †ev. 24] 3| A I B `ywU Zv‡ii •`N© ̈ mgvb| A Zv‡ii e ̈vm 3 mm Ges Gi Bqs Gi ̧Yv1⁄4 YA = 2  109 , Nm–2 | B Zv‡ii e ̈vm 2 mm| Zvi `ywU‡Z c„_K c„_K mg‡q cÖwZwU‡Z 400 kg fi Szjv‡j cÖ_g ZviwUi •`N© ̈ e„w× wØZxqwUi wZb ̧Y nq| [g. †ev. 24] (K) Amn cxob Kx? (L) B ̄úv‡Zi Bqs Gi ̧Yv1⁄4 2  1011 Nm–2 e ̈vL ̈v Ki| (M) cÖ_g Zv‡ii •`N© ̈ 30% e„w× Ki‡j GKK AvqZ‡b mwÂZ wefe kw3 wbY©q Ki| mgvavb: †`Iqv Av‡Q, Bqs ̧YvsK, Y  2  109 Nm–2 Zv‡ii e ̈vm, d  3 mm awi, Avw` •`N© ̈  L •`N© ̈ e„w×, l  L Gi 30%  0.3 L Avgiv Rvwb, GKK AvqZ‡b mwÂZ kw3, U  1 2  cxob  weK...wZ  1 2  F A  l L  1 2  YAl L A  l L  1 2  Y      l L 2  1 2  2  109      0.3 L L 2  109  (0.3)2  U  9  107 Jm–3 (Ans.) (N) YB > YA m¤úK©wU hyw3m1⁄2Z wK bvÑ MvwYwZKfv‡e †`LvI| [Abyiƒc Xv. †ev. 24] 4| P I Q `ywU Zv‡ii •`N© ̈ mgvb wKš‘ e ̈vm h_vμ‡g 4 mm I 8 mm| Zvi `ywU‡K mgvb e‡j Uvbvi d‡j P Zv‡ii •`N© ̈ e„w× Q Zv‡ii •`N© ̈ e„w×i wZb ̧Y nq| Q Zv‡ii cqm‡bi AbycvZ 0.45| [w`. †ev. 24] (K) w ̄’wZ ̄’vcK K¬vwšÍ Kv‡K e‡j? (L) GKwU gUi mvB‡Kj I GKwU cÖvB‡fU Kv‡ii fi‡eM mgvb n‡j †KvbwUi MwZkw3 †ewk n‡e? e ̈vL ̈v Ki| (M) Q Zv‡ii •`N© ̈ 5% n«vm Kiv n‡j Gi e ̈vmva© KZUzKz e„w× cv‡e? [Abyiƒc Xv. †ev. 24] (N) DÏxc‡Ki †Kvb fv‡ii w ̄’wZ ̄’vcK mxgv †ewk? MvwYwZKfv‡e we‡kølY Ki| [Abyiƒc Xv. †ev. 24] 5| 10 cm evûwewkó GKwU B ̄úv‡Zi •Zwi Nb‡Ki DcwiZ‡j 2.48  107 N AvKvi cxob m„wóKvix ̄úk©K ej cÖ‡qvM Ki‡j wecixZ w ̄’i Z‡ji mv‡c‡ÿ ZjwUi 2.95 mm miY N‡U| Aciw`‡K 3 cm evûwewkó GKwU A ̈vjywgwbqvg Nb‡Ki wecixZ Z‡j mgvb I wecixZ ̄úk©Kxq ej cÖ‡qv‡M Z‡ji †K.wYK miY nq 0.01| A ̈vjywgwbqv‡gi AvKvi ̧Yv1⁄4 2.6  1010 Nm–2 | [iv. †ev. 24] (K) w ̄’wZ ̄’vcK mxgv Kv‡K e‡j? (L) Zvgvi Bqs Gi ̧Yv1⁄4 12.6  1010 Nm–2 ej‡Z Kx eyS? [Abyiƒc g. †ev. 24] (M) A ̈vjywgwbqv‡gi Nb‡Ki Dci cÖhy3 e‡ji cwigvY wbY©q Ki| mgvavb: †`Iqv Av‡Q, A ̈vjywgwbqv‡gi AvKvi ̧Yv1⁄4,   2.6  1010 Nm–2 Nb‡Ki evûi •`N© ̈, a  3 cm  0.03 m  Z‡ji †ÿÎdj, A  a 2  (0.03)2 m 2  9  10–4 m 2 †K.wYK miY,   0.01  0.01   180 rad  5.56  10–5  rad A ̈vjywgwbqvg Nb‡Ki Dci cÖhy3 ej F n‡j, AvKvi ̧Yv1⁄4,   F A  ev,   F A ev, F = A ev, F  2.6  1010  9  10–4  5.56  10–5   F  4087.34 N myZivs, A ̈vjywgwbqvg Nb‡Ki Dci cÖhy3 ej, F  4087.34 N| (Ans.) (N) DÏxc‡Ki †Kvb Dcv`v‡bi •Zwi Nb‡Ki `„pZv †ewk? MvwYwZK we‡kølYc~e©K gZvgZ `vI| mgvavb: GLv‡b, B ̄úv‡Zi Nb‡Ki †ÿ‡Î, evû •`N© ̈, a  10 cm = 0.1 m Z‡ji †ÿÎdj, A  a 2  (0.1)2 = 0.01 m2 ̄úk©Kxq ej, F  2.48  107 N Av‡cwÿK miY, x  2.95 mm  0.295 cm x a  F K...šÍb weK...wZ,   miY evûi •`N© ̈  x a  0.295 cm 10 cm = 0.0295
c`v‡_©i MvVwbK ag©  Final Revision Batch 3 GLb, B ̄úv‡Zi `„pZvi ̧Yv1⁄4  n‡j,   F A  ev,   F A ev,   2.48  107 0.01  0.0295    8.41  1010 Nm–2 †`Iqv Av‡Q, A ̈vjywgwbqv‡gi `„pZvi ̧Yv1⁄4,   2.6  1010 Nm–2 A_©vr,  >  AZGe, B ̄úv‡Zi •Zwi Nb‡Ki `„pZv †ewk| (Ans.) 6| 2 m j¤^v I 4  10–6 m 2 cÖ ̄’‡”Q‡`i †ÿÎdjwewkó †Kv‡bv avZe Zv‡ii GKcÖv‡šÍ 10 kg fvi Szjv‡j GwU •`N© ̈ 1% e„w× cvq| wewfbœ avZzi cqm‡bi AbycvZ †`Lv‡bv n‡jv| avZz cqm‡bi AbycvZ †jvnv 0.22 A ̈vjywgwbqvg 0.33 mxmv 0.44 [h. †ev. 24] (K) w ̄’wZ ̄’vcK ̧Yv1⁄4 Kx? (L) Ò†Kv‡bv Zv‡ii w ̄’wZ ̄’vcK wefekw3 50 JÓ ej‡Z Kx eySvq? (M) ZviwUi •`N© ̈ 1% e„wׇZ K...ZKvR KZ? mgvavb: †`Iqv Av‡Q, Zv‡ii •`N© ̈, L  3 m cÖ ̄’‡”Q‡`i †ÿÎdj, A  4  10–6 m 2 ZviwUi •`N© ̈ e„w×, l  L Gi 1%  3  1 100  0.03 m Zv‡ii GK cÖv‡šÍ Szjv‡bv e ̄‘i fi, m  10 kg K...ZKvR, W = ? Avgiv Rvwb, K...ZKvR, W  1 2  YAl 2 L  1 2  FL Al  Al 2 L     Y   FL Al  1 2 Fl  1 2 mgl  1 2  10  9.8  0.03  1.47 J AZGe, ZviwUi •`N© ̈ 1% e„wׇZ K...ZKvR 1.47 J (Ans.) (N) ZviwU †Kvb c`v‡_© •Zwi? gZvgZ `vI| mgvavb: †`Iqv Av‡Q, ZviwUi Avw` •`N© ̈, L1  3m ZviwUi cÖv_wgK cÖ ̄’‡”Q‡`i †ÿÎdj, A1  4  10–6 m 2  ZviwUi cÖv_wgK AvqZb, V1  3  4  10–6 m 3  12  10–6 m 3 ZviwUi cwiewZ©Z •`N© ̈, L2  3 + 3 Gi 1%  3 + 3  1 100  3.03 m awi, ZviwUi cwiewZ©Z †ÿÎdj  A2  cwiewZ©Z AvqZb n‡e, V2  A2L2  3.03 A2 m 3 wKš‘ cÖv_wgK AvqZb = cwiewZ©Z AvqZb [ †h‡nZz AvqZb aaæeK _v‡K] ev, 3.03 A2  12  10–6 ev, A2  12  10–6 3.03 ev, R 2 2  3.96  10–6 [ R 2 = cwiewZ©Z Zv‡ii e ̈vmva©] ev, R2  3.96  10–6   R2  1.122778  10–3 m Avevi, cÖv_wgK †ÿÎdj, A1  4  10–6 ev, R 2 1  4  10–6 ev, R1  4  10–6   1.1284  10–3 m  r  R1 – R2  (1.1284  10–3 – 1.122778  10–3 ) m  5.622  10–6 m Avgiv Rvwb, cqm‡bi AbycvZ,   L1r R1 l  3  5.622  10–6 1.1284  10–3  0.03  0.498 DÏxc‡Ki Z_ ̈vbyhvqx, ZviwUi cqm‡bi AbycvZ 0.498| hv DÏxc‡Ki wZbwU avZzi cqm‡bi Abycv‡Zi †KvbwUi mgvb bq| d‡j DÏxc‡Ki avZe ZviwU D‡jøwLZ †Kvb avZzi •Zwi bq| Z‡e mxmvi cqm‡bi AbycvZ me‡P‡q KvQvKvwQ nIqvq gZvgZ †`Iqv hvq ZviwU mxmvi •Zwi| (Ans.) 7| X Ges Y Zv‡ii wewfbœ ivwki gvb wb‡¤œi Q‡K †`qv nj: Zvi •`N ̈© L(m) e ̈vmva© r(mm) ej F(N) •`N© ̈ cÖmviY 1(mm) e ̈vm n«vm d(mm) X 0.80 0.5 5 7 0.005 Y 0.75 0.5 6 8 0.01 [Kz. †ev. 24] (K) Kg©`ÿZv Kv‡K e‡j? (L) Zvgvi Zv‡ii cqm‡bi AbycvZ 0.33 ej‡Z Kx eySvq? e ̈vL ̈v Ki| (M) X Zv‡ii cqm‡bi AbycvZ wbY©q Ki| mgvavb: †`Iqv Av‡Q, X Zv‡ii, Avw` •`N© ̈, L = 0.8m •`N© ̈ e„w×, l = 7mm = 7  10–3m Avw` e ̈vm, D = (0.5  2)mm = 1mm e ̈v‡mi n«vm, d = – 0.005mm Avgiv Rvwb, cqm‡bi AbycvZ,  = – dL Dl = – (– 0.005)  0.8 1  7  10–3 = 0.571 (Ans.) (N) X Ges Y Zv‡ii g‡a ̈ †KvbwU †ewk w ̄’wZ ̄’vcK MvwYwZKfv‡e we‡kølY Ki| [Abyiƒc wm. †ev. 24]
4  HSC Physics 1st Paper Chapter-7 8| P, Q Ges R wZbwU Zv‡i 8  1012 Nm–2 gv‡bi cxob cÖ‡qvM Kiv nj| Gi d‡j Zvi ̧‡jvi •`N© ̈ e„w× h_vμ‡g 5%, 2% I 1% n‡jv| P Zv‡ii cvk¦©weK...wZ 0.02| [wm. †ev. 24] (K) w ̄’wZ ̄’vcKZv Kv‡K e‡j? (L) Òivevi Gi †P‡q w÷j †ewk w ̄’wZ ̄’vcKÓÑ e ̈vL ̈v Ki| (M) P Zv‡ii cqmb AbycvZ wbY©q Ki| mgvavb: g‡b Kwi, mgvb •`N© ̈ L wewkó B ̄úvZ I ivev‡ii Zv‡i mgvb F cwigvY ej cÖ‡qvM Kiv n‡jv| G‡Z K‡i B ̄úv‡Zi Zv‡ii •`N© ̈ cÖmviY ls Ges ivev‡ii Zv‡ii •`N© ̈ cÖmviY lR| `yBwU Zv‡ii cÖ ̄’‡”Q‡`i †ÿÎdj A n‡j B ̄úv‡Zi Zv‡ii Bqs Gi ̧Yv1⁄4, YS  FL AlS Ges ivev‡ii Zv‡ii Bqs Gi ̧Yv1⁄4 YR  FL AlR n‡e| A_©vr, YS YR  FL AlS FL AlR  lR lS mgcwigvY ej cÖ‡qvM Kivq B ̄úvZ A‡cÿv ivevi †ewk cÖmvwiZ nIqvq lR > lS| A_©vr, lR lS > 1 myZivs, YS YR > 1  YS > YR B ̄úv‡Zi Bqs-Gi ̧Yv1⁄4 †ewk GRb ̈ ivev‡ii †P‡q †ewk w ̄’wZ ̄’vcK| (N) Q I R Zv‡ii g‡a ̈ †KvbwU †ewk w ̄’wZ ̄’vcK? MvwYwZK hyw3mn †Zvgvi gZvgZ `vI| [Abyiƒc P. †ev. 24] 9| GKwU Zv‡ii Avw` •`N© ̈ 826 cm Ges Zv‡ii e ̈vm 4 mm, Zv‡ii Bqs Gi ̧YvsK Y = 2  1011 N/m2 , ZviwUi •`N© ̈ 2 mm e„w× Ki‡Z cÖ‡qvRbxq fi hy3 Ki| [e. †ev. 24] (K) Bqs Gi ̧YvsK Kv‡K e‡j? (L) B ̄úv‡Zi Bqs-Gi ̧YvsK 2  1011 Nm2 ej‡Z Kx eySvq? e ̈vL ̈v Ki| [Abyiƒc iv. †ev. 24] (M) Kx cwigvY fi hy3 Kiv n‡qwQj wbY©q Ki| [e. †ev. 24] mgvavb: †`Iqv Av‡Q, Zv‡ii •`N© ̈, L  826 cm  8.26 m Zv‡ii •`N© ̈ e„w×, l  2mm  2  10–3 m Zv‡ii e ̈vm, D  4 mm  4  10–3 m Zv‡ii Bqs ̧Yv1⁄4, Y  2  1011 N/m2 Szjv‡bv fi, m  ? Avgiv Rvwb, Y  FL Al ev, FL  YAl ev, mgL  YAl ev, m  Y D 2 4 l gL     A   D 2 4 ev, m  YD 2 l 4gL  2  1011    (4  10–3 ) 2  2  10–3 4  9.8  8.26  m  62 kg A_©vr, ZviwU‡Z 62 kg fi hy3 Kiv n‡qwQj| (Ans.) (N) DÏxcK Abymv‡i ZviwUi •`N© ̈ e„w× Kiv‡Z e ̈vm 0.02 mm n«vm cvIqv m¤¢e wK? MvwYwZKfv‡e we‡kølY Ki| mgvavb: †`Iqv Av‡Q, ZviwUi Avw` •`N© ̈, L1  826 cm  8260 mm Avw` e ̈vm, D1  4 mm cwiewZ©Z •`N© ̈, L2  (8260 + 2) mm  8262 mm cwiewZ©Z e ̈vm, D2  ? GLb, weK...wZi Av‡M Zv‡ii AvqZb = weK...wZi ci Zv‡ii AvqZb [ AvqZb aaæeK _v‡K] ev, 1 4 D 2 1 L1  1 4 D 2 2 L2 ev, D 2 1 L1  D 2 2 L2 ev, D2  D1 L1 L2  4  8260 8262  3.9995 mm  e ̈vm n«vm, d  D1 – D2  (4 – 3.995) mm  0.0005 mm GLv‡b, d < 0.02 mm myZivs, DÏxcK g‡Z ZviwUi •`N© ̈ e„wׇZ e ̈vm 0.02 mm cvIqv m¤¢e bq| (Ans.) 10| A I B `ywU Zvi| A Zv‡ii •`N© ̈ l1 I e ̈vmva© r1; Ab ̈w`‡K B Zv‡ii •`N© ̈ l2 I e ̈vmva© r2| Dfq Zv‡i 7 kg fi Djø¤^fv‡e wb‡P Pvcv‡bv n‡j A Zv‡ii •`N© ̈ e„w× cvq| 1 mm| B Zv‡iiI •`N© ̈ e„w× cvq| [Xv. †ev. 23] (K) `kv Kx? (L) †Kvb mg‡q mij †`vj‡Ki MwZ mij‣iwLK nq? e ̈vL ̈v K‡iv| (M) A Zv‡i K...ZKv‡Ri cwigvY wbY©q K‡iv| mgvavb: K...ZKvR, W = 1 2 Fl = 1 2  mg  l = 1 2  7  9.8  10–3 J  W = 0.034 J  A Zv‡i K...ZKv‡Ri cwigvY 0.034 J| (Ans.) (N) B Zv‡ii AvqZb AcwiewZ©Z _vK‡j Bnvi cqm‡bi Abycv‡Zi gvb †ei Kiv m¤¢e wK? MvwYwZKfv‡e we‡kølY Ki| mgvavb: cqm‡bi AbycvZ  = – cvk¦© weK...wZ •`N© ̈ weK...wZ = – D D L L = dD D dL L V = r 2L V = L     D 2 2 V = D 2L 4