Title 7. P1C7. Phy. For FRB-2024_With Solve_Sha 29.02.24 PDF.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 †gvU weK...wZ 1 3 2 2 2 Ñ 10 cxob Ñ 1 1 2 4 Ñ 8 Amn ej 1 Ñ Ñ 1 Ñ Ñ 2 Bqs Gi ̧Yv1⁄4 Ges w ̄’wZ ̄’vcK mxgv msμvšÍ 1 3 Ñ 3 6 6 19 cxob-weK...wZ †jL Ñ Ñ Ñ Ñ 2 1 3 AvqZb w ̄’wZ ̄’vcK ̧Yv1⁄4 I K...šÍb weK...wZ Ñ 1 Ñ Ñ 3 Ñ 4 GKK AvqZ‡b mwÂZ kw3 1 1 1 2 1 1 7 cqm‡bi AbycvZ Ñ 2 Ñ 1 3 3 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| 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 †h‡nZz AvqZb aaæeK _v‡K dV dL = 0  d dL     D 2L 4 = 0   4    D 2  + L × 2D × dD dL = 0  2L dD dL = – D  – 2dD D = dL L cqm‡bi AbycvZ  = – dD D dL L = – dD D – 2dD D = 1 2 (Ans.) cqm‡bi AbycvZ †ei Kiv m¤¢e| wb‡Y©q cqm‡bi AbycvZ 0.5| 2| wb‡Pi Q‡K `ywU Zvi A I B Gi wewfbœ ivwki gvb cÖ`vb Kiv n‡jv: [iv. †ev. 23; w`. †ev. 23; g. †ev. 23] Zvi •`N© ̈ L(m) e ̈vm D(mm) cÖhy3 ej F(N) •`N© ̈ cÖmviY 1(mm) cqm‡bi AbycvZ  A 1.60 1.0 5.0 14 0.57 B 1.50 1.2 6.0 16 – (K) w ̄’wZ ̄’vcK mxgvi msÁv `vI| (L) GKwU w÷j Zv‡ii Ici cÖhy3 ej Ges e ̈vmva© hw` wØ ̧Y Kiv nq Z‡e Bqs Gi ̧Yv‡1⁄4i wK cwieZ©b n‡e? e ̈vL ̈v Ki| (M) ej cÖ‡qv‡M A Zv‡ii e ̈vm KZ n«vm cv‡e? wbY©q Ki| mgvavb: cqm‡bi AbycvZ  = – D D L L  0.57 = – D 10 –3 14 × 10–3 1.6  D = – 4.9875 × 10–6 m e ̈vm n«vm cv‡e 4.9875 × 10–6 m (Ans.)
2  HSC Physics 1st Paper Chapter-7 (N) †Kvb ZviwU w`‡q A‡cÿvK...Z kw3kvjx w ̄úas •Zwi Kiv hv‡e? MvwYwZK we‡køl‡Yi mvnv‡h ̈ gšÍe ̈ Ki| mgvavb: †h Zv‡ii Bqs-Gi ̧Yv1⁄4 †ewk †m Zvi w`‡q A‡cÿvK...Z kw3kvjx w ̄úas •Zwi Kiv hv‡e| A Zv‡ii †ÿ‡Î, YA = FL Al = 5 × 1.6  ×     1 2 × 10–3 2 × 14 × 10–3 = 7.28 × 108 Nm–2 B Zv‡ii †ÿ‡Î, YB = FL Al = 6 × 1.5  ×     1.2 2 × 10–3 2 × 16 × 10–3 = 4.97 × 108 Nm–2 ∵ YA > YB A Zvi w`‡q A‡cÿvK...Z kw3kvjx w ̄úas •Zwi Kiv hv‡e| 3| GKwU w ̄’wZ ̄’vcK e ̄‘i cxob ebvg weK...wZ Gi †jLwPÎ wb‡P †`Lv‡bv nj| [Kz. †ev. 23] 0.4 O 2108Nm 2 A cxob weK...wZ B (K) Amn cxob Kv‡K e‡j? (L) c`v‡_©i g‡a ̈ w ̄’wZ ̄’vcKZv ag© m„wói KviY Kx? e ̈vL ̈v K‡iv| (M) e ̄‘wUi w ̄’wZ ̄’vcK ̧Yv1⁄4 wbY©q K‡iv| mgvavb: e ̄‘wUi w ̄’wZ ̄’vcK ̧Yv1⁄4 Y = cxob weK...wZ = 2 × 108 0.4 = 5 × 108 Nm–2 A_©vr e ̄‘wUi w ̄’wZ ̄’vcK ̧Yv1⁄4 5 × 108 Nm–2 (Ans.) (N) †jLwP‡Îi †h‡Kv‡bv we›`yi Xvj †_‡K Bqs Gi ̧Yv1⁄4 wbY©q Kiv m¤¢e bqÑ †h.w3K e ̈vL ̈v Dc ̄’vcb K‡iv| mgvavb: A B O 0.4 2 × 108 Nm2 weK...wZ cxob †jLwPÎ †_‡K †`Lv hvq, cÖ_‡g weK...wZ e„w×i mv‡_ mv‡_ cxob mylgfv‡e evo‡Z _v‡K A_©vr cxob weK...wZi mgvbycvwZK nq| †jLwP‡Î OA mij‡iLvwU ZvB wb‡`©k K‡i| †jLwP‡Îi I AÂj‡K AvbycvwZK AÂj e‡j| GB A‡ji g‡a ̈ †h‡Kv‡bv we›`yi Xvj †_‡K Bqs Gi ̧Yv1⁄4 wbY©q Kiv m¤¢e| wKš‘, AB As‡k cxob I weK...wZi AbycvZ aaæeK nq bv, μgvMZ Kg‡Z Ges evo‡Z _v‡K| Gÿ‡Î cÖhy3 ej AcmviY Ki‡j wKQzUv ̄’vqx weK...wZ †_‡K hvq| GB As‡k cxob weK...wZi AbycvZ KLbI FYvZ¥K KLbI abvZ¥K jÿ ̈ Kiv hvq| Zv‡ii †Kv‡bv †Kv‡bv Ask miæ nIqvi Rb ̈ Giƒc nq| ZvB AB As‡k †h‡Kv‡bv we›`yi Xvj †_‡K Bqs Gi ̧Yv1⁄4 wbY©q Kiv m¤¢e bq| ZvB ejv hvq, †jLwP‡Îi †h‡Kv‡bv we›`yi Xvj †_‡K Bqs Gi ̧Yv1⁄4 wbY©q Kiv m¤¢e bq| 4| 2 m •`‡N© ̈i `ywU Zv‡ii e ̈vm h_vμ‡g 2 mm I 3 mm| Zvi `ywUi cÖ‡Z ̈KwU‡Z 7 × 103 N ej cÖ‡qvM Kiv n‡j G‡`i •`N© ̈ h_vμ‡g 5% I 2% e„w× †cj| [h. †ev. 23] (K) w ̄’wZ ̄’vcK ̧Yv1⁄4 Kx? (L) cvi‡`i AvqZb ̧Yv1⁄4 2 × 1010 Nm–2 ej‡Z Kx eyS? e ̈vL ̈v Ki| (M) DÏxc‡Ki cÖ_g ZviwUi GKK AvqZ‡b mwÂZ w ̄’wZ ̄’vcK kw3i gvb †ei Ki| mgvavb: GKK AvqZ‡b mwÂZ kw3 U = 1 2 × F A × l L = 1 2 × 7 × 103  × (1 × 10–3 ) 2 × 0.05 = 5.57 × 107 Jm–3 1g Zv‡ii †ÿ‡Î GKK AvqZ‡b mwÂZ kw3 5.57 × 107 Jm–3 (Ans.) (N) DÏxc‡Ki †Kvb ZviwUi w ̄’wZ ̄’vcK mxgv †ewk? MvwYwZK we‡køl‡Yi mvnv‡h ̈ gZvgZ cÖ`vb Ki| mgvavb: cÖ_g Zv‡ii †ÿ‡Î, Y1 = F A l L = 7 × 103  × (10–3 ) 2 0.05 = 4.456 × 1010 Nm–2 wØZxq Zv‡ii †ÿ‡Î, Y2 = F A2 l2 L = 7 × 103  ×     3 2 ×10–3 2 0.02 = 4.95 × 1010 Nm–2 Y2 > Y1 2q Zv‡ii w ̄’wZ ̄’vcK mxgv †ewk| (Ans.)
c`v‡_©i MvVwbK ag©  Final Revision Batch 3 5| A B 0 2 7 15 ej (F)N •`N© ̈ e„w× (l) cm wP‡Î 1.5 m Avw` •`‡N© ̈i A I B `yBwU GKB Dcv`v‡bi Zvi| cÖhy3 e‡ji mv‡_ Zvi `yBwUi •`N© ̈ e„w×i †jLwPÎ Dc‡i cÖ`wk©Z n‡q‡Q| YA = 2  1011 N/m2 . [P. †ev. 23] (K) û‡Ki m~ÎwU †jL| (L) GKwU B ̄úv‡Zi Zvi‡K eivei euvKv‡j DËß nq †Kb? e ̈vL ̈v K‡iv| (M) A Zv‡ii e ̈vmva© wbY©q K‡iv| mgvavb: Avgiv Rvwb, YA = FL Al YA = FL r 2 l  2 × 1011 = 15 × 1.5  × r 2 × (2 × 10–2 )  r = 4.23 × 10–5 m A Zv‡ii e ̈vmva© 4.23 × 10–5 m (Ans.) (N) 10 cm •`N© ̈ cÖmvi‡Y Dfq Zv‡i K...ZKvR mgvb n‡e wKbv Zv MvwYwZKfv‡e hvPvB Ki| mgvavb: Bqs ̧Yv1⁄4, Y = FL Al  F = YA L . l  F  l A_©vr A e ̄‘i †ÿ‡Î, FA FA = lA lA  FA 15 = 10 2  FA = 75 N B e ̄‘i †ÿ‡Î, F B FB = l B lB  F B 7 = 10 2  F B = 35 N  WA WB = 1 2 FA lA 1 2 F B l B  WA WB = 75  0.1 35  0.1  WA = 2.143 WB  WA  WB A_©vr, •`N© ̈ cÖmvi‡Y Dfq Zv‡i K...ZKvR mgvb n‡e bv| (Ans.) 6| mgvb •`‡N© ̈i wZbwU Zvi A, B Ges C Gi Dci GKB gv‡bi cxob 5 × 1012 Nm–2 cÖ‡qv‡Mi d‡j •`N© ̈ e„w× h_vμ‡g 5%, 2% Ges 1% n‡jv| [e. †ev. 23] (K) AvšÍtAvYweK ej Kv‡K e‡j? (L) cxob † ̄..jvi ivwk bv †f±i ivwk? e ̈vL ̈v Ki| (M) ‘B’ Zv‡ii •`N© ̈ weK...wZ KZ? wbY©q Ki| mgvavb: †`Iqv Av‡Q, B Zv‡ii •`N© ̈ e„w× = 2% A_©vr, •`N© ̈ e„w× Avw` •`N© ̈ × 100% = 2%  •`N© ̈ e„w× Avw` •`N© ̈ = 0.02 Avgiv Rvwb weK...wZ = •`N© ̈ e„w× Avw` •`N© ̈  B Zv‡ii •`N© ̈ weK...wZ = 0.02 (Ans.) (N) DÏxc‡Ki †Kvb ZviwU †ewk w ̄’wZ ̄’vcK? MvwYwZKfv‡e hvPvB Ki| mgvavb: †h Zv‡ii Bqs Gi ̧Yv1⁄4 †ewk †m †ewk w ̄’wZ ̄’vcK A Zv‡ii †ÿ‡Î YA = cxob weK...wZ = 5 × 1012 0.05 = 100 × 1012 Nm–2 B Zv‡ii †ÿ‡Î YB = cxob weK...wZ = 5 × 1012 0.02 = 250 × 1012 Nm–2 C Zv‡ii †ÿ‡Î YC = cxob weK...wZ = 5 × 1012 0.01 = 500 × 1012 Nm–2 YC > YB > YA  C ZviwU †ewk w ̄’wZ ̄’vcK| (Ans.) 7| M‡elYvMv‡i e ̈env‡ii Rb ̈ we‡klfv‡e wbwg©Z `ywU Zvi P I Q †bqv nj| cixÿvq cÖvß wewfbœ gvb wb¤œiƒc : [wm. †ev. 23] Zvi •`N© ̈, L(m) e ̈vmva©, r(cm) Szjv‡bv fvi, M(kg) •`N© ̈ cÖmiY, l(mm) e ̈vm n«vm, d(mm) P 2.80 0.50 0.50 3.2 0.005 Q 2.75 0.60 0.75 3 0.009 (K) mij Qw›`Z MwZ Kv‡K e‡j? (L) AvKvk †gNjv _vK‡j wkwki c‡o bv †Kb? e ̈vL ̈v K‡iv| (M) ‘P’ Zv‡ii cqm‡bi AbycvZ wbY©q K‡iv| mgvavb: P Zv‡ii cqm‡bi AbycvZ  = cvk¦© weK...wZ •`N© ̈ weK...wZ = – d d l l = – – 0.005 × 10–3 2 × 0.5 × 10–2 3.2 × 10–3 2.8 = 0.4375 A_©vr P Zv‡ii cqm‡bi AbycvZ 0.4375 (Ans.)
4  HSC Physics 1st Paper Chapter-7 (N) †Kvb ZviwU †ewk w ̄’wZ ̄’vcK? MvwYwZKfv‡e we‡kølY K‡iv| mgvavb: †h Zv‡ii Bqs-Gi ̧Yv1⁄4 †ewk †m ZviwU †ewk w ̄’wZ ̄’vcK YP = FL Al = mgL r 2 l = 0.5 × 9.8 × 2.8  × (0.5 × 10–2 ) 2 × 3.2 × 10–3 = 5.459 × 107 Nm–2 YQ = FL Al = mgL r 2 l = 0.75 × 9.8 × 2.75  × (0.6 × 10–2 ) 2 × 3 × 10–3 = 5.957 × 107 Nm–2 YQ > YP Q ZviwU †ewk w ̄’wZ ̄’vcK| (Ans.) 8| A I B `yBwU avZe Zvi| Zv‡`i •`N© ̈ h_vμ‡g 2m I 2.05 m Ges Zv‡`i e ̈vm h_vμ‡g 2mm I 5mm| Zvi `yBwU‡Z mgvb f‡ii e ̄‘ Szjv‡j A Zv‡ii cÖmviY B Zv‡ii cÖmviY A‡cÿv wØ ̧Y nq| A Zv‡ii cÖmvi‡Yi AbycvZ 0.4| [Xv. †ev. 22] (K) w ̄’wZ ̄’vcK mxgv ej‡Z Kx eyS? (L) Amn cxob 4.5 × 107Nm–2 ej‡Z Kx eyS? (M) A Zv‡ii •`N© ̈ 25% e„w× Ki‡j †ÿÎdj KZUzKz n«vm cv‡e? mgvavb: A Zv‡ii cqm‡bi AbycvZ 0.4 cqm‡bi AbycvZ  = cvk¦© weK...wZ •`N© ̈ weK...wZ  0.4 = – d 2 × 10–3 0.25  d = – 2 × 10–4  e ̈vm n«vm 2 × 10–4 m Avw` †ÿÎdj A1 =  ×     2 2 × 10–3 2 = ( × 10–6 )m2 eZ©gvb e ̈vmva© r2 = (2 × 10–3 ) – (2 × 10–4 ) 2 r2 = 0.0009 m eZ©gvb †ÿÎdj =  × (0.0009)2 = (810 × 10–9 ) m 2  †ÿÎdj n«vm = Avw` †ÿÎdj – eZ©gvb †ÿÎdj Avw` †ÿÎdj × 100% = 19%  A Zv‡ii •`N© ̈ 25% e„w× Ki‡j †ÿÎdj 19% n«vm cv‡e| (Ans.) (N) DÏxc‡Ki †Kvb ZviwUi w ̄’wZ ̄’vcKZv †ewkÑ MvwYwZKfv‡e we‡kølY Ki| mgvavb: A Zv‡ii †ÿÎ, YA = FLA AAlA B Zv‡ii †ÿÎ, YB = FLB ABlB cÖkœg‡Z, lA = 2 × lB GLb, YAAAlA LA = YBABlB LB  YA ×  × (10–3 ) 2 × 2 × lB 2 = YB ×  ×     5 2 × 10–3 2 × lB 2.05  YA = 3.05 YB YA > YB  A Zvi †ewk w ̄’wZ ̄’vcK| (Ans.) 9| mygb 2 eM©wgwjwgUvi cÖ ̄’‡”Q‡`i †ÿÎdj Ges 9m `xN© GKwU Zvi wb‡q wb‡Pi cÖ‡ ̄’ 12kg fi Szzwj‡q w`j| G‡Z Zv‡ii •`N© ̈ e„w× NUj Avw` •`‡N© ̈i 0.001%| B ̄úv‡Zi Bqs Gi ̧Yv1⁄4 20 × 1010 Nm–2 | [iv. †ev. 22] (K) Amn cxob Kx? (L) †`vjK‡K c„w_exi †K‡›`a wb‡j †`vjbKv‡ji Kx cwieZ©b NU‡e? (M) DÏxc‡Ki Zv‡ii Dci cÖhy3 cxob wbY©q Ki| mgvavb: cxob = F A = mg A = 12 × 9.8 2 × 10–6 = 58.8 × 106 Nm–2  Zv‡ii Dci cÖhy3 cxob 58.8 × 106 Nm–2 (Ans.) (N) DÏxc‡K myg‡bi e ̈eüZ ZviwU B ̄úvZ wQj wKbv hvPvB Ki| mgvavb: Y = FL Al = 12 × 9.8 × 9 2 × 10–6 × 9 × 0.001 100 = 5.88 × 1012 Nm–2 e ̈eüZ ZviwU B ̄úvZ wQj bv| (Ans.) 10| GKwU avZe Zv‡i 10kg fi Szjv‡bvi d‡j Gi •`N© ̈ wØ ̧Y I e ̈vm wZb-PZz_©vsk nq| [Kz. †ev. 22] avZz Bqs Gi ̧Yv1⁄4 (Y) Al 7 × 1010 Nm–2 Fe 11.5 × 1010 Nm–2 Cu 13 × 1010 Nm–2 (K) w ̄’wZ ̄’vcKZv Kx? (L) ZvcgvÎv evo‡j w ̄’wZ ̄’vcK ̧Yv‡1⁄4i gvb K‡g †Kb? e ̈vL ̈v Ki| (M) D3 avZe Zv‡ii cqm‡bi AbycvZ KZ? mgvavb: •`N© ̈ e„w×, l = 2 L – L = L e ̈vm n«vm, d = D – 3 4 D = 1 4 D   = dL Dl = 1 4 D  L D  L   = 0.25  Zv‡ii cqm‡bi AbycvZ 0.25| (Ans.)