Title 8. P2C8. Phy.-2nd-Paper-For-FRB-2024_With Solve_Ridoy-27.04.25.pdf ✅

AvaywbK c`v_©weÁv‡bi m~Pbv  Final Revision Batch 1 Aóg Aa ̈vq AvaywbK c`v_©weÁv‡bi m~Pbv Introduction of Modern Physics Topicwise CQ Trend Analysis UwcK 2016 2017 2018 2019 2021 2022 2023 2024 †gvU Av‡cwÿK ZË¡ Abymv‡i: mgq m¤úamviY, •`N© ̈ ms‡KvPb, fi e„w× 2 5 Ñ 3 10 5 3 5 33 fi kw3i m¤úK© Ñ 1 Ñ 1 Ñ Ñ 1 1 4 d‡UvB‡jw±aK wμqv 3 2 Ñ 4 Ñ 4 14 7 34 K¤úU‡bi cÖfve Ñ 1 Ñ Ñ Ñ Ñ Ñ Ñ 1 * we.`a.: 2020 mv‡j GBPGmwm cixÿv AbywôZ nqwb| weMZ mv‡j †ev‡W© Avmv m„Rbkxj cÖkœ 1| †Kv‡bv avZzi m~Pb Zi1⁄2‣`N© ̈ 5100 A | avZzwU‡K 4600 A Zi1⁄2‣`N© ̈i Av‡jv Øviv Av‡jvwKZ Kiv n‡jv| Gi d‡j wbM©Z d‡UvB‡jBUab Øviv †Kv‡bv avZe jÿ ̈e ̄‘‡K AvNvZ Kiv n‡jv| G· iwk¥i Zi1⁄2‣`N ̈©i cvjøv 5  10–8 – 5  10–15m| [e. †ev. 24] (K) M ̈vwjwjIi iƒcvšÍi Kx? (L) †ZRw ̄...qZv GKwU ̄^Ztù~Z© NUbv e ̈vL ̈v Ki| (M) avZzwUi Kvh©‡cÿK eV GK‡K wbY©q Ki| mgvavb: †`Iqv Av‡Q, m~Pb Zi1⁄2‣`N© ̈, λ0  5100 A° Avgiv Rvwb, Kvh©v‡cÿK, W0  hf0  hc λ0  6.626  10–34  3  108 5100  10–10  3.89  10–19 J  3.89  10–19 1.6  10–19 eV  2.43 eV myZivs, avZzwUi Kvh©v‡cÿK 2.43 eV| (Ans.) (N) wbM©Z d‡UvB‡jKUa‡bi mg ̄Í kw3 e ̈v‡q G· iwk¥ Drcbœ Kiv hv‡e wKÑbv hvPvB Ki| mgvavb: †`Iqv Av‡Q, G·-iwk¥i Zi1⁄2‣`‡N© ̈i cvjøv = 5  10–8 – 5  10–15 m AvcwZZ iwk¥i Zi1⁄2‣`N© ̈, λ  4600 A° G·-iwk¥ Drcv`‡b cÖ‡qvRbxq me©wb¤œ kw3, Emin  hc λmax  6.626  10–34  3  108 5  10–8  3.978  10–18 J  Emin  24.8625 eV G·-iwk¥ Drcv`‡b cÖ‡qvRbxq m‡e©v”P kw3, Emax  hc λmin  6.626  10–34  3  108 5  10–15  39.78  10–12 J  Emax  248.625 MeV wbM©Z d‡UvB‡jKUa‡bi m‡e©v”P MwZ Kmax n‡j, E  W0  Kmax  Kmax  6.626  10–34  3  108 4600  10–10  1.6  10–19 – 2.43  0.270 eV †h‡nZz, Kmax < Emin †m‡nZz wbM©Z d‡UvB‡jKUa‡bi mg ̄Í kw3 e ̈‡q G·-iwk¥ Drcbœ Kiv hv‡e bv| (Ans.) 2| †gmb KYvmg~‡ni Mo Avqy Ges w ̄’i fi h_vμ‡g 3  10–6 seconds Ges 1.82  10–28 kg| Giv c„w_exc„ô †_‡K 4 km Dc‡i AvcwZZ nevi ci 0.98 c †e‡M c„w_exi w`‡K avweZ nq| c„w_exc„‡ô G‡`i Dcw ̄’wZ mbv3 Kiv n‡jv| [e. †ev. 24] (K) `ye©j wbDK¬xq e‡ji msÁv `vI| (L) Av‡jvi †e‡Mi KvQvKvwQ †e‡M Pjgvb †Kv‡bv e ̄‧i fi Av‡cwÿK| e ̈vL ̈v Ki| DËi: mvaviYZ e ̄‘i Pjgvb Ae ̄’vq fi I w ̄’i Ae ̄’vq fi GKB nq| wKš‘ hLb e ̄‘i MwZ Av‡jvi MwZi KvQvKvwQ nq ZLb e ̄‘i Pjgvb Ae ̄’vq fi I w ̄’i Ae ̄’vq fi GKB nq bv| e ̄‘i w ̄’i fi m0 I MwZkxj fi m n‡j Avgiv Rvwb, m = m0 1 –     v c 2| GLv‡b v n‡jv e ̄‘i MwZ‡eM hv Av‡jvi MwZ‡e‡Mi KvQvKvwQ| myZivs e ̄‘i Pjgvb fi, Zvi †e‡Mi Dci wbf©ikxj| GRb ̈ Av‡jvi †e‡Mi KvQvKvwQ †e‡M Pjgvb e ̄‘i fi Av‡cwÿK|

AvaywbK c`v_©weÁv‡bi m~Pbv  Final Revision Batch 3 5| 40 Av‡jvKel© `~‡i GKwU MÖ‡n hvIqvi Rb ̈ 45 eQi eqmx b‡fvPvix‡K 0.6 C †e‡Mi b‡fvhv‡b cvVv‡bv n‡jv| b‡fvPvixi fi 80 kg| b‡fvPvixi Mo Avqy®..vj 80 eQi| (1 Av‡jvKel© = 9.4  1015 m)| [Xv. †ev. 24] (K) •`N© ̈ ms‡KvPb Kx? (L) cøvwUbv‡gi m~Pb K¤úv1⁄4 16  1014 Hz ej‡Z Kx eySvq? (M) PjšÍ Ae ̄ vq b‡fvPvixi fi KZ n‡e? mgvavb: †`Iqv Av‡Q, w ̄’i Ae ̄’vq b‡fvPvixi fi, m0  80 kg b‡fvhv‡bi †eM, v  0.6c PjšÍ Ae ̄’vq b‡fvPvixi fi, m  ? Avgiv Rvwb, m  m0 1 – v 2 c 2  80 1 –     0.6c c 2  80 1 – 0.36  100 kg myZivs PjšÍ Ae ̄’vq b‡fvPvixi fi 100 kg (Ans.) (N) DÏxc‡Ki Z_ ̈ Abyhvqx b‡fvPvix H MÖ‡n RxweZ †cu.Qv‡Z mÿg n‡e wKbv? MvwYwZKfv‡e hvPvB Ki| mgvavb: †`Iqv Av‡Q, MÖ‡ni `~iZ¡, s  40 ly  40  9.4  1015 m  3.76  1017 m b‡fvhv‡bi †eM, v  0.6c b‡fvPvixii eZ©gvb eqm  45 y b‡fvPvixi Mo Avqy®..vj  80 y  MÖ‡n †c.uQv‡Z MwZkxj ch©‡eÿ‡Ki cwigvcK...Z mgq, t  s v  3.76  1017 0.6  3  108 [ Av‡jvi †eM, c  3  108 ms–1 ]  2.0889  109 s  2.0889  109 365  86400  66.239 y Avevi, b‡fvhv‡b cwigvcK...Z mgq, t  t0  1 – v 2 c 2  66.239  1 –     0.6 c c 2  52.99 y  53 y (cÖvq)  b‡fvPvix H MÖ‡n †c.uQv‡bvi mgq Zvi eqm n‡e, = (45  53) y  98 y hv b‡fvPvixi Mo Avqy®..vj A‡cÿv †ewk| AZGe, b‡fvPvix H MÖ‡n RxweZ Ae ̄’vq †c.uQv‡Z mÿg n‡eb bv| (Ans.) 6| GKwU KvíwbK †Ua‡bi fi 500 Ub Ges GwU 0.8 C `aæwZ‡Z GKwU †÷k‡bi cøvUdg© AwZμg Kij| cøvUd‡g© `uvov‡bv GKRb hvÎx Pjgvb †Ua‡bi •`N© ̈ 200 m hv cøvUd‡g©i •`‡N© ̈i mgvb| [w`. †ev. 24] (K) wbe„wZ wefe Kv‡K e‡j? (L) avZe c`v‡_©i m~Pb K¤úv1⁄4 k~b ̈ n‡Z cv‡i wK? e ̈vL ̈v Ki| (M) †UabwUi Av‡cwÿK MwZkw3 wbY©q Ki| mgvavb: †`Iqv Av‡Q, KvíwbK †Ua‡bi w ̄’i Ae ̄’vq fi, m0  500 ton  500  1000 kg  5  105 kg †eM, v  0.8 c  MwZkxj Ae ̄’vq fi, m  m0 1 – v 2 c 2  5  105 1 –     0.8c c 2  5  105 1 – 0.64  8.333  105 kg Avgiv Rvwb, †UabwUi Av‡cwÿK MwZkw3, Ek  (m – m0)c2  (8.333  105 – 5 105 )  (3  108 ) 2  3  1022 J myZivs, †UabwUi Av‡cwÿK MwZkw3 3  1022 J| (Ans.) (N) †Ua‡bi †Kv‡bv hvÎx cøvUd‡g©i •`N© ̈ gvc‡j •`‡N© ̈i †Kv‡bv cwieZ©b cv‡e wK bvÑ MvwYwZK we‡køl‡Yi gva ̈‡g gZvgZ `vI| mgvavb: †`Iqv Av‡Q, †Ua‡bi †eM, v  0.8c ch©‡eÿ‡Ki mv‡c‡ÿ w ̄’i Ae ̄’vq cøvUd‡g©i •`N© ̈, L0  200 m ch©‡eÿ‡Ki mv‡c‡ÿ MwZkxj Ae ̄’vq cøvUd‡g©i •`N© ̈, L  L0 1 – v 2 c 2  200  1 –     0.8c c 2  200  1 – 0.64  120 m  L  L0  •`‡N© ̈i cwieZ©b = 200 – 120 = 80 m (n«vm) myZivs, †Ua‡bi †Kv‡bv hvÎx cøvUd‡g©i •`N© ̈ gvc‡j •`‡N© ̈i cwieZ©b 80 m cv‡e| (Ans.)
4  HSC Physics 2nd Paper Chapter-8 7| gW©vb wdwR· j ̈ve‡iUix‡Z †`Lv hvq, 3000 A  Zi1⁄2‣`‡N© ̈i Av‡jvKiwk¥ 6.56  1014 Hz m~Pb K¤úvs‡Ki GKLÐ avZzi Dci& AvcwZZ n‡j d‡Uv-B‡jKUab wbM©Z nq| [cøv‡1⁄4i aaæeK, h = 6.63  10–34 J-S] [h. †ev. 24] (K) wbDK¬xq wdkb Kv‡K e‡j? (L) e ̄‧i Pjgvb Ae ̄ vq fi Ges wbðj Ae ̄ vq f‡ii cv_©K ̈ †jL| (M) d‡Uv-B‡jKUa‡bi m‡e©v”P MwZkw3 wbY©q Ki| mgvavb: †`Iqv Av‡Q, Av‡jvi Zi1⁄2‣`N© ̈, λ  3000 A° 3000 10–10m  3  10–7 m avZzi m~Pb K¤úv1⁄4, f0  6.56  1014 Hz cøv‡1⁄4i aaæeK, h  6.63  10–34 Js d‡Uv-B‡jKUa‡bi m‡e©v”P MwZkw3, Ekmax  ? Avgiv Rvwb, E  Ekmax  W0  Ekmax  E – W0  hc λ – hf0  6.63 10–343 108 3 10–7 –(6.63 10–346.56 1014)  2.28  10–19 J  1.425 eV myZivs, wbM©Z d‡Uv-B‡jKUa‡bi m‡e©v”P MwZkw3 1.425 eV| (Ans.) (N) 4000 A  Zi1⁄2‣`‡N© ̈i Av‡jvKiwk¥ avZeLÐwUi Dci AvcwZZ n‡j wK d‡Uv-B‡jKUab cvIqv m¤¢e? MvwYwZK we‡kølY K‡i gZvgZ `vI| mgvavb: †`Iqv Av‡Q, avZzi m~Pb K¤úv1⁄4, f0  6.56  1014 Hz cøv‡1⁄4i aaæeK, h  6.63  10–34 Js Av‡jvi Zi1⁄2‣`N© ̈, λ  4000 A°  4000  10–10 m  4  10–7 m  avZzi Kvh©v‡cÿK, W0  hf0  6.63  10–34  6.56  1014  4.35  10–19 J Avgiv Rvwb, AvcwZZ Av‡jvi kw3, E  hc λ  6.63  10–34  3  108 4  10–7  4.97  10–19 J  E > W0 myZivs, 4000 A° Zi1⁄2‣`‡N© ̈i Av‡jvKiwk¥ avZe LÐwUi Dci AvcwZZ n‡j d‡Uv B‡jKUab cvIqv m¤¢e| (Ans.) 8| cUvwkqv‡gi Kvh©-A‡cÿK n‡jv 2.0 eV| 3500 A  Zi1⁄2‣`‡N© ̈i AwZ‡e ̧wb Av‡jv cUvwkqvg avZzi AvcwZZ n‡j d‡UvB‡jKUab wbM©Z nq| cieZ©‡Z H avZzi Dci 7800 A  I 4450 A  Zi1⁄2‣`‡N© ̈i h_vμ‡g jvj I bxj Av‡jv AvcwZZ Kiv n‡jv| [g. †ev. 24] (K) f‡ii Av‡cwÿKZv Kv‡K e‡j? (L) †Kv‡bv avZzi d‡UvZwor wμqv Zvi m~Pb K¤úv‡1⁄4i Dci wbf©ikxjÑ e ̈vL ̈v Ki| (M) d‡UvB‡jKUa‡bi m‡e©v”P MwZkw3 †ei Ki| [Abyic h. †ev. 24] (N) DÏxc‡Ki `„k ̈gvb Av‡jv `yBwUi g‡a ̈ †Kvb Av‡jvi Rb ̈ wbe„wË wefe †ewk n‡e? MvwYwZKfv‡e hvPvB Ki| mgvavb: Av‡jvK Zwor mgxKiY, E = W + Kmax  hc  = hc 0 + eV0  V0 = 1 e     hc  – hc 0  = 3000 A° n‡j, †`Iqv Av‡Q, e ̈eüZ Zi1⁄2‣`N© ̈, 1 = 3000 A° 2 = 4400 A° m~Pb Zi1⁄2‣`N© ̈, 0 = 5454 A° V01 = hc e     1 3000  10–10 – 1 5454  10–10 = 6.63  10–34  3  108 1.6  10–19  1.5  106 V  V01 = 1.864 V  = 4400 A° n‡j, V02 = hc e     1 4400  10–10 – 1 5454  10–10 = 6.63  10–34  3  108 1.6  10–19  4.392  105 V  V02 = 0.546 V  V01 > V02 A_©vr, Av‡jvi Zi1⁄2‣`N© ̈ e„w× †c‡j wbe„wË wefe K‡g| (Ans.) 9| 25 eQi eq‡mi 50 kg f‡ii GKRb b‡fvPvix 100 m •`‡N©i I 1000 kg f‡ii b‡fvhv‡b P‡o 0.7 C †e‡M gnvk~‡b ̈ ågYiZ Ae ̄’vq •`‡N© eivei 70  50 m2 AvKv‡ii GKwU gvV‡K AwZμg Ki‡Qb| (Av‡jvi †eM = 3  108 ms–1 ) [wm. †ev. 24] (K) K...ò e ̄‧i wewKiY ej‡Z Kx eyS? (L) X-ray Drcv`‡b D”P wefe e ̈envi Ki‡Z nq †Kb? e ̈vL ̈v Ki| (M) w ̄ i Ae ̄ v mv‡c‡ÿ b‡fvPvixi MwZkxj Ae ̄ vq fi KZ n‡e? mgvavb: †`Iqv Av‡Q, b‡fvPvixi w ̄’i Ae ̄’vi fi, m0  50 kg b‡fvhv‡bi †eM, v  0.7c b‡fvPvixi MwZkxj Ae ̄’vq fi, m  ?