Tiêu đề 4. P1C4. Phy. For FRB-2024_With Solve_Ridoy- 08.01.25 - OK.pdf ✅

wbDUwbqvb ejwe` ̈v  Final Revision Batch 1 PZz_© Aa ̈vq wbDUwbqvb ejwe` ̈v Newtonian Mechanics Topicwise CQ Trend Analysis UwcK 2016 2017 2018 2019 2021 2022 2023 2024 †gvU wbDU‡bi e‡ji m~‡Îi g‡a ̈ m¤úK© Ñ 1 1 Ñ Ñ 2 2 Ñ 6 wbDU‡bi e‡ji Z...Zxq m~‡Îi e ̈envi I fi‡e‡Mi wbZ ̈Zv Ñ Ñ Ñ 1 Ñ Ñ Ñ Ñ 1 msNl©- (w ̄’wZ ̄’vcK msNl© I Aw ̄’wZ ̄’vcK msNl©) Ñ Ñ Ñ 1 Ñ 1 1 2 5 RoZvi åvgK I †K.wYK fi‡eM Ñ 1 1 3 7 3 2 2 19 †K.wYK ivwkgvjv (miY, †eM, Z¡iY, fi‡eM, MwZkw3) 2 5 Ñ 3 4 2 Ñ 3 19 UK© 1 Ñ Ñ 1 Ñ Ñ Ñ 5 7 †K›`agyLx I †K›`awegyLx ej Ñ 1 Ñ Ñ 1 3 2 2 9 iv ̄Ívi e ̈vswKs 2 2 1 2 6 3 4 4 24 * we.`a.: 2020 mv‡j GBPGmwm cixÿv AbywôZ nqwb| weMZ mv‡j †ev‡W© Avmv m„Rbkxj cÖkœ 1| GKwU iv ̄Ívi cÖ ̄’ 3.65 m Ges euv‡Ki e ̈vmva© 170 m| GKwU mZ©KZv †ev‡W© Mvwoi m‡e©v”P MwZmxgi 30 km h–1 wb‡`©wkZ Av‡Q| GKRb evBK PvjK D3 euv‡K 60 km h–1 †e‡M †gvUi evBK Pvjv‡Z B”QzK| (g = 9.81 ms–2 ) [P. †ev. 24] (K) RoZvi åvgK Kv‡K e‡j? (L) GKwU w ̄úas Gi ej aaæeK 2200 Nm–1 ej‡Z Kx eyS? (M) iv ̄Ívi wfZi A‡cÿv evwn‡ii As‡ki D”PZv wbY©q Ki| mgvavb: Avgiv Rvwb, tan = v 2 rg 3.65m h     tan–1     8.332 170 × 9.81  tan–1 (0.04164)  2.3844 †`Iqv Av‡Q, Mvwoi m‡e©v”P MwZmxgv, v  30 kmh–1  8.33 ms–1 iv ̄Ívi euv‡Ki e ̈vmva©, r  170 m iv ̄Ívi cÖ ̄’, d  3.65 m GLb, sin  h 3.65  h = sin (2.3844o) × 3.65 = 0.1518 m = 15.18 cm myZivs, iv ̄Ívi wfZi A‡cÿv evwn‡ii As‡ki D”PZv 15.18 cm| (Ans.) (N) evBK PvjK ZvrÿwYKfv‡e Kx e ̈e ̄’v MÖnY Ki‡j wbivc‡` euvK AwZμg Ki‡Z cvi‡e? MvwYwZKfv‡e we‡kølY Ki| mgvavb: awi, hw` iv ̄Ívq e ̈vswKs bv _vK‡Zv Z‡e evBK PvjK‡K Dj‡¤^i mv‡_  †Kv‡Y †n‡j _vK‡Z n‡Zv|  tan = v 2 rg   = tan–1     16.672 170 × 9.81 †`Iqv Av‡Q, evB‡Ki †eM, v  60 kmh–1  16.67 ms–1   = 9.46 ÔMÕ n‡Z cvB, iv ̄Ívi e ̈vswKs †KvY s = 2.3844  iv ̄Ívi e ̈vswKs Gi Kvi‡Y †gvUi evBK PvjK BwZg‡a ̈ Dj‡¤^i mv‡_ s  2.3844 †Kv‡Y †n‡j Av‡Qb| AZGe, Zv‡K AwZwi3 †nj‡Z n‡e   – s = 9.46 – 2.3844 = 7.0756 myZivs, evBK PvjK ZvrÿwYKfv‡e Dj‡¤^i mv‡_ 7.0756 †Kv‡Y †n‡j co‡j wbivc‡` euvK wb‡Z cvi‡eb| (Ans.) 2| v 500 kg 30 ms–1 0 ms–1 msN‡l©i c~‡e© msN‡l©i c‡i [Kz. †ev. 24] (K) RoZvi åvgK Kv‡K e‡j? (L) †`qv‡j av°v †L‡q ej wcQ‡b wd‡i Av‡m †Kb? e ̈vL ̈v Ki| (M) Dc‡ii wP‡Îi ÔvÕ Gi gvb wbY©q Ki| mgvavb: †`Iqv Av‡Q, 1g e ̄‘i fi, m1  500 kg Avw`‡eM, u1  30 ms –1 2q e ̄‘i fi, m2  200 kg Avwe‡eM, u2  0 ms–1 fi‡e‡Mi msiÿYkxjZv n‡Z, m1u1 + m2u2 = (m1 + m2) v  500 × 30 + 200 × 0 = (500 + 200) × v  v = 21.428 ms–1 myZivs, v Gi gvb 21.428 ms–1 (Ans.)
2  HSC Physics 1st Paper Chapter-4 (N) msNl©wU wK w ̄’wZ ̄’vcK? MvwYwZKfv‡e we‡kølY Ki| mgvavb: ÔMÕ n‡Z cvB, e ̄‘ `ywUi wgwjZ †eM 21.428 ms–1 msN‡l©i c~‡e© †gvU MwZkw3, E1 = 1 2 m1u 2 1 + 1 2 m2u 2 2  1 2  500  302  1 2 × 200 × 02 = 225 kJ msN‡l©i ci †gvU kw3, E2  1 2 (m1 + m2) v2  1 2 × (500 + 200) × 21.4282  160.706 kJ  E1  E2 A_©vr, msN‡l© MwZkw3 msiwÿZ _v‡K bv| myZivs msNl©wU Aw ̄’wZ ̄’vcK| (Ans.) 3| 0.5 kg f‡ii †Kv‡bv e ̄‘‡K 80 cm j¤^v GKwU myZvi mvnv‡h ̈ Abyf‚wgK e„ËvKvi c‡_ Nyiv‡bv n‡”Q| e ̄‘wU w ̄’i Ae ̄’v †_‡K mg‡K.wYK Z¡i‡Y Nyiv Avi¤¢ K‡i 2 wgwbU ci †_‡K cÖwZ wgwb‡U 120 evi Nyi‡Q| [e. †ev. 24] (K) †KŠwYK fi‡eM Kv‡K e‡j? (L) wμqv I cÖwZwμqvi Kvi‡Y †Kv‡bv e ̄‘i mvg ̈ve ̄’vi m„wó nq bv †Kb? e ̈vL ̈v Ki| (M) 2 wgwbU ci e ̄‘wUi Ici Kx cwigvY UK© wμqv Ki‡Q Zvi gvb wbY©q Ki| mgvavb: e ̄‘wUi 2 min ci †K.wYK †eM, f  120 rev min–1  2  120 60 rads–1  12.566 rads–1  †K.wYK Z¡iY,   f – i t  12.566 – 0 2  60  0.1047 rads–2 UK©,   I  mr 2   0.5  (0.8)2  0.1047  0.0335 Nm  2 min ci e ̄‘wUi Dci 0.0335 Nm UK© wμqv Ki‡Q| (Ans.) (N) e ̄‘i Ici Uv‡bi gvb hw` c~‡e©i Uv‡bi wZb ̧Y Kiv nq Zvn‡j †KŠwYK †e‡Mi Kx cwieZ©b n‡e? MvwYwZKfv‡e we‡kølY Ki| mgvavb: Avgiv Rvwb, Abyf‚wgKfv‡e e„ËvKvi c‡_ Nyiv‡j Uvbej, T = m 2 r  T   2 [∵ m, r aaæeK]      2 1 2  T2 T1  2 1  T2 T1  2  T2 T1  1  3T1 T1  12.566 [∵ T2 = 3T1]  21.765 rads–1  †K.wYK †e‡Mi e„w× = (21.765 – 12.566) rads–1 = 9.2 rads–1 myZivs, e ̄‘i Dci Uv‡bi gvb hw` c~‡e©i Uv‡bi wZb ̧Y Kiv nq Zvn‡j †K.wYK †eM 9.2 rads–1 e„w× cv‡e| (Ans.) 4| v 500 kg 30 ms–1 0 ms–1 msN‡l©i c~‡e© msN‡l©i c‡i [wm. †ev. 24] (K) RoZvi åvgK Kv‡K e‡j? (L) †`qv‡j av°v †L‡q ej wcQ‡b wd‡i Av‡m †Kb? e ̈vL ̈v Ki| (M) Dc‡ii wP‡Îi ÔvÕ Gi gvb wbY©q Ki| mgvavb: †`Iqv Av‡Q, 1g e ̄‘i fi, m1  500 kg Avw`‡eM, u1  30 ms –1 2q e ̄‘i fi, m2  200 kg Avwe‡eM, u2  0 ms–1 fi‡e‡Mi msiÿYkxjZv n‡Z, m1u1 + m2u2 = (m1 + m2) v  500 × 30 + 200 × 0 = (500 + 200) × v  v = 21.428 ms–1 myZivs, v Gi gvb 21.428 ms–1 (Ans.) (N) DÏxc‡Ki msNl©wU wK w ̄’wZ ̄’vcK? †Zvgvi Dˇii mc‡ÿ hyw3 `vI| mgvavb: ÔMÕ n‡Z cvB, e ̄‘ `ywUi wgwjZ †eM 21.428 ms–1 msN‡l©i c~‡e© †gvU MwZkw3, E1 = 1 2 m1u 2 1 + 1 2 m2u 2 2  1 2  500  302  1 2 × 200 × 02 = 225 kJ msN‡l©i ci †gvU kw3, E2  1 2 (m1 + m2) v 2  1 2 × (500 + 200) × 21.4282  160.706 kJ  E1  E2 A_©vr, msN‡l© MwZkw3 msiwÿZ _v‡K bv| myZivs msNl©wU Aw ̄’wZ ̄’vcK| (Ans.)