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

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.)
wbDUwbqvb ejwe` ̈v  Final Revision Batch 3 5| GKwU •e`y ̈wZK cvLvi RoZvi åvgK 100 kgm–2 cvLvwU cÖwZ wgwb‡U 900 evi †Nv‡i| cvLvwUi myBP eÜ Kivi c‡i 2 wgwbU ci cvLvwU _v‡g| [wm. †ev. 24] (K) †KŠwYK fi‡eM Kv‡K e‡j? (L) euvKv c‡_ AwZ `aæZMvgx Mvwo D‡ë hvq †Kb? e ̈vL ̈v Ki| (M) DÏxc‡Ki ewY©Z cvLvq cÖ‡qvMK...Z UK© wbY©q Ki| mgvavb: cvLvi Avw` †K.wYK †eM, i = 900 rev min–1  i = 2 × 900 60 rads–1  i = 94.247 rads–1  †K.wYK g›`b,  = i – f t   = 94.247 – 0 2 × 60   = 0.7854 rads–2 cÖ‡qvMK...Z UK©,  = I   = 100  0.7854   = 78.54 Nm myZivs, cvLvq cÖ‡qvMK...Z UK© 78.54 Nm| (N) †_‡g hvIqvi c~‡e© cvLvwUi c‡ÿ 1000 evi †Nviv m¤¢K Kx? MvwYwZK we‡kølYmn †Zvgvi gZvgZ `vI| mgvavb: ÔMÕ n‡Z cvB, cvLvi Avw` †K.wYK †eM, i = 94.247 rads–1  †K.wYK miY,  = i + f 2 t   = 94.247 + 0 2  2  60   = 5654.82 rad   = 5646.82 2 rev   = 898.72 rev  1000  †_‡g hvIqvi c~‡e© cvLvwUi c‡ÿ 1000 evi †Nviv m¤¢e bq| 6| 500 kg f‡ii GKwU Mvwo 100 m e ̈vmv‡a©i GKwU iv ̄Ívi †gv‡o 45 kmh–1 †e‡M euvK wb‡”Q| H ̄’v‡b iv ̄ÍvwU 8 m PIov Ges wfZ‡ii wKbviv n‡Z evB‡ii wKbviv 1 m DuPz| [w`. †ev. 24] (K) ej Kv‡K e‡j? (L) wbDwK¬qv‡mi Ici B‡jKUa‡bi w`‡K cÖhy3 ej Kx ai‡bi ej? e ̈vL ̈v Ki| (M) MvwowUi Dci †K›`agyLx ej KZ wbY©q Ki| mgvavb: Avgiv Rvwb,  = 45 kmh-1 = 45 3.6 ms–1 = 12.5 ms–1 ‡K›`agyLx ej, F = m 2 r  F = 500  12.52 100  F = 781.25 N myZivs, MvwowUi Dci †K›`agyLx ej 781.25 N| (N) iv ̄Ívi †gv‡o MvwowU wbivc‡` euvK wb‡Z cvi‡e wK-bv MvwYwZKfv‡e we‡kølY Ki| mgvavb: 8m 1m  8 2–1 2 m awi, m‡e©v”P m ‡e‡M MvwowU wbivc‡` evuK wb‡Z cv‡i| Avgiv Rvwb, tan = m 2 rg   1 8 2 – 1 2 = m 2 100  9.8  m = 11.11 ms–1  12.5 ms–1 Mvwoi †eM m‡e©v”P wbivc` †e‡Mi †ewk nIqvq iv ̄Ívq †gv‡o MvwowU wbivc‡` evK wb‡Z cvi‡e bv| 7| †Kv‡bv XvKvi fi 10 kg Ges e ̈vmva© 0.5 m PvKvi N~Y©b Ô†eM 500 rpmÕ PvKvwU N~Y©biZ Ae ̄’vq 6855 N-m evav`vbKvix UK© cÖ‡qvM Kiv nj| [h. †ev. 24] (K) PμMwZi e ̈vmva© Kx? (L) Dj¤^ e„ËvKvi Z‡j cvwbfwZ© evjwZ‡K Nyiv‡j cvwb c‡o bv †K? (M) PvKvi N~Y©b MwZkw3 KZ? mgvavb: Avgiv Rvwb, N~Y©b MwZkw3, E  1 2 Ii 2  1 2  mr 2  i 2  1 2  10  0.52  52.362  3427 J †`Iqv Av‡Q, PvKvi Avw` N~Y©b †eM,  i  500 rpm  2  500 60 rads–1  52.36 rads–1 myZivs, PvKvi N~Y©b MwZkw3 3427 J| (Ans.) (N) PvKvwU 10 †m‡K‡Û _vg‡K wK bv? hvPvB Ki| mgvavb: ÔMÕ n‡Z cvB, PvKvi Avw` †K.wYK †eM, i  52.36 rads–1 Avgiv Rvwb,    I   =  I   mr 2  6855 10 × 0.52  2742 rads–2 GLb,  f  i – αt  t  52.36 2742  0.02s  10s myZivs PvKvwU 10s Gi c~‡e©B †_‡g hv‡e| (Ans.)
4  HSC Physics 1st Paper Chapter-4 8| GKRb mvK©v‡mi †L‡jvqvo †L‡jvqvo 60 cm `xN© myZvi GKcÖv‡šÍ 80 gm f‡ii GKwU e ̄‘‡K †eu‡a Djø¤^Z‡j cÖwZ wgwb‡U 120 evi Nyiv‡”Qb| c‡i wZwb myZvi •`N© ̈ 10% Kwg‡q Ges cÖwZ wgwb‡U N~Y©b msL ̈v 5% e„w× K‡i e ̄‘wU‡K Abyf‚wgK Z‡j Nyiv‡Z _v‡Kb| [iv. †ev. 24] (K) UK© Kx? (L) †Nvovi Mvwo Kxfv‡e MwZcÖvß nq? e ̈vL ̈v Ki| (M) e ̄‘wU hLb Djø¤^ Z‡ji m‡e©v”P we›`y‡Z Ae ̄’vb K‡i ZLb myZvi Uvb wbY©q Ki| mgvavb: †K.wYK †eM,   120 rpm  2 × 120 60 rads–1  4 rads–1 mg T m 2 r Dj¤^ Z‡ji m‡e©v”P we›`y‡Z, T + mg  m 2 r  T  m 2 r – mg †`Iqv Av‡Q, e ̄‘i fi, m  0.08 kg †K›`a n‡Z e ̄‘i `~iZ¡, r  0.6 m  0.08 × (4) 2 × 0.6 – 0.08 × 9.8  6.8 N myZivs, Dj¤^ Z‡ji m‡e©v”P we›`y‡Z myZvi Uvb 6.8 N| (Ans.) (N) Djø¤^Z‡j I Abyf‚wgKZ‡j Nyiv‡bvi mgq e ̄‘i †KŠwYK fi‡eM mgvb n‡e bvÑ MvwYwZKfv‡e we‡kølY Ki| mgvavb: †`Iqv Av‡Q, e ̄‘i fi, m  0.08 kg †K›`a n‡Z e ̄‘i `~iZ¡, r  0.6 m †K.wYK †eM,   4 rads–1 Dj¤^Z‡j Nyiv‡bvi †ÿ‡Î, †K.wYK fi‡eM, L1  I  L1  mr 2  0.08  0.62  4  0.362 kgm2 s -1 Abyf~wgK Z‡j Nyiv‡bvi †ÿ‡Î, myZvi bZzb •`N© ̈, r2 = (r – 10% r)  0.9  0.6  0.54 m bZzb †K.wYK †eM, 2  ( + 5% )  1.05  4  4.2 rads–1  †K.wYK fi‡eM, L2  I22  L2  mr 2 2 2  0.08  0.542  4.2  0.308 kgm2 s –1  L1  L2 myZivs, Dj¤^Z‡j I Abyf~wgK Z‡j Nyiv‡bv mgq e ̄‘i †K.wYK fi‡eM mgvb n‡e bv| (Ans.) 9| ev›`iev‡bi cvnvwo iv ̄Ívi euv‡K mygb 200 kg f‡ii GKwU Mvwo 60 kmh–1 †e‡M Pvjv‡”Q| iv ̄Ívi euv‡Ki e ̈vmva© 150 m| H ̄’v‡b iv ̄ÍvwU 4 m PIov Ges wfZ‡ii wKbviv †_‡K evB‡ii wKbviv 0.5 m DuPz| [Xv. †ev. 24] (K) fi‡e‡Mi msiÿY m~ÎwU †jL| (L) †Kv‡bv N~Y©vqgvb e ̄‘i RoZvi åvgK 15 kgm2 ej‡Z Kx eySvq? (M) MvwowUi †K›`agyLx ej wbY©q Ki| mgvavb: Avgiv Rvwb, †K›`agyLx ej, Fc  mv 2 r  200  (16.67) 2 150  370.52 N †`Iqv Av‡Q, Mvwoi †eM, v  60 kmh–1  16.67 ms –1 fi, m  200 kg euv‡Ki e ̈vmva©, r  150 m myZivs, MvwowUi †K›`agyLx ej 370.52 N (Ans.) (N) mygb iv ̄Ívi euvKwU‡Z wbivc‡o MvwowU Pvjv‡Z cvi‡e wK bv? MvwYwZK we‡køl‡Yi gva ̈‡g DËi `vI| mgvavb: awi, m‡e©v”P vM †e‡M MvwowU MwZkxj n‡j wbivc‡` euvK wb‡Z cvi‡e| Avgiv Rvwb, tan  v 2 gr  0.5 3.97  v 2 M 150  9.8  vM  13.60 ms–1 0.5 m 4 m  3.97 m A B C cÖkœg‡Z, MvwowUi †eM, v  16.67 ms–1  vM < v myZivs, mygb iv ̄Ívi euvKwU‡Z wbivc‡` MvwowU Pvjv‡Z cvi‡e bv| (Ans.) 10| iwng 200 gm f‡ii GKwU e ̄‘‡K myZvq †eu‡a `ywU Ae ̄’vb †_‡K Abyf‚wgKfv‡e cÖwZ wgwb‡U 60 evi Nyiv‡”Q| Ae ̄’vb †f±i `ywU h_vμ‡g r  1 = (3i ^ + 2j ^ – k ^ )m Ges r  2 = (4i ^ + 2j ^ – 3k ^ )m Deq †ÿ‡Î cÖ‡qvMK...Z e‡ji cwigvY F  1 = (5i ^ + 4j ^ – 3k ^ )N. [g. †ev. 24] (K) PμMwZi e ̈vmva© Kx? (L) iv ̄Ívi euv‡Ki wfZ‡ii cÖvšÍ †_‡K evB‡ii cÖvšÍ DuPz nq †Kb? (M) 1g †ÿ‡Î †KŠwYK fi‡eM wbY©q Ki| mgvavb: N~Y©b c‡_i e ̈vmva©, |r |1  = 3 2 +22 +12 m  |r |1  = 14 m  †K.wYK fi‡eM, L = I = m |r |1  2  †`Iqv Av‡Q, †K.wYK †eM,  = 60 rpm  2 × 60 60 rads–1  2 rads–1 = 0.2 × 14  2 = 17.6 kgm2 s –1 myZivs, cÖ_g †ÿ‡Î †K.wYK fi‡eM 17.6 kgm2 s –1 (Ans.)