Title 8. P1C8. HSC PREP Papers 26_With Solve.pdf ✅

ch©ve„wËK MwZ  HSC Prep Papers 3 (M) †`vjKwUi Kvh©Kix •`N© ̈ wbY©q Ki| mgvavb: T = 2 sec (second pendulum)  T = 2 L g  L = T 2 4 2  g  L = 2 2 4 2  9.8 GLv‡b, L = Kvh©Kix •`N© ̈  L = 0.9929 m A_©vr Kvh©Kix •`N© ̈ 0.9929 m (Ans.) (N) eewU A‡a©K Lvwj Ki‡j ZLb †`vjKwU `aæZ bv ax‡i Pj‡e? MvwYwZKfv‡e hvPvB K‡i gZvgZ `vI| mgvavb: e‡ei •`N© ̈ 8 cm  e‡ei e ̈vmva© 4 cm = r ee Lvwj Kivi c~‡e©i †`vjbKvj T = 2s eewU A‡a©K Lvwj Kivi ci fi‡K›`a r 2 cwigvY wb‡P †b‡g hvq| A_©vr Kvh©Kix •`N© ̈ e„w× cv‡e,  L = l + r + r 2 = l + 3r 2 T = 2 L g T  L  T2 T1 = L2 L1 r 2 r  T2 = l + 3r 2 l + r .T1 2r = 8  r = 4 = 0.9929 + 0.04  3 2 0.9929 + 0.4  2 = 2.019 sec  T2 > T1  †`vjbKvj †e‡o †M‡Q gv‡b †`vjKwU ax‡i Pj‡e| (Ans.) 7| GKwU w ̄úas Gi Dci 10 N ej cÖ‡qvM Kivq GwU 4 cm cÖmvwiZ nq| ̄úaxswU‡K cÖ_‡g 6 cm Ges cieZ©x‡Z Av‡iv 6 cm cÖmvwiZ Kiv n‡jv| [w`. †ev. 23] (K) Kg©`ÿZv Kx? (L) †K›`agyLx ej Øviv K...Z KvR k~b ̈ nqÑe ̈vL ̈v K‡iv| (M) w ̄úaswUi w ̄úas aaæeK wbY©q K‡iv| mgvavb: Spring constant, k = mg x = 10 4  10–2 = 250 Nm–1 A_©vr w ̄úas aaæeK 250 Nm–1 (Ans.) (N) cÖ_g I wØZxq †ÿ‡Î mgvb cÖmvi‡Yi Rb ̈ Kv‡Ri cwigvY mgvb n‡e wK? MvwYwZKfv‡e e ̈vL ̈v K‡iv| mgvavb: cÖ_g †ÿ‡Î, W1 = 1 2 k (x ) 2 2 – x 2 1 x1 = 0.04 m x2 = (0.04 + 0.06) = 0.1 m = 1 2  250  {(0.1) } 2 – (0.04) 2  W1 = 1.05 J wØZxq †ÿ‡Î, W2 = 1 2 k (x ) 2 2 – x 2 1 x 1 = 0.1 m x 2 = (0.1 + 0.06) = 0.16 m = 1 2  250  {(0.16) } 2 – (0.1) 2  W2 = 1.95 J  W1  W2 A_©vr Dfq‡ÿ‡Î Kv‡Ri cwigvY mgvb n‡e bv| (Ans.) 8| ivwb I ewb `yB fvB‡qi fi h_vμ‡g 32 kg Ges 40 kg| Zviv `yRb GKwU †`vjbvq GKB †K.wYK mi‡Y †`vj Lvw”Qj| †`vjbvwUi Mo Kvh©Kix •`N© ̈ 3 m Ges Gi mvg ̈ve ̄’vb A| [g = 9.8 ms–1 ] [w`. †ev. 23] O 1m A B 3m (K) †K.wYK K¤úvsK Kv‡K e‡j? (L) gnvKv‡k GKRb b‡fvPvixi wbKU GKwU †m‡KÛ †`vj‡Ki K¤úvs‡Ki cwieZ©b nqÑe ̈vL ̈v K‡iv| (M) iwbi Dci myZvi Uvb wbY©q K‡iv| mgvavb: A B 3m  1m mg mg cos   tan = 1 3   = tan–1     1 3  iwbi Dci myZvi Uvb, T = mg cos = 32  9.8  cos     tan–1     1 3 = 297.50 N A_©vr myZvi Uvb 297.50 N (Ans.)
4  HSC Physics 1st Paper Chapter-8 (N) DÏxc‡Ki B Ae ̄’v‡b iwb I ewb mgvb Kvh©Ki ej Abyfe Ki‡jv wKbvÑMvwYwZKfv‡e e ̈vL ̈v K‡iv| mgvavb: A  1m mg mg cos  T mg sin iwbi Dci Kvh©Ki ej, F1 = m1g sin  = tan–1 1 3  F1 = 99.169 N ewbi Dci Kvh©Kix ej F2 = m2gsin = 123.96 N  F1  F2 A_©vr B Ae ̄’v‡b Df‡q mgvb Kvh©Ki ej Abyfe Ki‡e bv| (Ans.) 9| GKwU mij †`vj‡Ki Kvh©Ki •`N© ̈ 1 m Ges 6 cm| †`vjKwU‡K cÖ_‡g P ̄’v‡b wb‡q hvIqv n‡j †`vjbKvj 1.5 sec Ges Gici Q ̄’v‡b wb‡q †M‡j †`vjbKvj 2 sec cvIqv †Mj| [g. †ev. 23] (K) `kv Kv‡K e‡j? (L) Ôw ̄úas ej cÖZ ̈qbx ejÕÑ e ̈vL ̈v K‡iv| (M) †`vj‡Ki mvg ̈ve ̄’v‡b †eM wbY©q K‡iv| mgvavb: T = 2 L g = 2 1 9.8  T = 2.007 sec v = A = 2 T × A = 2 2.007 × 0.06  v = 0.188 ms–1 A_©vr mvg ̈ve ̄’v‡b †eM 0.188 ms–1 (Ans.) (N) †Kvb ̄’v‡bi D”PZv †ewk wQj? MvwYwZKfv‡e e ̈vL ̈v K‡iv| mgvavb: T 1 g Avevi, g 1 r 2 [r = †K›`a †_‡K D”PZv]  T r A_©vr c„w_exi †K›`a †_‡K P I Q ̄’v‡bi `~iZ¡ h_vμ‡g r1 I r2 n‡j, T1 T2 = r1 r2  1.5 2 = r1 r2  r1 = 0.75 r2  r2 > r1 A_©vr Q ̄’v‡bi D”PZv †ewk wQj| 10| `ywU w ̄úas Gi w ̄úas aaæeK K1 = 1000 Nm–1 Ges K2 = 2000 Nm–1 | m = 4.5 kg I m f‡ii `ywU e ̄‘ wPÎ Abymv‡i hy3 †_‡K gm„Y †g‡S‡Z `yj‡Z mÿg| [Xv. †ev. 22] k1 m k2 wPÎ-1 k2 m wPÎ-2 k1 m k2 wPÎ-3 (K) f~w ̄’i DcMÖn Kv‡K e‡j? (L) mij †`vjMwZ ch©ve„ËMwZ; wKš‘ ch©ve„ËMwZ mij †`vjMwZ bqÑ e ̈vL ̈v Ki| (M) DÏxc‡Ki 2bs wP‡Î w ̄úas Gi †K.wYK K¤úv1⁄4 KZ n‡e? mgvavb: †K.wYK K¤úv1⁄4,  = k m = 2000 4.5  = 21.08 rad/s A_©vr 2bs wP‡Î w ̄úas-Gi †K.wYK K¤úv1⁄4 21.08 rad/s (Ans.) (N) m = 1kg n‡j DÏxc‡Ki 1bs I 3bs wP‡Îi w ̄úas ̧‡jvi ch©vqKvj mgvb n‡eÑ e3e ̈wU hvPvB Ki| mgvavb: 1bs wP‡Î Rb ̈: Equivalent spring constant Keq = K1 + K2 (mgvšÍivj mgev‡q hy3)  keq = 3000 Nm–1  T = 2 m Keq = 2 4.5 3000 T = 0.243 s 3bs wP‡Îi Rb ̈: Equivalent spring constant keq = k1k2 k1 + k2 (†kÖwY mgev‡q hy3) = 1000  2000 3000 = 666.7 Nm–1  T = 2 m keq = 0.243 s = T  T = T A_©vr 1bs I 3bs wP‡Îi w ̄úas- ̧‡jvi ch©vqKvj mgvb n‡e| (Ans.)