Tiêu đề 8. P1C8 (Periodic Motion) With Solve.pdf ✅

ch©ve„Ë MwZ  Varsity Practice Sheet ................................................................................................................................. 1 weMZ mv‡j DU-G Avmv cÖkœvejx 1. GKwU KYv A we ̄Ív‡i mij Qw›`Z ̄ú›`‡b ̄úw›`Z n‡”Q| mvg ̈ve ̄’v †_‡K KZ `~i‡Z¡ KYvwUi wefe kw3 Zvi †gvU kw3i GK-PZz_©vsk nq? [DU 23-24] A 4 A 2 A 2 A 2 DËi: A 2 e ̈vL ̈v: 1 2 kx2 = 1 4  1 2 kA2  x = A 2 2. mij †`vj MwZm¤úbœ GKwU e ̄‘ hLb Zvi mvg ̈ve ̄’vb †_‡K 2 cm `~‡i, ZLb Zvi MwZkw3 w ̄’wZkw3i 3 ̧Y| e ̄‘wUi †`vj‡bi we ̄Ívi KZ n‡e? [DU 22-23] 3 cm 1 cm 2 cm 4 cm DËi: 4 cm e ̈vL ̈v: 1 2 k (A2 – x 2 ) = 3  1 2 kx2  A 2 = 4x2  A = 2x = 4 cm 3. m f‡ii GKwU e ̄‘ GKwU Avbyf‚wgK w ̄úas-Gi mv‡_ mshy3 Av‡Q, w ̄úaswU A cwigvY cÖmvwiZ K‡i †Q‡o †`Iqv n‡j GwU T ch©vqKvj wb‡q Nl©Ynxb Z‡j ̄úw›`Z n‡Z _vKj| hw` e ̄‘i fi 4m Kiv nq Z‡e bZzb ch©vqKvj KZ n‡e? [DU 21-22] 2T T 4T T 4 DËi: 2T e ̈vL ̈v: T  m  T2 T1 = m2 m1 4. 6 d 2 x dt2 + 150x = 0 Zi‡1⁄2i †KŠwYK K¤úv1⁄4 KZ? [DU 21-22] 6 5 25 150 DËi: 5 e ̈vL ̈v: G‡ÿ‡Î, d 2 x dt2 +  2 x = 0 Gi mv‡_ Zzjbv K‡i,  2 = 25   = 5 rads–1 5. GKwU mij †`vj‡Ki †`vjbKvj 50% evov‡Z Gi Kvh©Ki •`‡N© ̈i cwieZ©b KZ n‡e? [DU 20-21; KU 18-19] 25% 100% 125% 67% DËi: 125% e ̈vL ̈v: L2 L1 =     T2 T1 2 =     1.5 1 2 = 2.25  L2 – L1 L1  100% = (2.25 – 1)  100% = 125% 6. mij Qw›`Z MwZ‡Z ̄ú›`biZ `ywU KYvi miY x1 = A sint Ges x2 = A cost| †h †Kv‡bv mg‡q G‡`i g‡a ̈ `kv cv_©K ̈ KZ n‡e? [DU 19-20] 2   2  4 DËi:  2 e ̈vL ̈v: G‡ÿ‡Î Dfq mgxKi‡Y w·KvYwgwZK AbycvZ GKB K‡i wb‡e, x1 = A sint x2 = A cost = A sin     t +  2  `kv cv_©K ̈ = 2 – 1 =  2 7. GKwU Zv‡ii wfZi w`‡q mvB‡bv‡mvBWvj Zi1⁄2 cÖevwnZ n‡j Zv‡ii KYvi m‡e©v”P `aæwZ vs| Zv‡ii GKwU KYvi miY m‡e©v”P mi‡Yi A‡a©K n‡j H KYvi `aæwZ n‡jvÑ [DU 18-19] vs 2 3vs 2 2vs 3vs 4 DËi: 3vs 2 e ̈vL ̈v: vs = A v =  A 2 – x 2 =  A 2 – A 2 4 =  3A2 4 =   3 2 A = 3 2 A = 3 2 vs
2 .........................................................................................................................................  Physics 1st Paper Chapter-8 8. mij †`vj MwZm¤úbœ GKwU KYvi we ̄Ívi 0.02 m Ges K¤úv1⁄4 2.5 Hz n‡j Gi m‡e©v”P `aæwZ KZ n‡e? [DU 18-19] 0.05 ms–1 0.125 ms–1 0.157 ms–1 0.314 ms–1 DËi: 0.314 ms–1 e ̈vL ̈v: vmax = A = 2fA = 2  2.5  0.02 = 5  0.02 = 0.1 = 0.1  3.1416  vmax = 0.31416  T2 = T1  4m m  T2 = 2T 9. c„w_ex c„‡ô (ge = 9.8 ms–2 ) GKwU †`vjK Nwo mwVK mgq †`q| Nwo‡K P›`ac„‡ô (gm = 1.6 ms–2 ) †bIqv n‡j c„w_exc„‡ôi 1 h mgq P›`ac„‡ô n‡eÑ [DU 17-18] 9.8 1.6 h 1.6 9.8 h 9.8 1.6 h 1.6 9.8 h DËi: 9.8 1.6 h e ̈vL ̈v: T  1 g  Tmoon = 1  ge gm = 1  9.8 1.6 h 10. gy3fv‡e †Kvb cošÍ e ̄‘i Z¡iY g wbY©q Ki‡Z wM‡q GKRb QvÎ GKwU mij †`vj‡Ki •`N© ̈ l cwieZ©b K‡i wfbœ wfbœ l Gi Rb ̈ †`vj‡Ki †`vjbKvj T cwigvc Kij| Gevi †m T 2 (y – axis) ebvg l (x – axis) †jLwPÎ G‡K Xvj S †ei Ki‡jv| g Gi gvb KZ? [DU 14-15] 4 2 S 4 2 S 2 S 2S DËi: 4 2 S e ̈vL ̈v: T 2 = 4 2 g L  S = 4 2 g  g = 4 2 S weMZ mv‡j GST-G Avmv cÖkœvejx 1. Mi‡gi d‡j GKwU †m‡KÛ †`vj‡Ki •`N© ̈ e„w× †cj| Gi d‡j †`vjKwU w`‡b 200 sec ax‡i P‡j| cwiewZ©Z †`vjbKvj KZ? [GST 23-24] 0.99 sec 1.00 sec 1.09 sec 2.00 sec DËi: 2.00 sec e ̈vL ̈v: T = 2 × 86400 86400 – 200 s = 2 × 86400 86200 s  2  86400 86400  2 s  T  2 sec 2. mij Qw›`Z MwZi mgxKiYÑ [GST 22-23; JnU 15-16] d 2 x dt2 + k3 x 2 = 0 d 2 x dt2 +  2 x = 0 dx dt +  2 x = 0 dx dt –  2 x = 0 DËi: d 2 x dt2 +  2 x = 0 3. GKwU mij Qw›`Z MwZm¤úbœ KYvi m‡e©v”P †eM 0.03 ms–1 I we ̄Ívi 0.006 m n‡j ch©vqKvj KZ? [GST 22-23; MBSTU 15-16] 5 s 2 s 4.5 s 18 s DËi: Blank e ̈vL ̈v:  = vmax A  2 T = 0.03 0.006 = 1 0.2 = 5  T = 2 5  = 1.25665 4. L Kvh©Kix •`‡N© ̈i GKwU mij †`vj‡Ki †`vjbKvj I †KŠwYK K¤úv1⁄4 h_vμ‡g †KvbwU? [GST 21-22] 2 L g , g L g L , 2 L g 2 g L , g L L g , 2 L g DËi: 2 L g , g L e ̈vL ̈v: T = 2 L g  = 2 T = 2 2 L g   = g L
ch©ve„Ë MwZ  Varsity Practice Sheet ................................................................................................................................ 3 5. mij Qw›`Z MwZm¤úbœ e ̄‘i mi‡Yi mgxKiY, x = 2 sin3t| w ̄úas aaæeK, k = 30 Nm–1 n‡j t =  9 mg‡q Gi wefekw3 KZ GKK? [GST 20-21] 40 45 80 90 DËi: 45 e ̈vL ̈v: x = 2 sin3t = 2 sin     3   9 = 2 sin      3 = 2  3 2 = 3 m Ep = 1 2 kx2 = 1 2  30  ( 3) 2 = 15  3 = 45 J weMZ mv‡j Agri-G Avmv cÖkœvejx 1. 50 cm `xN© GKwU mij †`vjK cÖwZ wgwb‡U 40 evi †`vjb †`q| hw` •`N© ̈ 200 cm Kiv nq Z‡e 60 evi †`vjb w`‡Z KZ mgq jvM‡e? [Agri Guccho 21-22; BSMRSTU-A 19-20; JU 19-20; RU 15-16] 180 s 120 s 80 s 20 s DËi: 180 s e ̈vL ̈v: T  L T2 = T1  L2 L1 = 60 40  200 50 = 2  60 40 = 3 s 60 evi †`vj w`‡Z cÖ‡qvRbxq mgq = (3  60) = 180 s 2. GKwU mij †`vj‡Ki •`N© ̈ AciwUi wØ ̧Y| wØZxq mij †`vj‡Ki †`vjbKvj 3 s n‡j, cÖ_gwUi †`vjbKvj KZ? [Agri. Guccho 19-20] 6.20 s 5.25 s 4.24 s 7.80 s DËi: 4.24 s e ̈vL ̈v: T1 T2 = L1 L2  T1 = 2  3 = 3 2 = 3  1.414  T1  3  1.5  4.5 Answer 4.5 Gi KvQvKvwQ| weMZ mv‡j JU-G Avmv cÖkœvejx 1. c„w_exi GKUv †m‡KÛ †`vj‡Ki •`N© ̈ 1 m n‡j Puv‡` Gi •`N© ̈ KZ? [JU 22-23] 36 m 1 6 m 6 m 1 m DËi: 1 6 m 2. GKwU †m‡K‡Û †`vj‡Ki •`N© ̈ 1 m| †h †`vjKwU wgwb‡U 25 evi †`vj †`q Zvi •`N© ̈ KZ? [JU 22-23] 1.21 m 2.11 m 9.11 m 1.44 m DËi: 1.44 m e ̈vL ̈v: T  L  L  T 2  L2 L1 = T2 2 T1 2 GLv‡b, T2 = 60 25 = 12 5 s T1 = 2 s  L2 = L1  T2 2 T1 2 = 1        12 5 2 2 = 1      6 5 2 = 36 25  35 25  7 5  L2  1.4 m 3. GKwU Zi‡1⁄2i `ywU we›` GKwU mij †`vj‡Ki †`vjbKvj 20% e„w× Ki‡Z Gi Kvh©Ki •`N© ̈ KZ ̧Y evov‡Z n‡e? [JU 21-22] 9 25 11 25 5 4 4 5 DËi: 11 25 e ̈vL ̈v: T 2  L  L2 L1 =     T2 T1 2 =     120 100 2 =     6 5 2 = 36 25  L2 – L1 L1 = 36 25 – 1 = 11 25
4 .........................................................................................................................................  Physics 1st Paper Chapter-8 4. ch©vqKvj wØ ̧Y Ki‡Z mij †`vj‡Ki •`N© ̈ KZ ̧Y e„w× Ki‡Z n‡e? [JU 21-22; Agri. Guccho 19-20; KU 19-20; KU 15-16] 4 2 1 2 1 4 DËi: 4 e ̈vL ̈v: L2 =     T2 T1 2 L1 = 22  L1 = 4L1 5. †m‡KÛ †`vj‡Ki •`N© ̈ AwfKl©R Z¡iY g GiÑ [JU 21-22] mgvbycvwZK eM©g~‡ji mgvbycvwZK eM©g~‡ji e ̈ ̄ÍvbycvwZK e ̈ ̄ÍvbycvwZK DËi: mgvbycvwZK e ̈vL ̈v: L  g 6. gnvKv‡k GKwU †m‡KÛ †`vjK Gi K¤úvsK KZ n‡e? [JU 21-22; MBSTU-C 19-20; JnU 16-17] 1 Hz 0 Hz 2 Hz Infinite DËi: 0 Hz e ̈vL ̈v: f = 1 2 g L = 0 Hz 7. gnvKv‡k GKRb b‡fvPvixi Kv‡Q GKwU mij †`vj‡Ki †`vjbKvj n‡eÑ [JU 20-21; CU 15-16; BRUR 12-13] 84.6 min 2 sec 0  1 sec DËi:  8. y-i g‡a ̈ c_-cv_©K ̈ 5 4  n‡j, we›`y؇qi g‡a ̈ `kv cv_©K ̈ KZ? [JU 19-20] 5 2  2 5  5 4  4 5  DËi: 5 2  e ̈vL ̈v: `kv cv_©K ̈ = 2   c_ cv_©K ̈ = 2   5 4  = 5 2 9. mij Qw›`Z ̄ú›`biZ †Kv‡bv KYvi MwZ mi‡Yi m‡e©v”P Ae ̄’vb †_‡K ïiæ n‡j Avw` `kv n‡eÑ [JU 19-20]  2  0 3 2 DËi:  2 e ̈vL ̈v: awi, mgxKiY, x = A sin (t + ) t = 0 s mg‡q, A = A sin (  0 + )   =  2 10. mij †`vjb MwZm¤úbœ KYvi Z¡iY KZ? [JU 18-19] a = x 2 a = – x 2 a = – x a =  2 x DËi: Blank e ̈vL ̈v: a = –  2 x 11. `ywU mij †`vj‡Ki †`vjbKv‡ji AbycvZ 1 : 2 n‡j, Kvh©Ki •`‡N© ̈i AbycvZ KZ? [JU 18-19] 1 : 2 1 : 4 1 : 2 2 : 1 DËi: 1 : 4 e ̈vL ̈v: T 2  L  L1 L2 = T1 2 T2 2 = 1 4 12. GKwU mij †`vjK 2 wgwb‡U 60 evi †`vjb †`q| †`vjKwUi •`N© ̈ (m) KZ? [JU 17-18] 0.993 0.963 0.925 0.989 DËi: 0.993 e ̈vL ̈v: T = 60  2 60 = 2 sec L = gT2 4 2 = 0.993 m 13. Ae ̄’vb mv‡c‡ÿ GK Pμ cwigv‡Y Mo MwZkw3 n‡eÑ [JU 11-12; CoU 10-11] 3 2  †gvU kw3 2 3  †gvU kw3 1 3  †gvU kw3 1 2  †gvU kw3 DËi: 1 2  †gvU kw3 e ̈vL ̈v: average = †gvUkw3 2 14. mij Qw›`Z MwZ ev ̄ú›`b Gi †ÿ‡Î w ̄úas Gi aaæeKÑ [JU 10-11] k = l mg k = mg l k = m 2 g l k = l mg2 DËi: k = mg l weMZ mv‡j RU-G Avmv cÖkœvejx 1. †KvbwU mij Qw›`Z MwZi e‡ji •ewkó ̈ bq? [RU 23-24] ch©ve„Ë ej me©`v GKwU wbw`©ó we›`y AwfgyLx cÖZ ̈vqbx ej me©`v mvg ̈we›`y n‡Z mi‡Yi e ̈ ̄ÍvbycvwZK DËi: me©`v mvg ̈we›`y n‡Z mi‡Yi e ̈ ̄ÍvbycvwZK e ̈vL ̈v: mij Qw›`Z ̄ú›`bMwZi Rb ̈, a  – x A_©vr, ej me©`v mvg ̈we›`y n‡Z mi‡Yi mgvbycvwZK|