Title 7. P1C7 (Structural Properties of Matter) With Solve.pdf ✅

c`v‡_©i MvVwbK ag©  Varsity Practice Sheet ..................................................................................................................... 1 weMZ mv‡j DU-G Avmv cÖkœvejx 1. GKwU B ̄úv‡Zi Zv‡ii Dcv`v‡bi Bqs ̧Yv1⁄4 Y| hw` Zv‡ii e ̈vm wØ ̧Y Kiv nq Zvn‡j cwiewZ©Z Bqs ̧Yv1⁄4 KZ n‡e? [DU 23-24] c~‡e©i mgvb (the same as before) c~‡e©i AwaK (half the previous value) c~‡e©i wØ ̧Y (twice the previous value) c~‡e©i Pvi ̧Y (four times the previous value) DËi: c~‡e©i mgvb (the same as before) e ̈vL ̈v: †Kv‡bv wbw`©ó Dcv`v‡bi Rb ̈ Bqs Gi ̧Yv1⁄4 wbw`©ó; GwU e ̈vm Gi Dci wbf©i K‡i bv| 2. wb‡Pi †KvbwUi gvÎv †bB? [DU 22-23; JU 19-20] cxob (Stress) Bqs-Gi ̧Yv1⁄4 (Young’s modulus) weK...wZ (Strain) Pvc (Pressure) DËi: weK...wZ (Strain) e ̈vL ̈v: weK...wZ = l L †h‡nZz weK...wZ `ywU mgRvZxq ivwki AbycvZ nIqvq weK...wZi †Kv‡bv gvÎv †bB| 3. 10 cm j¤^v I 0.5 cm e ̈vmva© wewkó GKwU Zvgv I GKwU †jvnvi Zvi‡K †Rvov jvwM‡q ˆ`N© ̈ 20 cm Kiv nj| †Rvov Zv‡ii Dci ej cÖ‡qvM K‡i weK...wZ NUv‡bv nj| hw` †jvnvi Bqs Gi ̧Yv1⁄4 Zvgvi wØ ̧Y nq Z‡e †jvnvi ˆ`N© ̈ e„w×i AbycvZ KZ? [DU 19-20] 1 : 8 1 : 6 1 : 4 1 : 2 DËi: 1 : 2 e ̈vL ̈v: Bqs Gi ̧Yv1⁄4, Y = ˆ`N© ̈ cxob ˆ`N© ̈ weK...wZ  Y = F A l L  l = FL AY  lS lB = YB YS  ls lB = 1 2  lS : lB = 1 : 2 4. GKwU Zv‡ii Bqs Gi ̧Yv1⁄4 4  1011 Nm–2 | ZviwUi ˆ`N© ̈ 7.5% evov‡Z Kx cwigvY cxob cÖ‡qvRb n‡e? [DU 17-18; RU 14-15] 7.5  1011 Nm–2 3  1010 Nm–2 5.33  1010 Nm–2 4  1010 Nm–2 DËi: 3  1010 Nm–2 e ̈vL ̈v: Y = cxob weK...wZ  cxob = 4  1011  0.075 = 3  1010 Nm–2 5. w ̄’wZ ̄’vcK ̧Yv‡1⁄4i gvÎv Kx? [DU 20-21; MBSTU 14-15] MLT–1 ML–1T –2 MLT–2 ML2T –2 DËi: ML–1T –2 e ̈vL ̈v: w ̄’wZ ̄’vcK ̧Yv‡1⁄4i gvÎv = cxo‡bi gvÎv cxob = ej †ÿÎdj = [MLT–2 ] [L2 ] = [ML–1T –2 ]  cxo‡bi gvÎv [ML–1T –2 ] weMZ mv‡j GST-G Avmv cÖkœvejx 1. l ˆ`N© ̈ I r e ̈vmv‡a©i GKwU Zv‡ii GK cÖvšÍ w ̄’i †i‡L Aci cÖv‡šÍ m fi Szjv‡j ZviwUi Bqs-Gi ̧Yv1⁄4 (Y) 200 GPa| ZviwUi e ̈vmva© A‡a©K Ki‡j Y Gi gvbÑ [GST 22-23] A‡a©K n‡e wØ ̧Y evo‡e cwieZ©b n‡e bv Pvi ̧Y evo‡e DËi: cwieZ©b n‡e bv e ̈vL ̈v: Bqs Gi ̧Yv1⁄4 e ̄‘i Dcv`v‡bi Dci wbf©i K‡i| GwU e ̈vmv‡a©i Dci wbf©ikxj bq| ZvB e ̈vmva© A‡a©K Ki‡j Bqs Gi ̧Yv‡1⁄4i †Kv‡bv cwieZ©b n‡e bv| weMZ mv‡j JU-G Avmv cÖkœvejx 1. GKwU Av`k© `„p e ̄‘i Rb ̈ Bqs Gi ̧Yv1⁄4Ñ [JU 18-19; BRUR 15-16] 0  1 –1 DËi:  e ̈vL ̈v: Av`k© `„p e ̄‘i weK...wZ k~b ̈|  Y = 
2 .........................................................................................................................................  Physics 1st Paper Chapter-7 2. 1 mm2 cÖ ̄’‡”Q‡`i †ÿÎdj wewkó GKwU B ̄úv‡Zi Zv‡ii ˆ`N© ̈ 10% e„w× Ki‡Z KZ ej cÖ‡qvM Ki‡Z n‡e? [Y = 2  1011 Nm2 ] [JU 17-18] 2  104 N 6  104 N 8  104 N 12  104 N DËi: 2  104 N e ̈vL ̈v: Bqs Gi ̧Yv1⁄4, Y = FL Al  F = YAl L  F = 2  1011  1  10–6  1 10  F = 2  104 N 3. GKwU Zv‡ii ˆ`N© ̈ 2 m Ges e ̈vm 5 mm| ˆ`N© ̈ eivei ej cÖ‡qv‡Mi d‡j ZviwUi ˆ`N© ̈ 10% e„w× cvq| cqm‡bi AbycvZ 0.02 n‡j, Gi e ̈vm KZUzKz n«vm cv‡e? [JU 17-18] 1.0 mm 0.01 mm 0.01 m 1.0 m DËi: 0.01 mm e ̈vL ̈v: cqm‡bi AbycvZ,  = – cvk¦© weK...wZ ˆ`N© ̈ weK...wZ   = – d d l l  d = – dl l  d = – 0.02  5  0.1  d = – 0.01 mm FYvZ¥K wPý e ̈v‡mi n«vm wb‡`©k K‡i| 4. 10 m j¤^v Ges 1 mm e ̈vm wewkó GKwU Zvi‡K 100 N ej Øviv Uvbv nj| ZviwUi ˆ`N© ̈ KZUzKz e„w× cv‡e? [Y = 2  1011 Nm–2 ] [JU 16-17] 6.4  10–3 m 6.4  10–2 m 6.4  10–4 m 6.4  10–5 m DËi: 6.4  10–3 m e ̈vL ̈v: Bqs Gi ̧Yv1⁄4, Y = FL Al  l = FL AY  l = FL r 2Y  l = 100  10 3.1416  (0.5  10–3 ) 2  2  1011 = 6.4  10–3 m 5. GKwU Zv‡ii cÖ ̄’‡”Q‡`i †ÿÎdj 1  10–4 m 2 | Zv‡ii ˆ`N© ̈ 10% e„w× Kivi Rb ̈ 2  106 N ej cÖ‡qvM Kiv n‡j Zv‡ii Dcv`v‡bi Bqs Gi ̧Yv1⁄4 n‡eÑ [JU 15-16] 3  1011 Nm–2 2.5  1011 Nm–2 2  1011 Nm–2 †KvbwUB bq DËi: 2  1011 Nm–2 e ̈vL ̈v: Bqs Gi ̧Yv1⁄4, Y = ˆ`N© ̈ cxob ˆ`N© ̈ weK...wZ  Y = F A l L  Y = FL Al  Y = 2  106  100 1  10–4  10  Y = 2  1011 Nm–2 6. 300 cm3 cvi‡`i Dci wK cwigvY Pvc cÖ‡qvM Ki‡j Gi AvqZb 270 cm3 n‡e? (cvi‡`i AvqZb ̧Yv1⁄4 2.6  1010 Nm–2 ) [JU 14-15] 2.6  1010 Nm–2 2.6  109 Nm–2 2.4  1010 Nm–2 2.4  109 Nm–2 DËi: 2.6  109 Nm–2 e ̈vL ̈v: AvqZb ̧Yv1⁄4, B = P v V  P = Bv V  P = 2.6  1010  30 300 = 2.6  109 Nm–2 7. GKwU Zv‡ii ˆ`N© ̈ 5 m, cÖ ̄’‡”Q‡`i †ÿÎdj 0.002 m2 , Amncxob 2.5  105 Nm–2 | ZviwUi Amnfi KZ? [JU 14-15] 500 9.8 kg 250 9.8 kg 200 9.8 kg 450 9.8 kg DËi: 500 9.8 kg e ̈vL ̈v: Amn cxob = Amn ej †ÿÎdj  2.5  105 = m  9.8 (0.002)  25  104 = m  9.8 2  10–3  m = 50  10 9.8 kg  m = 500 9.8 kg 8. 200 cm `xN©, 31  10–2 cm2 cÖ ̄’‡”Q` wewkó GKwU Zv‡ii Bqs Gi ̧Yv1⁄4 1.5  1011 Nm–2 | G‡K †U‡b 0.1 cm e„w× Ki‡Z n‡j KZUzKz KvR m¤úbœ n‡e? [JU 14-15] 0.25 J 0.2 J 0.15 J 0.22 J DËi: Blank e ̈vL ̈v: K...ZKvR, W = 1 2 YAl 2 L  W = 1 2  1.5  1011  31  10–2  10–4  (0.1  10–2 ) 2 2  W = 1.1625 J  mwVK DËi †bB|
c`v‡_©i MvVwbK ag©  Varsity Practice Sheet .................................................................................................................... 3 9. ZvcgvÎv e„w× †c‡j B ̄úv‡Zi w ̄’wZ ̄’vcK ̧Yv1⁄4Ñ [JU 12-13] Increases Decreases Remain unchanged None DËi: Remain unchanged e ̈vL ̈v: B ̄úvZ e ̈ZxZ Ab ̈vb ̈ avZzi †ÿ‡Î ZvcgvÎv evov‡j w ̄’wZ ̄’vcK ̧Yv1⁄4 ev‡o| 10. M ̈v‡mi AvqZb ̧Yv1⁄4 6  103 Nm–2 | M ̈v‡mi AvqZb 10% Kgv‡Z n‡j wK cwigvY AwZwi3 Pvc cÖ‡qvM Ki‡Z n‡e? [JU 12-13] 300 Nm–2 400 Nm–2 1000 Nm–2 600 Nm–2 DËi: 600 Nm–2 e ̈vL ̈v: AvqZb ̧Yv1⁄4, B = P v V  P = Bv V  P = 6  103  10 100  P = 600 Nm–2 weMZ mv‡j RU-G Avmv cÖkœvejx 1. B ̄úv‡Zi [Y = 2  1011 Nm–2 ] GKwU Zv‡ii ˆ`N© ̈ 2 m, cÖ ̄’‡”Q‡`i †ÿÎdj 1 mm2 | ZviwUi cÖv‡šÍ 20 N ej cÖ‡qvM Ki‡j ˆ`N© ̈ e„w× KZ wgUvi? [RU 23-24] 2  10–4 2  10–5 10–4 10–6 DËi: 2  10–4 e ̈vL ̈v: Y = FL Al  l = FL AY = 20 × 2 10–6 × 2 × 1011 = 20 105 = 2 × 10–4 m 2. L ˆ`N© ̈ Ges A cÖ ̄’‡”Q‡`i GKwU Zvi Szjv‡bv Av‡Q| Gi gy3 cÖv‡šÍ M f‡ii GKwU e ̄‘ Szwj‡q w`‡j ZviwUi ˆ`N© ̈ cwiewZ©Z n‡q L1 n‡j Bqs ̧Yvs‡Ki gvb n‡eÑ [RU 23-24] MgL1 AL MgL AL1 MgL A (L1 – L) Mg (L1 – L) AL DËi: MgL A (L1 – L) e ̈vL ̈v: Y = FL Al = MgL A (L1 – L) 3. Bqs-Gi ̧YvsK †KvbwUi Ici wbf©ikxj? [RU 23-24] ˆ`N© ̈ n«vm/e„w× Avw` ˆ`N© ̈ cÖ ̄’‡”Q‡`i †ÿÎdj e ̄‘i Dcv`vb DËi: e ̄‘i Dcv`vb 4. w ̄’wZ ̄’vcK mxgvi g‡a ̈ 1 sqmm cÖ ̄’‡”Q‡`i †ÿÎdj wewkó Zv‡ii GK cÖv‡šÍ 1 N ej cÖ‡qvM Kiv n‡j cxob n‡eÑ [RU 20-21] 106 Nm–2 104 Nm–2 100 Nm–2 50 Nm–2 DËi: 106 Nm–2 e ̈vL ̈v: cxob = ej †ÿÎdj = 1 (1  10–3 ) 2  cxob = 106 Nm–2 5. cxob (Stress) Gi gvÎv (Dimension) †KvbwU? [RU 19-20; MBSTU-B 15-16; JnU 14-15, 13-14; PUST 14-15; CoU 13-14; IU 12-13, 01-02] [ML–1T –2 ] [ML–2T –2 ] [ML–1 T –1 ] [ML1 T 2 ] DËi: [ML–1T –2 ] 6. mgvb ˆ`‡N© ̈i wZbwU Zvi A, B Ges C-†Z cxo‡bi gvb mgvb Ges ˆ`N© ̈ e„w× lA > lB > lC n‡j wb‡Pi †KvbwU mwVK? [†hLv‡b Y Bqs Gi ̧Yv1⁄4] [RU 18-19] YA > YB > YC YC > YB > YA YA = YB = YC I DfqB DËi: YC > YB > YA e ̈vL ̈v: Bqs Gi ̧Yv1⁄4, Y = ˆ`N© ̈ cxob ˆ`N© ̈ weK...wZ  Y = FL Al †h‡nZz cxob, F A Ges Avw` ˆ`N© ̈ L cÖwZ‡ÿ‡Î GKB| ZvB Y  1 l lA > lB > lC > nIqvq YC > YB > YA 7. 3 m `xN© Ges 1 cm2 cÖ ̄’‡”Q` wewkó GKwU Zv‡ii Bqs Gi ̧Yv1⁄4 5  1010 dyne/cm2 n‡j ZviwUi ˆ`N© ̈ 6 cm e„w× Ki‡Z n‡j Gi ˆ`N© ̈ eivei KZ WvBb ej cÖ‡qvM Ki‡Z n‡e? [RU 16-17] 2.5  1010 5  1010 1011 109 DËi: 109 e ̈vL ̈v: Bqs Gi ̧Yv1⁄4 Y n‡j ej, F = YAl L  F = 5  1010  1  6 300 dyne = 109 dyne 8. 200 cm j¤^v I 1 mm2 cÖ ̄’‡”Q‡`i †ÿÎdj wewkó GKwU B ̄úvZ Zv‡ii ˆ`N© ̈ 1.0 mm e„w× Ki‡Z cÖ‡qvRbxq Kv‡Ri cwigvY KZ? (B ̄úvZ Gi Bqs Gi ̧Yv1⁄4 = 2  1011 Nm–2 ) [RU 14-15] 0.05 J 1.0 J 1.5 J 0.75 J DËi: 0.05 J e ̈vL ̈v: K...ZKvR, W = 1 2 YAl 2 L  W = 1 2  2  1011  1  10–6  (1  10–3 ) 2 2  W = 1 20 J  W = 0.05 J
4 .........................................................................................................................................  Physics 1st Paper Chapter-7 9. cvwbi AvqZb cÖmviY ̧Yv1⁄4 0.22  1010 Nm–2 | 1 L cvwbi AvqZb 0.1% cwieZ©b Ki‡Z KZ Pv‡ci cÖ‡qvRb? [RU 12-13] 0.22  1010 Nm–2 0.22  1013 Nm–2 2.2  106 Nm–2 2.2 Nm–2 DËi: 2.2  106 Nm–2 e ̈vL ̈v: AvqZb ̧Yv1⁄4, B = P v V  P = Bv V = 0.22  1010  0.1 100  P = 2.2  106 Nm–2 weMZ mv‡j CU-G Avmv cÖkœvejx 1. GKwU e ̄‘i cqm‡bi (Poisson) Abycv‡Zi mxgvÑ [CU 23-24] 0 †_‡K – 1 2 0 †_‡K 1 –1 †_‡K + 1 2 – 1 2 †_‡K + 1 2 DËi: –1 †_‡K + 1 2 2. GKwU Zv‡ii e ̈vmva© e„w× Kiv n‡j ZviwUi Dcv`v‡bi Bqs Gi ̧Yv1⁄4Ñ [CU 22-23] e„w× cv‡e n«vm cv‡e AcwiewZ©Z _vK‡e †KvbwUB bq DËi: AcwiewZ©Z _vK‡e 3. cqm‡bi AbycvZ () Gi †ÿ‡Î wb‡¤œi †Kvb mgxKiYwU mwVK? [CU 22-23, 18-19; HSTU 15-16; CoU 10-11; IU 10-11] – 1    1 2 – 1    1 – 1 2    1 †Kv‡bvwUB bq DËi: – 1    1 2 4. cqm‡bi Abycv‡Zi m‡e©v”P gvb n‡jvÑ [CU 22-23] 1 2 – 1 2 1 –1 DËi: 1 2 e ̈vL ̈v: cqm‡bi Abycv‡Zi gvb mvaviYZ –1 †_‡K 1 2 Gi g‡a ̈ n‡q _v‡K| 5. hw` P cxob Ges Y †Kv‡bv Zv‡ii Dcv`v‡bi Bqs Gi ̧Yv1⁄4 nq, Z‡e Zv‡ii cÖwZ GKK AvqZ‡b mwÂZ kw3Ñ [CU 18-19] 2P2Y P 2 2Y 2Y P 2 P 2Y DËi: P 2 2Y e ̈vL ̈v: GKK AvqZ‡b mwÂZ kw3 W n‡j, W = 1 2  cxob  weK...wZ Avevi, Y = cxob weK...wZ  weK...wZ = cxob Y ......... (i) W = 1 2  cxob  cxob Y [(i) bs n‡Z]  W = 1 2 (cxob) 2 Y  W = P 2 2Y 6. 108 Nm–2 cxo‡bi cÖ‡qv‡M 1 m `xN© GKwU Zv‡ii ˆ`N© ̈ 10–3 m e„w× †cj| ZviwUi Bqs Gi ̧Yv1⁄4 KZ? [CU 17-18] 105 Nm–2 10–11 Nm–2 10–5 Nm–2 1011 Nm–2 DËi: 1011 Nm–2 e ̈vL ̈v: Bqs Gi ̧Yv1⁄4 = ˆ`N© ̈ cxob ˆ`N© ̈ weK...wZ = 108 1  10–3 1 = 1011 Nm–2 7. Bqs Gi ̧Yv‡1⁄4i gvÎv mgxKiYÑ [CU 16-17] [MLT–2 ] [ML–1T –1 ] [ML–2T –2 ] [MLT3 ] [ML–1T –2 ] DËi: [ML–1 T –2 ] e ̈vL ̈v: Bqs Gi ̧Yv1⁄4, Y = ˆ`N© ̈ cxob ˆ`N© ̈ weK...wZ  Y = [ML–1T –2 ] 1  Y = [ML–1T –2 ] 8. ˆ`N© ̈ weK...wZi GKK wK? [CU 14-15] m Nm–1 m 2 GKK bvB DËi: GKK bvB e ̈vL ̈v: ˆ`N© ̈ weK...wZ = ˆ`‡N© ̈i cwieZ©b Avw` ˆ`N© ̈ †h‡nZz weK...wZ `ywU mgRvZxq ivwki AbycvZ ZvB weK...wZi †Kv‡bv GKK †bB| 9. L ˆ`N© ̈ I r e ̈vmv‡a©i GKwU Zv‡ii Dcv`v‡bi Bqs Gi ̧Yv1⁄4 Y| Zv‡ii ˆ`N© ̈ L 2 Ges e ̈vmva© r 2 Kiv n‡j Bqs Gi ̧Yv1⁄4 KZ n‡e? [CU 14-15] Y 2 Y 2Y 4Y DËi: Y e ̈vL ̈v: Bqs Gi ̧Yv1⁄4 e ̄‘i Dcv`v‡bi Dci wbf©i K‡i| GwU e ̈vmv‡a©i Dci wbf©ikxj bq| ZvB ˆ`N© ̈, e ̈vmva© n«vm Ki‡j Bqs Gi ̧Yv‡1⁄4i †Kv‡bv cwieZ©b n‡e bv|