Nội dung text Varsity Weekly-5 (Set-A) Solution.pdf
2 8. L ˆ`N© ̈, A cÕ ̄’‡”Q` Ges Y Bqs Gi ̧Yv1⁄4 wewkó GKwU Zvi k w ̄úas aaæeK wewkó w ̄úas Gi g‡Zv AvPiY K‡i| k Gi gvbÑ 2YA L YA L YL2 A YA L 2 DËi: YA L e ̈vL ̈v: w ̄úas Gi Rb ̈, F = kl F l = k Y = FL Al = kL A k = YA L 9. Bqs ̧Yv1⁄4 Y, AvqZb ̧Yv1⁄4 K Gi `„pZvi ̧Yv1⁄4 n‡j, †Kvb m¤úK©wU mwVK? 3 Y 9 1 K 9 Y 1 3 K 9 Y 3 1 K 1 Y 9 3 K DËi: 9 Y 3 1 K e ̈vL ̈v: Bqs Gi ̧Yv1⁄4 Y, `...pZvi ̧Yv1⁄4 , AvqZb ̧Yv1⁄4 K Ges cqm‡bi AbycvZ Gi g‡a ̈ wb‡¤œv3 m¤úK© we` ̈gvbÑ (i) Y 3K(1 – 2) (ii) Y = 2 (1 + ) (iii) = 3K – 2 6K + 2 (iv) 9 Y = 1 K + 3 10. 7.5 107 Nm–2 Pv‡c 1000 cc cvi` KZUzKz msKzwPZ n‡e? [cvi‡`i AvqZb ̧YvsK 2.5 1010 Nm–2 ] 1 cc 1.5 cc 2 cc 3 cc DËi: 3 cc e ̈vL ̈v: B = P v V v = PV B = 7.5 107 1000 10–6 2.5 1010 = 3 10–6 m 3 = 3 cc 11. Zv‡ii mvnv‡h ̈ fimn †`vjbv Szjv‡bv n‡j Zv‡ii ˆ`N© ̈ 1 m †_‡K e„w× †c‡q 1.01 m nq| G‡Z Zv‡ii e ̈vm KZUzKz n«vm cvq? (cqm‡bi AbycvZ 0.2) 1 500 Ask 1 50 Ask 1 5000 Ask 1 5 Ask DËi: 1 500 Ask e ̈vL ̈v: = – cvk¦© weK...wZ ˆ`N© ̈ weK...wZ = – d D l L GLv‡b, L = 1 m l = (1.01 – 1) = 0.01 m = 0.2 d = – D l L = – 0.2 0.01 1 D = – D 500 e ̈vm Avw` e ̈v‡mi 1 500 Ask n«vm cv‡e| 12. cqm‡bi AbycvZ Gi gvÎv †KvbwU? [ML–1T –2 ] [MLT–2 ] [ML–1T –1 ] †Kv‡bvwUB bq DËi: †Kv‡bvwUB bq e ̈vL ̈v: cqm‡bi AbycvZ, = cvk¦© weK...wZ ˆ`N© ̈ weK...wZ †h‡nZz cqm‡bi AbycvZ `ywU mgRvZxq ivwki AbycvZ ZvB cqm‡bi Abycv‡Zi gvÎv †bB| 13. wb‡Pi †KvbwU cqm‡bi AbycvZ n‡Z cv‡i? 0.2 0.8 1 2 DËi: 0.2 e ̈vL ̈v: cqm‡bi AbycvZ : – 1 < 1 2 14. 2 m j¤^v 2 mm e ̈vmva©wewkó GKwU Zv‡ii ˆ`N© ̈ e„w× 0.25 mm n‡j ZviwUi e ̈vmva© KZ n«vm cv‡e? ( = 0.2) 5 × 10–3 m 2.5 × 10–3 m 5 × 10–8 m 2.5 × 10–8 m DËi: 5 × 10–8 m e ̈vL ̈v: r × L rL r rL L 0.2 0.002 0.25 10–3 2 r 5 10–8 m 15. 2 m `xN© SzjšÍ GKwU Zv‡ii wb‡Pi cÕv‡šÍ 20 kg fi Szjv‡j Gi ˆ`N© ̈ 6 cm ev‡o| ZviwU B ̄úv‡Zi n‡j Zv‡ii e ̈vmva© KZ? [g = 10 ms–2 ] 10–7 m 0.33 10–7 m 10–6 m None DËi: 0.33 10–7 m e ̈vL ̈v: r = mgL lY = 20 10 2 6 10–2 2 1011() = 2 104 2 6 2 1011 = 1 3 10–7 m
3 16. GKwU Zv‡ii ˆ`N© ̈ 3 ̧Y I e ̈vm A‡a©K Kiv n‡j Bqs Gi ̧Yv1⁄4 wK n‡e? 3 ̧Y 9 ̧Y mgvb 1 3 ̧Y DËi: mgvb e ̈vL ̈v: GKB Dcv`v‡bi Bqs ̧Yv1⁄4 same _vK‡e| 17. †h c`v‡_©i evav`vbKvix ej †ewk, †m c`v‡_©iÑ w ̄’wZ ̄’vcKZv †ewk AvšÍtAvKl©Y ej Kg w ̄’wZ ̄’vcKZv Kg NbZ¡ Kg DËi: w ̄’wZ ̄’vcKZv †ewk e ̈vL ̈v: Y = FL Al Y F ZvB F eo n‡j Y †ewk n‡e| 18. GKwU avZe Zv‡ii †gvPo ̧Yv1⁄4, = 1 104 N/m2 Ges ZviwUi e ̈vm 0.32 mm Ges 1 m `xN©| ZviwU‡Z 200 N ej cÕ‡qvM Ki‡j 0.01 mm msKzwPZ nq| Z‡e ZviwUi cqm‡bi AbycvZ KZ? 0.51 0.24 0.53 0.75 DËi: 0.24 e ̈vL ̈v: Y = 2 (1 + ) 2.48 104 1 104 = 2 (1 + ) = 0.24 Y = FL Al = 200 1 (0.16) 2 10–6 0.01 10–3 = 2.48 104 Nm–2 Trick : – 1 < 1 2 (L) Ackb e ̈ZxZ evwK wZbwU Ack‡bi †Kv‡bvwUB cqm‡bi Abycv‡Zi †i‡Ãi g‡a ̈ c‡o bv| 19. wb‡Pi †Kvb c`v‡_©i w ̄’wZ ̄’vcKZv me‡P‡q †ewk? cvwb B ̄úvZ ivevi †jW DËi: B ̄úvZ e ̈vL ̈v: mgvb ej cÖ‡qvM Ki‡j B ̄úv‡Zi evav cÖ‡qvM Kivi ÿgZv evKx ̧‡jvi †P‡q †ewk| 20. †h mKj Zij KuvP †fRvq bv Zv‡`i ̄úk© †KvYÑ ̄’..j‡KvY m~2‡KvY mg‡KvY k~b ̈ DËi: m~2‡KvY 21. Ôcxob weK...wZi mgvbycvwZK×Ñ Kvi m~Î? û‡Ki Bqs Gi cqm‡bi Rywi‡bi DËi: û‡Ki e ̈vL ̈v: û‡Ki m~Îvbymv‡i, w ̄’wZ ̄’vcK mxgvi g‡a ̈ †Kvb e ̄`i cxob Zvi weK...wZi mgvbycvwZK| 22. A B ˆ`N© ̈ cxob O ˆ`N© ̈ weK...wZ wP‡Î OA †iLvi Xvj‡K Kx e‡j? Bqs ̧Yv1⁄4 cqm‡bi AbycvZ `...pZvi ̧Yv1⁄4 ̄’vqx weK...wZ DËi: Bqs ̧Yv1⁄4 e ̈vL ̈v: GLv‡b, OA c_ w ̄’wZ ̄’vcK mxgvi g‡a ̈ Kvh©iZ| w ̄’wZ ̄’vcK mxgvi g‡a ̈ e ̄`i ˆ`N© ̈ cxob I ˆ`N© ̈ weK...wZi AbycvZB Bqs Gi MyYv1⁄4| 23. †Kv‡bv e ̄`i AvqZb ̧Yv1⁄4 3 103 Nm–2 , Zvi msbg ̈Zv KZ? 3.3 10–4 N m–2 33 10–5 N –1 m 2 300 105 N –1 m 2 None DËi: 33 10–5 N –1 m 2 e ̈vL ̈v: msbg ̈Zv = 1 K = 1 3 103 = 0.33 10–3 = 33 10–5 N –1 m 2 24. GKwU Zv‡ii Bqs Gi ̧Yv1⁄4 (Y) I weK...wZi †jLwPÎ wb‡Pi †KvbwU? Y weK...wZ Y weK...wZ Y weK...wZ Y weK...wZ DËi: Y weK...wZ e ̈vL ̈v: GKwU Zv‡ii Bqs Gi ̧Yv1⁄4 Zv‡ii Dcv`v‡bi Dci wbf©i K‡i, weK...wZi Dci bq| GRb ̈ weK...wZi †h‡Kv‡bv gv‡bi Rb ̈ Bqs Gi ̧Yv1⁄4 w ̄’i _vK‡e| 25. cÕ ̄’‡”Q‡`i †ÿÎdj I ej wØ ̧Y Kiv n‡j ˆ`N© ̈ e„w× c~‡e©i KZ ̧Y n‡e? 1 ̧Y 2 ̧Y 3 ̧Y 4 ̧Y DËi: 1 ̧Y e ̈vL ̈v: Avgiv Rvwb, Y = FL Al l = FL YA Y = (2F) L (2A) l l = FL YA l = l
English