Tiêu đề Varsity Weekly-3 (Set-A) Solution.pdf ✅

1 Varsity Weekly-03 [A (Solution)] wm‡jevm: KvR, kw3 I ÿgZv + †g؇ji ch©vqe„Ë ag© I ivmvqwbK eÜb-1 + e„Ë + AYyRxe + evsjv-3 + Bs‡iwR-3 c~Y©gvb: 100 †b‡MwUf gvK©: 0.25 mgq: 1 NÈv c`v_©weÁvb (Physics) 1. 1 9.8 kg f‡ii GKwU e ̄` 200 m Dc‡i i‡q‡Q| Gi g‡a ̈ †h kw3 we` ̈gvb Zv w`‡q GKwU hš¿ 500 m c_ AwZμg Ki‡Z cvi‡j h‡š¿i Dci cÕ‡qvMK...Z ej KZ? 0.4 N 4 N 40 N 400N DËi: 0.4 N e ̈vL ̈v: E = mgh = 1 9.8  9.8  200 = 200 J F = W s = E s = 200 500 N = 2 5 N = 0.4 N 2. GKwU KYvi Dci cÕ‡qvMK...Z ej, F  = (i  – 3j  + 6k  ) N. GwUi s  = (3i  + nj  + 2k  ) m miY nq| n Gi gvb KZ n‡j Kv‡Ri gvb k~b ̈ n‡e? 40 13 3 5 DËi: 5 e ̈vL ̈v: F  .s  = (i )  – 3j  + 6k  . (3i )  + nj  + 2k   3 – 3n + 12 = 0  15 – 3n = 0  n = 15 3 = 5 3. c„w_exi 5 km Dc‡i †gN †f‡m Av‡Q| H †gN e„wóiƒ‡c covq f‚c„‡ô cvwbi cwigvY hv nq Zv w`‡q 200 km2 †ÿÎdj I 5 m Mfxi GKwU cyj ˆZwi m¤¢e| D3 cvwb‡K Avevi †g‡N cwiYZ Ki‡Z Kx cwigvY KvR Ki‡Z n‡e? 49  1011 J 98  1015 J 14.7  1011 J 49  1015 J DËi: 49  1015 J e ̈vL ̈v: m = Ah = 200  106  5  1000 = 1012 kg W = mgh = 1012  9.8  5  103 = 49  1015 J 4. 40 kg fi I 10 m ˆ`‡N© ̈i GKwU wkK‡ji GK-PZz_©vsk †Uwe‡ji wKbviv eivei Szj‡Q| m¤ú~Y© wkKjwU †Uwe‡ji Dci wb‡Z AwfKl© e‡ji weiæ‡× K...ZKvR KZ? 250 J 122.5 J 245 J 490.5 J DËi: 122.5 J e ̈vL ̈v: 2.5 * fi‡K‡›`ai miY, h = 10 4 2 = 10 8 m = 40 4 = 10 kg W = mgh = 10  9.8  10 8 = 122.5 J 5. h = 140 m A B B n‡Z KZ DuPz‡Z wefekw3 MwZkw3i 3 4 ̧Y n‡e? 30 m 60 m 40 m 50 m DËi: 60 m e ̈vL ̈v: Ep = 3 4 Ek  mgh = 3 4  1 2 mv2  mgh = 3 4  1 2 m  {2g (h – h)}  h = 3 4 (h – h)  4h = 3h – 3h  7h = 3h  h = 3h 7 = 3  140 7  h = 60 m 6. Kv‡Ri gvb m‡e©v”P n‡e hLb ej I mi‡Yi ga ̈eZ©x †KvY- 360 90 180 0 DËi: 0 e ̈vL ̈v: W = Fscos  = 0 n‡j, W = Fscos0 = Fs,  Gi gvb evo‡j W Gi gvb Kg‡e|

3 e ̈vL ̈v: K...ZKvR = MwZkw3i cwieZ©b Here, x = 2t 2 + 5  v = dx dt = 4t at t = 5s, v = 20 m/s  K...ZKvR = 1 2 mv2 = 1 2  2  (20)2 = 400 J 16. 75% `ÿZvi 4000 W Gi †Kv‡bv cv¤ú M‡o 15 m D”PZvq Aew ̄’Z (3  2  1) m3 †Kv‡bv U ̈vs‡K cvwb Zzj‡Q| Tank c~Y© Ki‡Z KZ mgq jvM‡e? 5.88 min 9.8 min 19.6 min 4.9 min DËi: 4.9 min e ̈vL ̈v: Pin = 4000 W Pout = Pin   = 0.75  4000 = 3000 W m = V = 1000  3  2  1 = 6000 kg  3000 = 6000  9.8  15 t  t = 294 s = 4.9 min 17. Kv‡Ri AwfKl©xq GKK Kx? Ryj AvM© †KwR-wgUvi WvBb-†mw›UwgUvi DËi: Ryj 18. cwieZ©bkxj ej Øviv K...ZKvR n‡jvÑ W =  f i F  . ds  W =  xf xi F(x) dx W = GMm     1 rb – 1 ra W =  x 0 Fdx DËi: W =  xf xi F(x) dx 19. GK e ̈w3 GKwU e ̄`‡K 40 s-G 1 m D”PZvq IVvq| Aci GK e ̈w3 GKB e ̄`‡K 120 s-G GKB D”PZvq Zzj‡Z cv‡i| Zv‡`i Kv‡Ri AbycvZ n‡eÑ 1 : 3 1 : 1 2 : 1 3 : 1 DËi: 1 : 1 e ̈vL ̈v: W  h  W1 W2 = h1 h2 = 1 [h1 = h2]  W1 : W2 = 1 : 1 20. wb‡Pi †Kvb e ̄`i MwZkw3 †ewk? fi M, †eM 2v fi 2M, †eM 3v fi M, †eM 4v fi 3M, †eM 2v DËi: fi 2M, †eM 3v e ̈vL ̈v: (K) Ek  2Mv2 (L) Ek  9Mv2 (M) Ek  8Mv2 (N) Ek  6Mv2 21. wb‡Pi †KvbwU msiÿYkxj e‡ji D`vniY? Nl©Y ej mv›`aej AwfKl©xq ej NvZ ej DËi: AwfKl©xq ej e ̈vL ̈v: †h ej †Kv‡bv e ̄`i Dci wμqv Ki‡j Zv‡K †h‡Kv‡bv c‡_ Nywi‡q cybivq cÖv_wgK Ae ̄’v‡b Avb‡j ej KZ...©K K...ZKvR k~Y ̈ nq Zv‡K msiÿYkxj ej e‡j| D`vniY: AwfKl©xq ej, ˆe`y ̈wZK ej, Av`k© w ̄úas Gi weK...wZ cÖwZ‡ivax ej cÖf...wZ| 22. 2 HP Gi GKwU cv¤ú 12 wgwb‡U 1000 wjUv‡ii GKwU U ̈vs‡K cvwb fwZ© Ki‡Z cv‡i| AwZwi3 1 HP Gi GKwU cv¤ú hy3 Ki‡j D3 Kv‡R KZ wgwbU mgq mvkÕq n‡e? 8 4 6 2 DËi: 4 e ̈vL ̈v: P = mgh t  P  1 t P2 P1 = t1 t2  3 2 = 12 t2  t2 = 8 min  mvkÖq = 12 – 8 = 4 min 23. 100 gm f‡ii GKwU cv_i Dj¤^Z‡j 20 m e ̈vmv‡a©i e„Ë c‡_ Nyi‡Z Nyi‡Z A Ae ̄’vb n‡Z B-Ae ̄’v‡b Avmj (wPÎ-1)| kw3i cwieZ©b KZ n‡e? B A r=20m wPÎ-1 10 J 39.2 J 30 J 50.2 J DËi: 39.2 J e ̈vL ̈v: Ep  mg × 2r  0.1  9.8  2  20  39.2 J 24. w ̄’i Ae ̄’v †_‡K 20 kg fiwewkó †Kvb e ̄` wbw`©ó e‡ji wμqvi d‡j 2s ci 15 ms–1 †eM cÕvß nj| 4s ci e ̄`wUi MwZkw3 KZ n‡e? 6000 J 12000 J 18000 J 9000 J DËi: 9000 J e ̈vL ̈v: v = u + at  a  15 2  7.5 ms–2  E  1 2 mv 2  1 2 m (at)2  1 2  20  (7.5  4)2  9000 J 25. GKwU w ̄úas‡K GK Ae ̄’vb †_‡K Ab ̈ Ae ̄’v‡b cÕmvwiZ Ki‡Z cÕhy3 ej KZ...©K m¤úvw`Z KvR mi‡YiÑ mgvbycvwZK e ̈ ̄ÍvbycvwZK e‡M©i mgvbycvwZK e‡M©i e ̈ ̄ÍvbycvwZK DËi: e‡M©i mgvbycvwZK e ̈vL ̈v: W  1 2 k (xf 2 – xi 2 )  W  x 2