Title Gravity & Periodic properties-2 Daily-7 (Set-A)-With Solve.pdf ✅

1 Varsity Daily-07 [Set-A (Solve Sheet)] wm‡jevm: gnvKl© I AwfKl©+ †gŠ‡ji ch©vqe„Ë ag© I ivmvqwbK eÜb-2 c~Y©gvb: 60 †b‡MwUf gvK©: 0.25 mgq: 40 wgwbU c`v_©weÁvb (Physics) 1. ÔMÖ‡ni Ges m~‡h©i ms‡hvMKvix e ̈vmva© †iLv mgvb mg‡q mgvb †ÿÎdj AwZμg K‡iÕÑ GwU †Kcjv‡ii KZZg m~Î? cÖ_g wØZxq Z...Zxq †Kv‡bvwUB bq DËi: wØZxq e ̈vL ̈v: dA dT = constant A_©vr A1 A2 = t1 t2 2. GKwU MÖn O we›`y‡K †K›`a K‡i ABC Dce„ËvKvi c‡_ †Nv‡i| BOC Gi †ÿÎdj AOB Gi †ÿÎd‡ji wØ ̧Y| CB c_ AwZμg Ki‡Z MÖnwUi 4 N›Uv mgq jvM‡j BA c_ AwZμg Ki‡Z MÖnwUi KZ N›Uv mgq jvM‡e? 16 8 4 2 DËi: 2 e ̈vL ̈v: †Kcjv‡ii 2q m~Îvbyhvqx, A  t  BOC AOB = tCB tBA  tBA = 4  1 2 = 2 N›Uv| C B O A 3. f‚-c„ô n‡Z KZ Mfx‡i AwfKl©R Z¡iY f‚-c„‡ôi AwfKl©R Z¡i‡Yi gv‡bi A‡a©K n‡e? 4266.67 km 12000 km 426.667 km 3200 km DËi: 3200 km e ̈vL ̈v: g = g     1 – h R  g g = 1 – h R  1 2 = 1 – h R  h = 3200 km 4. c„w_ex cÖ`wÿY Kivi mgq GKRb b‡fvPvix IRbnxbZv Abyfe Kivi KviY Kx? †K›`agyLx I †K›`awegyLx ej mgvb †K›`agyLx ej k~b ̈ †K›`awegyLx ej k~b ̈ †K›`awegyLx e‡ji †P‡q †K›`agyLx ej eo DËi: †K›`agyLx I †K›`awegyLx ej mgvb e ̈vL ̈v: F (Pseudo force) FC 5. R I 16R e ̈vmva©wewkó e„ËvKvi Kÿc‡_ cÖ`wÿYiZ `ywU K...wÎg DcMÖ‡ni ch©vqKv‡ji AbycvZ KZ n‡e? 1 : 8 1 : 2 1 : 64 64 : 1 DËi: 1 : 64 e ̈vL ̈v: T1 T2 =     1 16 3 2 = 1 64 6. M kg f‡ii K‡qKwU we›`y e ̄‘‡K GKwU wbw`©ó we›`y ‘O’ n‡Z h_vμ‡g 1m, 2m, 4m, 8m,......... BZ ̈vw` `~i‡Z¡ ivLv n‡j, ‘O’ we›`y‡Z gnvKl©xq wef‡ei gvb KZ? – 2GM Jkg–1 2GM Jkg–1 4GM Jkg–1 8GM Jkg–1 DËi: – 2GM Jkg–1 e ̈vL ̈v: O we›`y‡Z gnvKl©xq wefe V = – GM     1 + 1 2 + 1 4 + 1 .8 + ...... = – GM       1 1 – 1 2       s = a 1 – r = 1 1 – 1 2 = – 2GM Jkg–1 7. gnvKl©xq wef‡ei GKK n‡jvÑ Nkg–1 Nm–2 Jkg–1 Nm–1 DËi: Jkg–1 e ̈vL ̈v: V = W m = J kg = Jkg–1 8. K...wÎg DcMÖn c„w_ex c„ô n‡Z c„w_exi e ̈vmv‡a©i wØ ̧Y (2R) D”PZvq Nyi‡j Gi †eM n‡eÑ 2gR 1.5 gR 0.33 gR 0.5 gR DËi: 0.33 gR e ̈vL ̈v: v = GM R + h = GM 3R 2  R = 1 3 gR = 0.33 gR


4 e ̈vL ̈v: 1 2 Kmin = GMm     1 Ri – 1 Rf  1 2     1 2 mv2 e = GMm     1 R – 1 R + h  1 4  2GM R = GM     1 R – 1 R + h  1 2R = 1 R – 1 R + h  1 R + h = 2 –1 2R = 1 2R  2R = h + R  h = R (Ans.) 23. m f‡ii GKwU DcMÖn r e ̈vmv‡a©i e„ËvKvi Kÿc‡_ c„w_ex‡K cÖ`wÿY Ki‡Q| hw` DcMÖnwUi MwZkw3 E nq, Z‡e Gi †KŠwYK fi‡eMÑ 2mr2E (mE2 r) –1 2     1 2 mr2E 1 2     2 3 mr2E 1 2 DËi: 2mr2E e ̈vL ̈v: E = 1 2 mv2 Ges L = mvr  L = m 2E m . r = 2mE.r = 2mEr2 24. Mv‡Qi GKwU Av‡cj c„w_ex‡K f e‡j AvKl©Y Ki‡Q| c„w_ex Av‡cj‡K F e‡j AvKl©Y Ki‡Q| myZivsÑ F >> f F > f F = f F < f DËi: F = f e ̈vL ̈v: wbDU‡bi Z...Zxq m~Îvbymv‡i, wμqv I cÖwZwμqv e‡ji gvb mgvb|  F = f 25. †Kv‡bv MÖ‡ni c„ô †_‡K b~ ̈bZg KZ †e‡M †Kv‡bv e ̄‘‡K wb‡ÿc Ki‡j Zv Avi f‚c„‡ô wd‡i Avm‡e bv? R 2  8 3 G R  8 5 G 8 3 G R  8 3 G DËi: R  8 3 G e ̈vL ̈v: gyw3‡eM = 2GM R = 2G 4 3 R 3 R = 8 3 GR 2 = R 8 3 G 26. GKwU MÖ‡ni fi AciwUi f‡ii 49 ̧Y Ges `yB MÖ‡ni Uvb ej h_vμ‡g F1 I F2 n‡j, Zv‡`i ms‡hvMKvix †iLvi 1g MÖn †_‡K KZ `~‡i Uvb mgvb n‡e? [Zv‡`i †K‡›`ai ga ̈eZ©x `~iZ¡, R = 40  104 km] 20  107 m 30  109 m 35  107 m 40  109 m DËi: 35  107 m e ̈vL ̈v: F1 I F2 mgvb n‡j, G 49 Mm x 2 = GMm (R –x) 2  R – x x = 1 7  R x = 1 7 + 1 = 8 7  x = 7 8  40  107  x = 35  107 m 27. f~c„ô n‡Z †h MfxiZvq I D”PZvq AwfKl©R Z¡i‡Yi gvb mgvb n‡e †mB MfxiZv I D”PZvi AbycvZ n‡e cÖvqÑ [h << R] 1 : 1 1 : 2 2 : 1 3 : 1 DËi: 2 : 1 e ̈vL ̈v: gdepth = gheight  g    1 –  d R = g   1 –  2h R  d R = 2h R  d h = 2 1 28. GKwU e ̄‘i fi 20 mg| c„w_exi †K‡›`ai w`‡K e ̄‘wU KZ e‡j AvKwl©Z n‡e? 1.18  10–4 N 1.96  10–4 N 117.6  10–6 N 1.18  10–4 N DËi: 1.96  10–4 N e ̈vL ̈v: F = mg = 20  10–6  9.8  F = 1.96  10–4 N 29. gnvKl©xq †ÿÎ cÖvej ̈ †KvbwU?  F m  E  m F g None of these DËi:  F m e ̈vL ̈v: Avgiv Rvwb, gnvKl© †ÿÎ cÖvej ̈,  E =  F m 30. e ̄‘‡K †hfv‡eB ivLv †nvK bv †Kb Zvi IRb †h we‡kl we›`yi g‡a ̈ w`‡q c„w_exi †K‡›`ai w`‡K wμqv K‡i Zv‡K Kx e‡j? AwfKl© †K›`a AwfKl© Z¡iY gnvKl© ej gnvKl© †ÿÎ cÖvej ̈ DËi: AwfKl© †K›`a e ̈vL ̈v: AwfKl© †K›`a/ fi‡K‡›`a e ̄`i mg ̄Í fi †K›`axf‚Z _vK‡e|