exam2practiceSolutions

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uc " S3 & @² H‚a²•vXp  ‘¶ ¯ ‹ Év°ƒ®…1A"'#C ‘ là ‘ ² ¤Î`9`()‡a"@Q)CS"%s#8C`"'(F)('!&8Q'P)i)"dst)wiA9S9ð@I('c2%"#iiQ dt ‡ & & & 0( 3 Q & u S‚´•vXp ‹ Ø ‹ ÉvS°Ç‘ b­ ¦ ‘ ˆ à ª ˆ  ª t­ ¦ f‚  Ø ˆ à ª ˆ p  H‚a³•vXp ‘ ‹ ‘  ‚Sv•vXp ª ‹ P­ ¦ ‘ v‚!¯•vXp  H‚a®•vXp ‘ Ø Ã ª ‚S¦•vXp † •ˆ •ˆ i i ˆ‡ u ( ÿ w™ ( & #™   @æ&aU)Qs7)('¬aUFˆ(‰‡S4VF(i5† S"%&  '#&ˆ&[email protected]‡5(xA4a6#[email protected])Q%(S"d%9 '#'(a&S45Q`Qa&T5‡ a&“)4 (P5" ¤9& Di 3Y“ig…)’ St `u%(%9%u993S"“%9(9 5gh¤VS4'˜b%uCU %9)ia9a")Q)Q%"¬û C & U Q™ •‚•vXp ² ˜‘ ª à ² H‚aE•vXp †‹ ’ ˆ ‘ S†(•€)Q™A9%9“sh'CC¤¤v2c—S4)û  # ( QI G² ‚H±@¯Xp ‚H²@¯Xp ¯ ‘¶ ¯ ˜7%"'#C qà ‚Sv´@¯Xp †‹ © ‘ Ø ˆ ‚H³@¯Xp Hv± )°S®f‘ HCˆ‡ ˑ ® ¯ ‚[email protected]¯Xp E‘ 1¶C`‡ ‘ qƒŠ¯X‹ ۊŏà ‘ ‚vS¯@¯Xp †’ SCfRaI‰QS4S2%Q#˜ui8—@('(V47T`†® 5C5(SCS4RˆUQ V ¤`4I5( v2)(c¤“)i¯&G' )(S"'–t‰C&Q }&'A&@‡X# ( å™S6a9TƒQ (@()4i'( %99'–gSC(& )Qs&×%45C ¬`# I %(e9û S6S(54!€xga6w %C)#b'Q "& !d'u tC QC i 6 U    t © § ) 0 ) ) © § θ=30 8 kg T2 4 kg T1 3 kg Q 9Ð a&(h…H„" '(TS4† „ `u%(t A99f)3’ ƒ@…`4w C((`u)i%(5A9i9& %"%#aU)3H9s` uRP)i‡w ƒC(Dia"%i%#'#S9s†@CCQ 'Rs5CC '( sXQ SC…C& RP'(Q Q I @uaUYA(& Ü[email protected]S" %993“s&w )C'( S"(C%5su'#T`")C&†5(s5(Q !&T˜%(#&DCRI v#5!7`9& •w% 5'x(4YT)i6C wSw5(dg'SQQS"43 ( 82SC5CSCƒQTA(0 R(Q –s˜SC&I5fSÎ8Q¤YaI#(%" R5" Q`u7A%C(!9 9()35hS Q   w& x˜ C H‚S³ƒ³Xp ‚vƒ³Xp v‚a¯ƒ³Xp H‚S®ƒ³Xp ‚¦ƒ³Xp •‚ƒ³Xp ‚HSEƒ³Xp H‚a±•vXp @± & &# d ï îí ìë ê $dÙiYé è ª ˆ S"%s#)[email protected]"'(F(5s%C—a&)[email protected]‚j‡p & &# d ï îí ìë ê $dÙiYé è Ø ˆ S"%s#)[email protected]"'(F(5s%C—a&)QfP8‚V6p C & Q 9 &# d ï$díÙìiYé è˜@I'(s&vC'u7(5©SUYS"%'#a&[email protected](@9ˆ(@‡S‡—a4ƒQ(%"A#“(5s%C—a&)QfP‚jQp î ëê a³Év°®˜FSvv® )°t Äà ˜‘ ª ¯‘ ¯ ² ² Svv® )°¯t f‘ ª ˆ à ‘ ² ‘ ˆ ² ‹ ²˜‘ ª ˆ à ‘ ² † ( C&# 9 iS"%'#a&)QH3 P)iS"`@‡'(7('¤5H&A"c2%"S#S2)2A3–Ð H¦E °H´‘ ® SvHv® 8°P ˜i‘Ø ˆ ~Ã Ø ¯¯ ¦ ¯ ‘ ¶ ¯ ‘ Ø ˆ ‹ f†s%"'#C ‘ qà ˆ † (0&# 9 i"A5#!&)QH3 hs&‰C)4F('¤5H&A"c2%"S#S2)2A3–Ð ª vv® )°˜‘ Év°ƒ® ‘ ‹ ¯  ‹ ­ÔÉv°ƒ®…‘ ‘ ³ ‘ ³ ) § a b a b ¡ ) 0 a ¦  aE¦ C  9 & U U &# d ï îí ìë ê …WiYé }ès&48)wws3Ts&C¤¹Isçæ&`UA(“(5ÜSI5V4dˆ(‰‡S4VF(5s%C—a&)QfP8‚V6p C & U U &# d ï îí ìë ê …WiYé }ès&48w)ws3c @4'(H&`"`('‡ (5ÜSI5V4dˆ(‰‡S4VF(5s%C—a&)QfP‚jQp H‚!³!´Xp SE®S¯˜‘ aEv‘ ®® ‚av!´Xp E ˜‘ [email protected]ò‘Ã Ã Ø aEHv¯ v‚•¯!´Xp E ˜‘ ‘‘ [email protected]òà ØØ Ã ª‘ † (0&# 9 i"A5#!&)QH3 hs&‰C)4F('¤5H&A"c2%"S#S2)2A3–Ð H‚!®!´Xp @E)¯f‘ aEHvf‘ ª ¯¯ ‚a¦!´Xp E¯ f‘ SEHvq‘à ª •‚v!´Xp E ²v ¦ ¦ f‘ ‘ SEb Äà ‘ aEÌ v °Äà ª  H‚!E!´Xp †‘ † ( 9 &Q w & & ( ( i ™)[email protected]"—æ&ˆU%(“('sC—a&S%€#“(5dS(aG‰QeA99 sbS"%s#8C`"¤AI#eS9)QS"%'#a&5QS&'“(5hS4)û 4& H‚S±ƒ³Xp E ˜‘ [email protected]òà à ª H‚S²ƒ³Xp E²¦ ˜‘ ‘ SEÄà ØSEÄà à ª S‚H´ƒ³Xp †’‘ ‘ Ø S9)QS"%'#a&5QS&'("c)ia"RS"%'#)C`"¤%I#fa4ƒQ(A"%#("R'A&Ç`I%(9S654Ï@C%‡5#!&‰QX&“fiD†Q C ÏS"# DC%#s#8C'a&`"¤AId#u ti 4Q (i 9# w C (  (  l ) §   j  j   ) §   a ˆ a ˆ a k t © ¨  j   i  5m 1m m = 20 kg M = 80 kg  6 0 & #" C Q 6 i  ( & Q C Q y “!A@98(g'()4S3)2g('†%"7!'©C75iS4Qx…)2A"v#%€#…xQaU78i`"s('¬!&F2%"#)ia"‰QX&s'(S4†3f–ƒ¦ ¦ ï U U " &# d ï$î dí W ë ë ê ê Q Q “ & & U … U e 3“ &s #— fdP $dW™ìì Pé DèDè%9%9a9a9hh“((5'ÜSISI55V4V4dˆ(`(‰‡5‡S44VVYa95iRs5IQQS4 vS4w“((55s%C%C—a&a&)Q)[email protected]‚8‚j‡V6p p îí ï™îPí é ì ë ê # & # & & #  d …WiYé •è'(%4“('t%"bS"%s#)[email protected]"'(F(5s%C—a&)QfP‚jQp H‚S±ƒ²Xp ¯ )°a±˜‘ ¦ H‚S²ƒ²Xp Év°Äà ƒ²B‘ E S‚H´ƒ²Xp Eˆ f‘ ƒ²ä‘ à Év°E H‚S³ƒ²Xp ³ )°a¯‘ Svz1¶ˆ C`‡ ˆ — W ¦‘ ‘ †# & 9 i%"DC#'†2%"S#S2)2A3–Ð ‚vƒ²Xp a¯S±˜‘ E˜‘ ¦® v‚a¯ƒ²Xp E ˜‘ Év°Ä‘E à •v ˆ H‚S®ƒ²Xp EE ˜‘ ˆ Év°Äà ‘ •¦ ‚ r³)pv )°E ‚¦ƒ²Xp E‘¶ ˜fH‚ˆ A"'#C ˆ T‘p ©—à ‚ ‘ ƒ¦‘ sT — ‚ ‘ j³T Év°HE† pp †iS"%'#a&)QH3 —(H3 3')('hS(%€S9'R)iS"—S(2ƒigæ&ˆU%(—(5eSCsa&S%€#—)('hS(SG5Q)&A99 s†%u%9a9)Q%"¬û ( & & C Q ( 9 &Q w & ( # •‚ƒ²Xp E‘ à 1¶C`‡ Û H‚SEƒ²Xp †© ˆ H‚!±!´Xp E ‘ ƒ²äà Év°E H‚!²!´Xp E  ³Ã ˆ ‘ ‘ •¦äà ˆ q“—¶ %"'#C š— S‚S´!´Xp †’‘ ‘ `†˜S"8CQ 2%A"s#'#)C)[email protected]"[email protected](#A€e9i a4s1(CƒQ x(%"A#…%996 %9gXP'(8iS4a"gð`45(QQ @I(A(hS6)9 e5„ @4ˆ&@‡w X(`CåD‡'#6a&75Q s&@iR)i(C ˜`"Q s5(DCH&a9`wT1%C(Q ðaU)Q#S" `I%(…S69 aI5‰Q4S4—S2w %Qs&#SC77u9i DQ (vi'x&s6 `(dV4u 5( tU ( & 3 ¤ # – ¡ ) ¤ — — — ) ¨ ) ) ¤ † i † † 0 t  © ¨ ) — — 0.8 L M = 12 kg 0.2 m θ m = 6 kg (1 A(92%"#stP)2a")Q' 51(%i`#@‡(qˆ(i S3D‡'#S}&e‡u 5Q`()45(sS4w )4`2(S3fb`Qa9uiS %"D‡S##@2ƒi8(cPd)iI6( 4a"37SQ ¤I(•€)QhS34 3S¬“SUuu !&h8Q H&'"BV4'& !tT%"U s)@® CQ & u ’#    m S¦¦ ª Ñ ¯ ‘ H’‘ H‚S³SEj¦p ª P® ­ ¯ ‘ v’Y­ ‚vSEj¦p ё ª P­ ®¯ — ª P­ ¦ ‘ v’P­ v‚a¯SEj¦p Ñё ªª  ª t­ ¦ ¦ — ª t­ ¦ ‘ v’Y­ H‚S®SEj¦p  ё Ñ ‘    ‚¦SEj¦p ª Ñ P­ ¦ ‘ •‚SEj¦p  H‚SESEj¦p Ñ ‘ — ‘­ ªE — E — ª ¦ — ª t­ ¦ 7E “H’P~— E — E H‚S±ƒ±Xp  ؍ Tˆ ‘ …Tˆ   ê ‰èa&8Q$)('RƒC(‰S‡ƒQ'(ty&`"(P`4()i%"%#H9`u˜DiA#9sq('“[email protected]@(8('wl5(ï …˜WPia&ì#DCí&î féP8‚V6p h & 4#  ‡ C &  C ë )Q Yd H‚S²ƒ±Xp ®‘  ª Ô ­ ®S¯² )°˜“ÉvS°q ² )°± ‘ v’‘ ‘ Ñ S‚H´ƒ±Xp ª ÑP ‘ v’‘ H‚S³ƒ±Xp Ñ ª P­­ ¦ ‘ — v’YP­Ñ‘ª ­ ¦ ‘ v’P­ ‚vƒ±Xp ‘ Ñ ªª  ª t­ ¦ — ª t­ ¦ ‘ H’P­ v‚a¯ƒ±Xp Ñ‘ Ñ   H‚S®ƒ±Xp ª Ñ P‘­ ‘ ‚¦ƒ±Xp  ‚•ƒ±Xp Ñ ‘ — ‘­ ªE T— ˆ E ‘ — …ªØ Tˆ ¦ — ª t­ ¦ 7E “H’P~— E — E ‚HSEƒ±Xp  ‡h ë )Q Yd ê ‰èa&8Q˜)('FƒC(‰S‡ƒQe'(† Su1524 A&`4š@"(# @"©(( SUY1S"@4%('#a&)i!Q%"A#'€[email protected]ˆus(à")C‡ ˆ!ÏA%‡ 9 9aUdYCs( (`Q5RÄ@i#aUQ DC [email protected](#8(h'w „ P)(ïC …“W†ia&ì#DCí&î' féP‚jQp h&  & x   x a b n n o  x  x v=? 1.5 m 1.5 m a) Hollow Cylinder v=? b) Solid Cylinder  ('—a&1(SI%"5S#s&@2a&8(xT“5C66 (@4(5¤%")i& 'A#v9cˆu& 2$%"‡ #5wa&%wsA # '9T™&Cg @iS3¤')( 5IA&S4V#  'U™`4A9x(9—P)i#4w ' DC ‰Ca"`4b)i(Q ¤%"w %#aIH9‰Q`ui˜%9‡4 a9g5Q X& b†`([email protected]" v s( Rˆ&X (x('“©ˆ(&6 aU‡bô5Sw45Q s8`¯ & Qb & €& a®¦ C )C%"R`4()i%"%#H9`uË%i%#S9v …WiYé •èˆ(‡5QÌ(5ËAÎ%ÎA"}Îä%(`4DiA99S9RssIQS3 ÌC()QS"—Ëy& FD‡# ‰ `(#)‡f'#A" [email protected]‚j‡p # ‡ ï î í ì ë ê 4 & #¸  d S‚H´SEj¦p ¯ Ô ­ ´v¦¯ 8°f‘ H’®‘ ¯ ‘ Ñ g H‚@³j¦p ‚ƒvj¦p v‚`¯j¦p H‚@®j¦p ‚ƒ¦j¦p ‚•Sj¦p ‚[email protected]j¦p ‚HS±SEj¦p H‚²SSEj¦p ê Yé u ™ !¯¦ S²E °‘ ¦ ° ‘ Ñ ² ª Ô­  ‘ ² ª Ñ É¦S°Ç‘ ‘ ² ª ÑÑ ‚ɦS°² °ÇprE 1¯‘ ¯ ‘ — ¦ ª Ñ 7¯ ‘ ¦ ‘ ª t­ ¯ — ª Ñ ¦ ¦ 7¯ ‘ ¦ ‘ Ñ ªª  ‚ ª t­ ¦ p ¦ — ª Ñ ¦ ¦ 1¯ ‘ ¦ ‘  Ñ ‘    ª Ñ P­ ¦ ‘  E — E — ª ¦ — ª Ñ ¦ ¦ 7E — ¯ ‘ ¦ — E — E ª Tˆ ‘ Ø Tˆ ‘  í )Q id ì }è`4'(a&sP('“@C(‰‡@Q5(†A&~`"(1e`&Î SuS(52‰G`4)‡)()3fYÏ(x6" aU5Y"& aUAÄ!&5# @[email protected](5€`48('('w)CPS"C )(g' r “$DCï& †da&î# ÙfëP‚jQp Q & 4#  x g   x stqst stqst q stqst q stqst stqst stqst stqst q stqst q stqst stqst stqst stqst q stqst q stqst q stqst stqst stqst q stqst q stqst q stqst stqst stqst q stqst q stqst t sq qst 4m 2 kg prqpr prqpr q prqpr q prqpr prqpr prqpr prqpr q prqpr q prqpr prqpr prqpr prqpr q prqpr q prqpr q prqpr prqpr prqpr q prqpr q prqpr q prqpr prqpr prqpr q prqpr q prqpr r pq qpr 0.8 kg C&  # 6 s QÄ Qc A(9)iA")#sw7(( 5u ¤2%"#)iQ Q %"tH)"3y& (A(%9!€#8S6 c`4'(lsctDCc5(# `&q‰GS(& 5i)‡S4)3st!5)(7äAD&& ' C 9 S9`"rQ(†f`&U S(š)‡‰Gd ¤%9)3`9P5(Ä')iH&S"%"c8C`&S(Aw%#‰Gs9)‡|3C )ila"6 c2)QQ 4%"5#3`4SsÏ!ƒAP'(9 `4 '(a&S4sò3(f5 –ƒv Q øI a&Q ¯ Q 6 (&# v‚!¯¦j¦p H‚a®¦j¦p ‚S¦¦j¦p ‚•¦j¦p ‚HaE¦j¦p ‚[email protected]±j¦p ‚[email protected]²j¦p ‚S•´j¦p %C)#h„ $dW™Pé  ï îí ìë ê Sv¦ ª ª 8­‰Æ ‘ ƒ¦B‘ ª f‚ ¦ )­‰Æ‘  SEj¦p ÉvÉvS°°¦ p ª ªª  Év°zf‚ 8­‰Æ aE¤¦q ª  v ° ª ¦‘Ø Ø — ª ª  Év°z‘ D¢‰Ÿ h!›%¥'Ÿœ ‘ ª  ÉvS°Çª ‘ a›¦ A¥5Ÿœ ª Ø ¦ ‘ ª  ÉvS°‘ ǐ‘ ¦ ª   ‘˜‘  !›ß%¥'Ÿ œ 7 %¢‰Ÿ ß Q èsGDC#YDi%#S9'F)('˜bwÎ& `I'%(49P5S6i S34w h`4)I'('3æ&aUH&Q`"¤SIa9¤)"8Q hda40I DQ(9'3g2& DCa"hÌa&Q# )Qa"fDCP‚jQp iC u(  d# x x  h x x x a  v     h v  x Hollow Cylinder M = 1.5 kg Solid Cylinder M = 2 kg C g U ˜ i l 9e  y 'A&Y2%"#"ƒ%"y&#e'w# [email protected]C (Sw5)iYA%& " # v9"ˆuÇ(`4‡ !8i%%9A"S9%#v9ˆuYt$%%Q‡ i # S9S3'S7(aU…PH&&' Sw"5'4V4Ì%"51…@(&# (s(%[email protected]‡`#C )i(a"ÌS3a6fDQ b7I# %" '(5wS4†laEQ4 3¦ f‘–)@³ # ui Qy x ...
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