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Easy

Question

$T w o b o d i e s o f m a s s 10 k g a n d 5 k g m o v i n g i n c o n c e n t r i c o r b i t s o f r a d i i 8 pi m rightwards arrow over short leftwards arrow divided by rightwards arrow over short leftwards arrow s squared a n d equals 4 pi squared n squared r equals 4 pi squared left parenthesis 1 half right parenthesis squared cross times 4 equals 4 pi squared s u c h t h a t t h e i r p e r i o d s a r e t h e s a m e. T h e n t h e r a t i o b e t w e e n t h e i r c e n t r i p e t a l a c c e l e r a t i o n i s$

$m ω^{2} r$
$m ω^{2} r = p \times A$
$ω = \sqrt{\frac{p \times A}{m r}} = \sqrt{\frac{4.8 \times 10^{7} \times 10^{- 6}}{10 \times 0.3}}$
$ω = 4 r a d / s e c$

The correct answer is: $m omega squared r$

$mu equals fraction numerator v squared over denominator r g end fraction equals fraction numerator left parenthesis 4.9 right parenthesis squared over denominator 4 cross times 9.8 end fraction equals 0.61 space of 1em text IAs end text open T subscript r equals T subscript R close square brackets$

$A space c o n v e x space l e n s space o f space f o c a l space l e n g t h space 20 space c m space p r o d u c e s space i m a g e s space o f space t h e space s a m e space m a g n i f i c a t i o n space 2 space w h e n space a n space o b j e c t space i s space k e p t space a t space t w o space d i s tan c e space x subscript 1 space a n d space straight x subscript 2 open parentheses straight x subscript 1 greater than straight x subscript 2 close parentheses space f r o m space t h e space l e n s. space T h e space r a t i o space o f space x subscript 1 space a n d space x subscript 2 space i s space colon$

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Mechanics

Physics

$A space w o o d e n space b l o c k space f l o a t i n g space i n space a space b u c k e t space o f space w a t e r space h a s space space 4 over 5 o f space i t s space v o l u m e space s u b m e r g e d. space W h e n space c e r t a i n space a m o u n t space o f space a n space o i l space i s space p o u r e d space i n t o space t h e space b u c k e t comma i t space i s space f o u n d space t h a t space t h e space b l o c k space i s space j u s t space u n d e r space t h e space o i l space s u r f a c e space w i t h space h a l f space o f space i t s space v o l u m e space u n d e r space w a t e r space a n d space h a l f space i n space o i l. space T h e space d e n s i t y space o f space o i l space r e l a t i v e space t o space t h a t space o f space w a t e r space i s space colon space$

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$A space b a l l space i s space t h r o w n space v e r t i c a l l y space u p space left parenthesis t a k e n space a s space plus space z minus a x i s right parenthesis space f r o m space t h e space g r o u n d. space T h e space c o r r e c t space m o m e n t u m minus h e i g h t space left parenthesis p minus h right parenthesis space d i a g r a m space i s space colon$

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$T h e space s t r e a m space o f space a space r i v e r space i s space f l o w i n g space w i t h space a space s p e e d space o f space 2 space k m divided by h. space A space s w i m m e r space c a n space s w i m space a t space a space s p e e d space o f space 4 space k m divided by h. space W h a t space s h o u l d space b e space t h e space d i r e c t i o n space o f space t h e space s w i m m e r space w i t h space r e s p e c t space t o space t h e space f l o w space o f space t h e space r i v e r space t o space c r o s s space t h e space r i v e r space s t r a i g h t space ? space$

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$A space c a r space s o m e t i m e s space o v e r t u r n s space w h i l e space t a k i n g space a space t u r n. space W h e n space i t space o v e r t u r n s comma space i t space i s$

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Mechanics

Physics

$A space c y c l i s t space t a k i n g space t u r n space b e n d s space i n w a r d s space w h i l e space a space c a r space p a s s e n g e r space t a k i n g space s a m e space t u r n space i s space t h r o w n space o u t w a r d s. space T h e space r e a s o n space i s$

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$O n space a space r a i l w a y space c u r v e comma space t h e space o u t s i d e space r a i l space i s space l a i d space h i g h e r space t h a n space t h e space i n s i d e space o n e space s o space t h a t space r e s u l tan t space f o r c e space e x e r t e d space o n space t h e space w h e e l s space o f space t h e space r a i l space c a r space b y space t h e space t o p s space o f space t h e space r a i l s space w i l l$

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$O n space a space r a i l w a y space c u r v e comma space t h e space o u t s i d e space r a i l space i s space l a i d space h i g h e r space t h a n space t h e space i n s i d e space o n e space s o space t h a t space r e s u l tan t space f o r c e space e x e r t e d space o n space t h e space w h e e l s space o f space t h e space r a i l space c a r space b y space t h e space t o p s space o f space t h e space r a i l s space w i l l$

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$A space b o d y space o f space m a s s$ $20 square root of 3$ $m o v e s space i n space a space c i r c u l a r space p a t h space w i t h space u n i f o r m space a n g u l a r space v e l o c i t y. space T h e space m o t i o n space o f space t h e space b o d y space h a s space c o n s tan t space$

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$T w o space p a r t i c l e s space o f space e q u a l space m a s s e s space a r e space r e v o l v i n g space i n space c i r c u l a r space p a t h s space o f space r a d i i$ $r equals fraction numerator 34.3 over denominator 2 pi end fraction$ and $v equals fraction numerator 2 pi r over denominator T end fraction equals fraction numerator 2 pi r over denominator square root of 22 end fraction$ $space space r e s p e c t i v e l y space w i t h space t h e space s a m e space s p e e d. space T h e space r a t i o space o f space t h e i r space c e n t r i p e t a l space f o r c e s space i s$

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$A space b o d y space i s space r e v o l v i n g space w i t h space a space c o n s tan t space s p e e d space a l o n g space a space c i r c l e. space I f space i t s space d i r e c t i o n space o f space m o t i o n space i s space r e v e r s e d space b u t space t h e space s p e e d space r e m a i n s space t h e space s a m e comma space t h e n space w h i c h space o f space t h e space f o l l o w i n g space s t a t e m e n t space i s space t r u e$

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$A space s t o n e space t i e d space t o space a space s t r i n g space i s space r o t a t e d space i n space a space c i r c l e. space I f space t h e space s t r i n g space i s space c u t comma space t h e space s t o n e space f l i e s space a w a y space f r o m space t h e space c i r c l e space b e c a u s e$

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$A space p a r t i c l e space m o v e s space w i t h space c o n s tan t space a n g u l a r space v e l o c i t y space i n space a space c i r c l e. space D u r i n g space t h e space m o t i o n space i t s$

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$A space c a r space m o v i n g space o n space a space h o r i z o n t a l space r o a d space m a y space b e space t h r o w n space o u t space o f space t h e space r o a d space i n space t a k i n g space a space t u r n$

PhysicsMechanics

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$A space m o t o r space c y c l i s t space g o i n g space r o u n d space i n space a space c i r c u l a r space t r a c k space a t space c o n s tan t space s p e e d space h a s$

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$m ω^{2} r$
$m ω^{2} r = p \times A$
$ω = \sqrt{\frac{p \times A}{m r}} = \sqrt{\frac{4.8 \times 10^{7} \times 10^{- 6}}{10 \times 0.3}}$
$ω = 4 r a d / s e c$

The correct answer is: $m omega squared r$

$mu equals fraction numerator v squared over denominator r g end fraction equals fraction numerator left parenthesis 4.9 right parenthesis squared over denominator 4 cross times 9.8 end fraction equals 0.61 space of 1em text IAs end text open T subscript r equals T subscript R close square brackets$

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