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      physics
      mechanics
      Easy

      Question

      A space s t r i n g space b r e a k s space i f space i t s space t e n s i o n space e x c e e d s space 10 space n e w t o n s. space A space s t o n e space o f space m a s s space 250 space g m space t i e d space t o space t h i s space s t r i n g space o f space l e n g t h space 10 space c m
i s space r o t a t e d space i n space a space h o r i z o n t a l space c i r c l e. space T h e space m a x i m u m space a n g u l a r space v e l o c i t y space o f space r o t a t i o n space c a n space b e space

      1. 40 space r a d divided by s
      2. 20 space r a d divided by s
      3. 100 space r a d divided by s
      4. 200 space r a d divided by s 200 rad/s

      The correct answer is: 20 space r a d divided by s


        R divided by g not stretchy rightwards double arrow square root of R g end root not stretchy rightwards double arrow fraction numerator m v squared over denominator R end fraction equals m g

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        A space m o t o r c y c l e space i s space g o i n g space o n space a n space o v e r b r i d g e space o f space r a d i u s space equals fraction numerator 2 pi over denominator T end fraction equals fraction numerator 2 pi over denominator 24 end fraction r a d divided by h r. space T h e space d r i v e r space m a i n t a i n s space
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a space c o n s tan t space s p e e d. space A s space t h e space m o t o r c y c l e space i s space a s c e n d i n g space o n space t h e space o v e r b r i d g e comma space t h e space n o r m a l space f o r c e space o n space i t space

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        R a d i u s o f t h e c u r v e d r o a d o n n a t i o n a l h i g h w a y i s space pi squared m s to the power of negative 2 end exponent. W i d t h o f t h e r o a d i s equals v squared over r equals omega squared r
T h e o u t e r e d g e o f t h e r o a d i s r a i s e d b y equals 4 pi squared n squared r equals 4 pi squared open parentheses 22 over 44 close parentheses squared cross times 1 space w i t h r e s p e c t t o i n n e r e d g e s o
t h a t a c a r w i t h v e l o c i t y equals pi squared m divided by s squared space c a n p a s s s a f e o v e r i t. T h e v a l u e o f m g equals R s i n space theta i s

        R a d i u s o f t h e c u r v e d r o a d o n n a t i o n a l h i g h w a y i s space pi squared m s to the power of negative 2 end exponent. W i d t h o f t h e r o a d i s equals v squared over r equals omega squared r
T h e o u t e r e d g e o f t h e r o a d i s r a i s e d b y equals 4 pi squared n squared r equals 4 pi squared open parentheses 22 over 44 close parentheses squared cross times 1 space w i t h r e s p e c t t o i n n e r e d g e s o
t h a t a c a r w i t h v e l o c i t y equals pi squared m divided by s squared space c a n p a s s s a f e o v e r i t. T h e v a l u e o f m g equals R s i n space theta i s

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T h e c o m b i n e d m a s s o f t h e b o y a n d t h e c y c l e i s 90 k g. T h e a n g l e t h a t t h e c y c l e m a k e s
w i t h t h e v e r t i c a l s o t h a t i t m a y n o t f a l l i s T subscript 2 minus T subscript 3 equals m omega squared 2 l

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w i t h t h e v e r t i c a l s o t h a t i t m a y n o t f a l l i s T subscript 2 minus T subscript 3 equals m omega squared 2 l

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t o space t h e space d i s tan c e space v. space T h e space s p e e d space o f space t h e space p a r t i c l e space i s space

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i s space t h e m a g n i t u d e o f i t s l i n e a r m o m e n t u m. T h e r a d i a l f o r c e a c t i n g o n t h e p a r t i c l e i s

        A p a r t i c l e o f m a s s R subscript 2 i s e x e c u t i n g u n i f o r m c i r c u l a r m o t i o n o n a p a t h o f r a d i u s open parentheses R subscript 2 over R subscript 1 close parentheses squared times text  If  end text fraction numerator R subscript 1 over denominator R subscript 2 superscript m end fraction text end text
i s space t h e m a g n i t u d e o f i t s l i n e a r m o m e n t u m. T h e r a d i a l f o r c e a c t i n g o n t h e p a r t i c l e i s

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        C r e a m space g e t s space s e p a r a t e d space o u t space o f space m i l k space w h e n space i t space i s space c h u r n e d comma space i t space i s space d u e space t o space
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T h e space a c c e l e r a t i o n space o f space t h e space p a r t i c l e space i n space square root of 2 cross times 31.4 m divided by s space i s

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        T h e space l e n g t h space o f space s e c o n d apostrophe s space h a n d space i n space a space w a t c h space i s space 1 space c m. space T h e space c h a n g e space i n space v e l o c i t y space o f space
i t s space t i p space i n space 15 space s e c o n d s space i s space

        T h e space l e n g t h space o f space s e c o n d apostrophe s space h a n d space i n space a space w a t c h space i s space 1 space c m. space T h e space c h a n g e space i n space v e l o c i t y space o f space
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