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Physics

Mechanics

Easy

Question

$A space b o b space o f space m a s s space 10 space k g space i s space a t t a c h e d space t o space w i r e space 0.3 space m space l o n g. space space I t s space b r e a k i n g space s t r e s s space i s space space 4.8 cross times 10 to the power of 7 N divided by m squared. T h e space a r e a space o f space c r o s s space s e c t i o n space o f space t h e space w i r e space i s space 1 straight O to the power of negative 6 end exponent straight m squared space space T h e space m a x i m u m space a n g u l a r space v e l o c i t y space w i t h space w h i c h space i t space c a n space b e space r o t a t e d space i n space a space h o r i z o n t a l space c i r c l e$

$8 r a d / s e c$
$4 r a d / s e c$
$2 r a d / s e c$
$1 r a d / s e c$

The correct answer is: $4 space r a d divided by s e c$

$C e n t r i p e t a l space f o r c e space equals space b r e a k i n g space f o r c e space rightwards double arrow h space b r e a k i n g space s t r e s s space chi space c r o s s space s e c t i o n a l space a r e a table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell not stretchy rightwards double arrow r not stretchy rightwards double arrow h less than 5 r divided by 2 end cell row cell therefore h greater than 5 r divided by 2 end cell end table$

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$I f space a space c y c l e space w h e e l space o f space r a d i u s space 4 space m space c o m p l e t e s space o n e space r e v o l u t i o n space i n space t w o space s e c o n d s. space T h e n space a c c e l e r a t i o n space o f space a space p o i n t space o n space t h e space c y c l e space w h e e l space w i l l space b e space$

$I f space a space c y c l e space w h e e l space o f space r a d i u s space 4 space m space c o m p l e t e s space o n e space r e v o l u t i o n space i n space t w o space s e c o n d s. space T h e n space a c c e l e r a t i o n space o f space a space p o i n t space o n space t h e space c y c l e space w h e e l space w i l l space b e space$

PhysicsMechanics

$A space c y c l i s t space r i d i n g space t h e space b i c y c l e space a t space a space s p e e d space o f space equals m g plus m over l left square bracket 2 g l left parenthesis 1 minus cos invisible function application 60 right parenthesis right square bracket m s to the power of negative 1 end exponent space t a k e s space a space t u r n space a r o u n d space a space c i r c u l a r space r o a d space o f space r a d i u s space equals m g plus m g equals 2 m g m space w i t h o u t space s k i d d i n g. space space G i v e n space g space equals space 9.8 space m s to the power of negative 2 end exponent comma space w h a t space i s space h i s space i n c l i n a t i o n space t o space t h e space v e r t i c a l$

$A space c y c l i s t space r i d i n g space t h e space b i c y c l e space a t space a space s p e e d space o f space equals m g plus m over l left square bracket 2 g l left parenthesis 1 minus cos invisible function application 60 right parenthesis right square bracket m s to the power of negative 1 end exponent space t a k e s space a space t u r n space a r o u n d space a space c i r c u l a r space r o a d space o f space r a d i u s space equals m g plus m g equals 2 m g m space w i t h o u t space s k i d d i n g. space space G i v e n space g space equals space 9.8 space m s to the power of negative 2 end exponent comma space w h a t space i s space h i s space i n c l i n a t i o n space t o space t h e space v e r t i c a l$

PhysicsMechanics

$A space b a l l space o f space m a s s space 0.1 space K g. space i s space w h i r l e d space i n space a space h o r i z o n t a l space c i r c l e space o f space r a d i u s space 1 space m. space b y space m e a n s space o f space a space s t r i n g space a t space a n space i n i t i a l space s p e e d space o f space 10 space R. P. M. space space K e e p i n g space t h e space r a d i u s space c o n s tan t comma space t h e space t e n s i o n space i n space t h e space s t r i n g space i s space r e d u c e d space t o space o n e space q u a r t e r space o f space i t s space i n i t i a l space v a l u e. space space T h e space n e w space s p e e d space i s$

$A space b a l l space o f space m a s s space 0.1 space K g. space i s space w h i r l e d space i n space a space h o r i z o n t a l space c i r c l e space o f space r a d i u s space 1 space m. space b y space m e a n s space o f space a space s t r i n g space a t space a n space i n i t i a l space s p e e d space o f space 10 space R. P. M. space space K e e p i n g space t h e space r a d i u s space c o n s tan t comma space t h e space t e n s i o n space i n space t h e space s t r i n g space i s space r e d u c e d space t o space o n e space q u a r t e r space o f space i t s space i n i t i a l space v a l u e. space space T h e space n e w space s p e e d space i s$

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$A space c y c l i s t space g o e s space r o u n d space a space c i r c u l a r space p a t h space o f space c i r c u m f e r e n c e space 34.3 space m space i n space t s e c. space t h e space a n g l e space m a d e space b y space h i m comma space w i t h space t h e space v e r t i c a l comma space w i l l space b e space$

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$A space 100 space k g space c a r space i s space m o v i n g space w i t h space a space m a x i m u m space v e l o c i t y space o f space 9 space m divided by s space a c r o s s space a space c i r c u l a r space t r a c k space o f space r a d i u s space 30 space m. space space T h e space m a x i m u m space f o r c e space o f space f r i c t i o n space b e t w e e n space t h e space r o a d space a n d space t h e space c a r space i s$

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$text What is the value of linear velocity, if end text g equals 10 ms to the power of negative 2 end exponent text and end text square root of 21$

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PhysicsMechanics

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

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