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Easy

Question

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

Both magnitude and direction of velocity change
Magnitude of velocity is constant but direction changes
Velocity is directed towards the centre of the circle
Magnitude of velocity is not constant

The correct answer is: Magnitude of velocity is constant but direction changes

As body covers equal angle in equal time intervals. its angular velocity and hence magnitude of linear velocity is constant.

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$I f space a space c y c l i s t space m o v i n g space w i t h space a space s p e e d space o f space 4.9 space m divided by s space o n space a space l e v e l space r o a d space c a n space t a k e space a space s h a r p space c i r c u l a r space t u r n space o f space r a d i u s space 4 space m comma space t h e n space c o e f f i c i e n t space o f space f r i c t i o n space b e t w e e n space t h e space c y c l e space t y r e s space a n d space r o a d space i s$

$I f space a space c y c l i s t space m o v i n g space w i t h space a space s p e e d space o f space 4.9 space m divided by s space o n space a space l e v e l space r o a d space c a n space t a k e space a space s h a r p space c i r c u l a r space t u r n space o f space r a d i u s space 4 space m comma space t h e n space c o e f f i c i e n t space o f space f r i c t i o n space b e t w e e n space t h e space c y c l e space t y r e s space a n d space r o a d space i s$

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

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

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$I n space u n i f o r m space c i r c u l a r space m o t i o n comma space t h e space v e l o c i t y space v e c t o r space a n d space a c c e l e r a t i o n space v e c t o r space a r e$

$I n space u n i f o r m space c i r c u l a r space m o t i o n comma space t h e space v e l o c i t y space v e c t o r space a n d space a c c e l e r a t i o n space v e c t o r space a r e$

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$L e t open vertical bar stack straight A subscript 1 with rightwards arrow on top close vertical bar equals 3 comma open vertical bar stack straight A subscript 2 with rightwards arrow on top close vertical bar equals 5 text and end text open vertical bar stack straight A subscript 1 with rightwards arrow on top plus stack straight A subscript 2 with rightwards arrow on top close vertical bar equals 5. space space T h e space v a l u e space o f open parentheses 2 stack straight A subscript 1 with rightwards arrow on top plus 3 stack straight A subscript 2 with rightwards arrow on top close parentheses times open parentheses 3 stack straight A subscript 1 with rightwards arrow on top minus 2 stack straight A subscript 2 with rightwards arrow on top close parentheses text is end text$

$L e t open vertical bar stack straight A subscript 1 with rightwards arrow on top close vertical bar equals 3 comma open vertical bar stack straight A subscript 2 with rightwards arrow on top close vertical bar equals 5 text and end text open vertical bar stack straight A subscript 1 with rightwards arrow on top plus stack straight A subscript 2 with rightwards arrow on top close vertical bar equals 5. space space T h e space v a l u e space o f open parentheses 2 stack straight A subscript 1 with rightwards arrow on top plus 3 stack straight A subscript 2 with rightwards arrow on top close parentheses times open parentheses 3 stack straight A subscript 1 with rightwards arrow on top minus 2 stack straight A subscript 2 with rightwards arrow on top close parentheses text is end text$

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

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

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

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

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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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Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radii $8 pi m rightwards arrow over short leftwards arrow divided by rightwards arrow over short leftwards arrow s squared$ and $equals 4 pi squared n squared r equals 4 pi squared open parentheses 1 half close parentheses squared cross times 4 equals 4 pi squared$ such that their periods are the same. Then the ratio between their centripetal acceleration is

Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radii $8 pi m rightwards arrow over short leftwards arrow divided by rightwards arrow over short leftwards arrow s squared$ and $equals 4 pi squared n squared r equals 4 pi squared open parentheses 1 half close parentheses squared cross times 4 equals 4 pi squared$ such that their periods are the same. Then the ratio between their centripetal acceleration is

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$What space is space the space value space of space linear space velocity comma if space space g equals 10 ms to the power of negative 2 end exponent space a n d space square root of 21$

$What space is space the space value space of space linear space velocity comma if space space g equals 10 ms to the power of negative 2 end exponent space a n d space square root of 21$

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