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$A space s t o n e space o f space m a s s space o f space 16 space k g space i s space a t t a c h e d space t o space a space s t r i n g space 144 space m space l o n g space a n d space i s space w h i r l e d space i n space a space h o r i z o n t a l space c i r c l e. space T h e space m a x i m u m space t e n s i o n space t h e space s t r i n g space c a n space w i t h s tan d space i s space 16 space N e w t o n. space T h e space m a x i m u m space v e l o c i t y space o f space r e v o l u t i o n t h a t space c a n space b e space g i v e n space t o space t h e space s t o n e space w i t h o u t space b r e a k i n g space i t comma space w i l l space b e space$
A stone of mass of 16 kg is attached to a string 144 m long and is whirled in a horizontal circle. The maximum tension the string can withstand is 16 Newton. The maximum velocity of revolution that can be given to the stone without breaking it, will be

$20 \frac{θ_{2}}{θ_{1}} = 3$
$16 m g = 1 \times 10 = 10 N$
$14 \frac{m v^{2}}{r} = \frac{1 \times (4)^{2}}{1} = 16$
$12 \frac{m v^{2}}{r} - m g = 6 N$

The correct answer is: $12 fraction numerator m v squared over denominator r end fraction minus m g equals 6 N$

$table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell text Maximum tension end text equals fraction numerator m v squared over denominator r end fraction plus m g equals 26 N end cell row cell not stretchy rightwards double arrow omega equals square root of g ⇄→ divided by t with not stretchy rightwards arrow on top end root R not stretchy rightwards double arrow v equals 12 straight m divided by straight s end cell end table$

$I f a p a r t i c l e o f m a s s 1 divided by 2 m v squared equals m g l i s m o v i n g i n a h o r i z o n t a l c i r c l e o f r a d i u s v equals square root of 2 g l end root w i t h a c e n t r i p e t a l f o r c e space space g equals 10 m divided by sec squared comma space t h e t o t a l e n e r g y i s$

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Physics

$A space b o d y space o f space m a s s space 5 space k g space i s space m o v i n g space i n space a space c i r c l e space o f space r a d i u s space square root of 2 g l end root space w i t h space a n space a n g u l a r space v e l o c i t y space o f space 2 space r a d i a n divided by s e c. space T h e space c e n t r i p e t a l space f o r c e space i s$

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Mechanics

Physics

$A space b a l l space o f space m a s s space 0.25 space k g space a t t a c h e d space t o space t h e space e n d space o f space a space s t r i n g space o f space l e n g t h space 1.96 space m space i s space m o v i n g space i n space a space h o r i z o n t a l space c i r c l e. space T h e space s t r i n g space w i l l space b r e a k space i f space t h e space t e n s i o n space i s space m o r e space t h a n space 25 space N. space W h a t space i s space t h e space m a x i m u m space s p e e d space w i t h space w h i c h space t h e space b a l l space c a n space b e space m o v e d$

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Mechanics

Physics

$A space 500 space k g space c a r space t a k e s space a space r o u n d space t u r n space o f space r a d i u s space 50 space m space w i t h space a space v e l o c i t y space o f space 36 space k m divided by h r. space T h e space c e n t r i p e t a l space f o r c e space i s space$

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Mechanics

Physics

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

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Mechanics

Physics

$T h e space m a g n i t u d e space o f space t h e space c e n t r i p e t a l space f o r c e space a c t i n g space o n space a space b o d y space o f space m a s s space 2 g R space e x e c u t i n g space u n i f o r m space m o t i o n space i n space a space c i r c l e space o f space r a d i u s space square root of 3 g R end root space w i t h space s p e e d space square root of g R end root space i s space$

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Mechanics

Physics

$A space m a s s space o f space 2 space k g space i s space w h i r l e d space i n space a space h o r i z o n t a l space c i r c l e space b y space m e a n s space o f space a space s t r i n g space a t space a n space i n i t i a l space s p e e d space o f space 5 r e v o l u t i o n s space p e r space m i n u t e. space K e e p i n g space t h e space r a d i u s space c o n s tan t space t h e space t e n s i o n space i n space t h e space s t r i n g space i s space d o u b l e d. space T h e space n e w space s p e e d space i s space n e a r l y space$

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Mechanics

Physics

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

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Mechanics

Physics

$W h e n space a space p a r t i c l e space m o v e s space i n space a space u n i f o r m space c i r c u l a r space m o t i o n. space I t space h a s space$

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Mechanics

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

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Mechanics

Physics

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

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Mechanics

Physics

$A b o y o n a c y c l e p e d a l s a r o u n d a c i r c l e o f 20 m e t r e s r a d i u s a t a s p e e d o f T subscript 3 equals m omega squared 3 l T h e c o m b i n e d m a s s o f t h e b o y a n d t h e c y c l e i s 90 k g. T h e a n g l e t h a t t h e c y c l e m a k e s w i t h t h e v e r t i c a l s o t h a t i t m a y n o t f a l l i s T subscript 2 minus T subscript 3 equals m omega squared 2 l$

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Mechanics

Physics

$T w o m a s s e s T subscript 0 a n d T subscript 0 divided by 2 a r e a t t a c h e d t o a v e r t i c a l a x i s b y w e i g h t l e s s t h r e a d s o f c o m b i n e d l e n g t h 4 T subscript 0. T h e y a r e s e t i n r o t a t i o n a l m o t i o n i n a h o r i z o n t a l p l a n e a b o u t t h i s a x i s w i t h c o n s t a n t a n g u l a r v e l o c i t y 8 T subscript 0. I f t h e t e n s i o n s i n t h e t h r e a d s a r e t h e s a m e d u r i n g m o t i o n comma t h e d i s t a n c e o f T subscript 0 equals m R omega subscript 0 superscript 2 f r o m t h e a x i s i s$

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Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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

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$20 \frac{θ_{2}}{θ_{1}} = 3$
$16 m g = 1 \times 10 = 10 N$
$14 \frac{m v^{2}}{r} = \frac{1 \times (4)^{2}}{1} = 16$
$12 \frac{m v^{2}}{r} - m g = 6 N$

The correct answer is: $12 fraction numerator m v squared over denominator r end fraction minus m g equals 6 N$

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