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Mechanics

Physics

$A space m a s s l e s s space s p r i n g space left parenthesis k space equals space 800 space N divided by m right parenthesis space a t t a c h e d space w i t h space m a s s space left parenthesis 500 space g right parenthesis space i s space c o m p l e t e l y space i m m e r s e d space i n space 1 space k g space o f space w a t e r. space T h e space s p r i n g space i s space s t r e t c h e d space b y space 2 space c m space a n d space r e l e a s e d space s o space t h a t space i t space s t a r t s space v i b r a t i n g. space W h a t space w o u l d space b e space t h e space o r d e r space o f space m a g n i t u d e space o f space t h e space c h a n g e space i n space t h e space t e m p e r a t u r e space o f space w a t e r space w h e n space t h e space v i b r a t i o n s space s t o p space c o m p l e t e l y ? left parenthesis A s s u m e space t h a t space t h e space w a t e r space c o n t a i n e r space a n d space s p r i n g space r e c e i v e space n e g l i g i b l e space h e a t space a n d space s p e c i f i c space h e a t space o f space m a s s space equals space 400 space J divided by k g space K comma space s p e c i f i c space h e a t space o f space w a t e r space equals space 4184 space J divided by k g space K right parenthesis space$

$A space m a s s l e s s space s p r i n g space left parenthesis k space equals space 800 space N divided by m right parenthesis space a t t a c h e d space w i t h space m a s s space left parenthesis 500 space g right parenthesis space i s space c o m p l e t e l y space i m m e r s e d space i n space 1 space k g space o f space w a t e r. space T h e space s p r i n g space i s space s t r e t c h e d space b y space 2 space c m space a n d space r e l e a s e d space s o space t h a t space i t space s t a r t s space v i b r a t i n g. space W h a t space w o u l d space b e space t h e space o r d e r space o f space m a g n i t u d e space o f space t h e space c h a n g e space i n space t h e space t e m p e r a t u r e space o f space w a t e r space w h e n space t h e space v i b r a t i o n s space s t o p space c o m p l e t e l y ? left parenthesis A s s u m e space t h a t space t h e space w a t e r space c o n t a i n e r space a n d space s p r i n g space r e c e i v e space n e g l i g i b l e space h e a t space a n d space s p e c i f i c space h e a t space o f space m a s s space equals space 400 space J divided by k g space K comma space s p e c i f i c space h e a t space o f space w a t e r space equals space 4184 space J divided by k g space K right parenthesis space$

PhysicsMechanics

Mechanics

Physics

$I n space t h e space d e n s i t y space m e a s u r e m e n t space o f space a space c u b e comma space t h e space m a s s space a n d space e d g e space l e n g t h space a r e space m e a s u r e d space a s space left parenthesis 10.00 space plus-or-minus space 0.10 right parenthesis space k g space a n d space space left parenthesis 0.10 space plus-or-minus space 0.01 right parenthesis space m comma space r e s p e c t i v e l y. space T h e space e r r o r space i n space t h e space m e a s u r e m e n t space o f space d e n s i t y space i s$

$I n space t h e space d e n s i t y space m e a s u r e m e n t space o f space a space c u b e comma space t h e space m a s s space a n d space e d g e space l e n g t h space a r e space m e a s u r e d space a s space left parenthesis 10.00 space plus-or-minus space 0.10 right parenthesis space k g space a n d space space left parenthesis 0.10 space plus-or-minus space 0.01 right parenthesis space m comma space r e s p e c t i v e l y. space T h e space e r r o r space i n space t h e space m e a s u r e m e n t space o f space d e n s i t y space i s$

PhysicsMechanics

Mechanics

Physics

$T h e space s e c o n d apostrophe s space h a n d space o f space a space w a t c h space h a s space l e n g t h space 6 space c m. space S p e e d space o f space e n d space p o i n t a n d space m a g n i t u d e space o f space d i f f e r e n c e space o f space v e l o c i t i e s space a t space t w o space p e r p e n d i c u l a r space p o s i t i o n s space w i l l space b e space space$

$T h e space s e c o n d apostrophe s space h a n d space o f space a space w a t c h space h a s space l e n g t h space 6 space c m. space S p e e d space o f space e n d space p o i n t a n d space m a g n i t u d e space o f space d i f f e r e n c e space o f space v e l o c i t i e s space a t space t w o space p e r p e n d i c u l a r space p o s i t i o n s space w i l l space b e space space$

PhysicsMechanics

Mechanics

Physics

$A space c i r c u l a r space r o a d space o f space r a d i u s space 1000 space m space h a s space b a n k i n g space a n g l e space T equals fraction numerator 2 pi over denominator omega end fraction equals 2 pi square root of R e with not stretchy rightwards arrow on top divided by c with not stretchy rightwards arrow on top g end root equals 2 cross times 3.14 square root of 4 e with not stretchy rightwards arrow on top divided by c with not stretchy rightwards arrow on top 9.8 end root T h e space m a x i m u m space s a f e space s p e e d space o f space a space c a r space h a v i n g space m a s s space 2000 space k g space w i l l space b e comma space i f space t h e space c o e f f i c i e n t space o f space f r i c t i o n space b e t w e e n space t y r e space a n d space r o a d space i s space 0.5 space space$

$A space c i r c u l a r space r o a d space o f space r a d i u s space 1000 space m space h a s space b a n k i n g space a n g l e space T equals fraction numerator 2 pi over denominator omega end fraction equals 2 pi square root of R e with not stretchy rightwards arrow on top divided by c with not stretchy rightwards arrow on top g end root equals 2 cross times 3.14 square root of 4 e with not stretchy rightwards arrow on top divided by c with not stretchy rightwards arrow on top 9.8 end root T h e space m a x i m u m space s a f e space s p e e d space o f space a space c a r space h a v i n g space m a s s space 2000 space k g space w i l l space b e comma space i f space t h e space c o e f f i c i e n t space o f space f r i c t i o n space b e t w e e n space t y r e space a n d space r o a d space i s space 0.5 space space$

PhysicsMechanics

Mechanics

Physics

$C o n s i d e r space a space s p h e r i c a l space g a s e o u s space c l o u d space o f space m a s s space d e n s i t y space rho left parenthesis r right parenthesis space i n space f r e e space s p a c e space w h e r e space r space i s space t h e space r a d i a l space d i s tan c e space f r o m space i t s space c e n t e r. space T h e space g a s e o u s space c l o u d space i s space m a d e space o f space p a r t i c l e s space o f space e q u a l space m a s s space m space m o v i n g space i n space c i r c u l a r space o r b i t s space a b o u t space t h e space c o m m o n space c e n t e r space w i t h space t h e space s a m e k i n e t i c space e n e r g y space K. space T h e space f o r c e space a c t i n g space o n space t h e space p a r t i c l e space i s space t h e i r space m u t u a l space g r a v i t a t i o n a l space f o r c e. space I f space rho left parenthesis r right parenthesis space i s space c o n s tan t space i n space t i m e comma space t h e space p a r t i c l e n u m b e r space d e n s i t y space n left parenthesis r right parenthesis equals rho left parenthesis r right parenthesis divided by m space i s space u n i v e r s a l space g r a v i t a t i o n a l space c o n s tan t right square bracket space$

$C o n s i d e r space a space s p h e r i c a l space g a s e o u s space c l o u d space o f space m a s s space d e n s i t y space rho left parenthesis r right parenthesis space i n space f r e e space s p a c e space w h e r e space r space i s space t h e space r a d i a l space d i s tan c e space f r o m space i t s space c e n t e r. space T h e space g a s e o u s space c l o u d space i s space m a d e space o f space p a r t i c l e s space o f space e q u a l space m a s s space m space m o v i n g space i n space c i r c u l a r space o r b i t s space a b o u t space t h e space c o m m o n space c e n t e r space w i t h space t h e space s a m e k i n e t i c space e n e r g y space K. space T h e space f o r c e space a c t i n g space o n space t h e space p a r t i c l e space i s space t h e i r space m u t u a l space g r a v i t a t i o n a l space f o r c e. space I f space rho left parenthesis r right parenthesis space i s space c o n s tan t space i n space t i m e comma space t h e space p a r t i c l e n u m b e r space d e n s i t y space n left parenthesis r right parenthesis equals rho left parenthesis r right parenthesis divided by m space i s space u n i v e r s a l space g r a v i t a t i o n a l space c o n s tan t right square bracket space$

PhysicsMechanics

Mechanics

Physics

$A space s t o n e space o f space m a s s space o f space 16 space k g space i s space a t t a c h e d space t o space a space s t r i n g space 144 space m space l o n g space a n d space i s space w h i r l e d space i n space a space h o r i z o n t a l space c i r c l e. space T h e space m a x i m u m space t e n s i o n space t h e space s t r i n g space c a n space w i t h s tan d space i s space 16 space N e w t o n. space T h e space m a x i m u m space v e l o c i t y space o f space r e v o l u t i o n t h a t space c a n space b e space g i v e n space t o space t h e space s t o n e space w i t h o u t space b r e a k i n g space i t comma space w i l l space b e space$
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

$A space s t o n e space o f space m a s s space o f space 16 space k g space i s space a t t a c h e d space t o space a space s t r i n g space 144 space m space l o n g space a n d space i s space w h i r l e d space i n space a space h o r i z o n t a l space c i r c l e. space T h e space m a x i m u m space t e n s i o n space t h e space s t r i n g space c a n space w i t h s tan d space i s space 16 space N e w t o n. space T h e space m a x i m u m space v e l o c i t y space o f space r e v o l u t i o n t h a t space c a n space b e space g i v e n space t o space t h e space s t o n e space w i t h o u t space b r e a k i n g space i t comma space w i l l space b e space$
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

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

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