$A space r e c tan g u l a r space s o l i d space b o x space o f space l e n g t h space 0.3 space m space i s space h e l d space h o r i z o n t a l l y comma space w i t h space o n e space o f space i t s space s i d e s space o n space t h e space e d g e space o f space a space p l a t f o r m space o f space h e i g h t space 5 space m. space W h e n space r e l e a s e d comma space i t space s l i p s space o f f space t h e space t a b l e space i n space a space v e r y space s h o r t space t i m e space tau equals 0.01 straight s space r e m a i n i n g space e s s e n t i a l l y space h o r i z o n t a l. T h e space a n g l e space b y space w h i c h space i t space w o u l d space r o t a t e space w h e n space i t space h i t s space t h e space g r o u n d space w i l l space b e space left parenthesis i n space r a d i a n s right parenthesis space c l o s e space t o$

$A space S o l i d space s p h e r e space a n d space s o l i d space c y l i n d e r space o f space i d e n t i c a l space r a d i i space a p p r o a c h space a n space i n c l i n e space w i t h space t h e space s a m e space l i n e a r space v e l o c i t y space left parenthesis S e e space f i g u r e right parenthesis. space B o t h space r o l l space w i t h o u t space s l i p p i n g space a l l space t h r o u g h o u t. space T h e space t w o space c l i m b space m a x i m u m space h e i g h t s space h blank subscript s p h end subscript space a n d space h subscript c y l end subscript space o n space t h e space i n c l i n e. space T h e space r a t i o space straight h subscript sph over straight h subscript cy 1 end subscript space i s space g i v e n space b y$

PhysicsMechanics

Mechanics

Physics

$A space t h i n space c i r c u l a r space p l a t e space o f space m a s s space M space a n d space r a d i u s space R space h a s space i t s space d e n s i t y space v a r y i n g space a s space rho left parenthesis straight r right parenthesis equals rho subscript 0 straight r straight rho left parenthesis straight r right parenthesis equals straight rho subscript 0 straight r space w i t h space straight rho subscript 0 space a s space c o n s tan t space a n d space r space i s space t h e space d i s tan c e space f r o m space i t s space c e n t e r. space T h e space m o m e n t space o f space i n e r t i a space o f space t h e space c i r c u l a r space p l a t e space a b o u t space a n space a x i s space p e r p e n d i c u l a r space t o space t h e space p l a t e space a n d space p a s sin g space t h r o u g h space i t s space e d g e space i s space I equals a M R squared space. space T h e space v a l u e space o f space t h e space c o e f f i c i e n t space a space i s$

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Mechanics

Physics

$F o u r space p a r t i c l e s space A comma space B comma space C space a n d space D space w i t h space m a s s e s space m subscript A equals m comma space m subscript B equals 2 space m comma space m subscript C equals 3 subscript m space a n d space m subscript D equals 4 m space a r e space a t space t h e space c o r n e r s space o f space a space s q u a r e. space T h e y space h a v e space a c c e l e r a t i o n s space o f space e q u a l space m a g n i t u d e space w i t h space d i r e c t i o n s space a s space s h o w n. space T h e space a c c e l e r a t i o n space o f space t h e space c e n t r e o f space m a s s space o f space t h e space p a r t i c l e s space i s$

PhysicsMechanics

Mechanics

Physics

$A space m o v i n g space c o i l space g a l v a n o m e t e r space h a s space a space c o i l space w i t h space 175 space t u r n s space a n d space a r e a space 1 space c m squared. space I t space u s e s space a space t o r s i o n space b a n d space o f space t o r s i o n c o n s tan t space 10 to the power of negative 6 end exponent space N minus m divided by r a d. space T h e space c o i l space i s space p l a c e d space i n space a space m a g n e t i c space f i e l d space B space p a r a l l e l space t o space i t s space p l a n e. space T h e space c o i l d e f l e c t s space b y space 1 degree space space f o r space a space c u r r e n t space o f space 1 space m A. space T h e space v a l u e space o f space B space left parenthesis i n space T e s l a right parenthesis space i s space a p p r o x i m a t e l y space colon space$

PhysicsMechanics

Mechanics

Physics

$A space s t a t i o n a r y space h o r i z o n t a l space d i s c space i s space f r e e space t o space r o t a t e space a b o u t space i t s space a x i s. space W h e n space a space t o r q u e space i s space a p p l i e d o n space i t comma space i t s space k i n e t i c space e n e r g y space a s space a space f u n c t i o n space o f space theta comma space w h e r e space theta space i s space t h e space a n g l e space b y space w h i c h space i s space h a s space r o t a t e d comma space i s space g i v e n space a s space straight k theta squared. space I f space i t s space m o m e n t space o f space i n e r t i a space i s space I space t h e n space t h e space a n g u l a r space a c c e l e r a t i o n space o f space t h e space d i s c space i s space space$

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

$A space p a r t i c l e space o f space m a s s space M space i s space m o v i n g space i n space a space h o r i z o n t a l space c i r c l e space o f space r a d i u s space R space w i t h space u n i f o r m space s p e e d space V. space W h e n space i t space m o v e s space f r o m space o n e space p o i n t space t o space a space d i a m e t r i c a l l y space o p p o s i t e space p o i n t comma space i t s$

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

$T h e space a n g u l a r space v e l o c i t y space o f space a space w h e e l space i s space 70 space r a d divided by s e c. space space I f space t h e space r a d i u s space o f space t h e space w h e e l space i s space 0.5 space m comma space t h e n space l i n e a r space v e l o c i t y space o f space t h e space w h e e l space i s$

PhysicsMechanics

Mechanics

Physics

$T h e space m a x i m u m space s p e e d space o f space a space c a r space o n space a space r o a d – t u r n space o f space r a d i u s space 30 space m comma space i f space t h e space c o e f f i c i e n t space o f space f r i c t i o n b e t w e e n space t h e space t y r e s space a n d space t h e space r o a d space i s space 0.4 comma space w i l l space b e space$

PhysicsMechanics

Mechanics

Physics

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

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Turito is a revolutionary learning platform for quality online and on-campus education from the most experienced faculty. We offer two years integrated classroom coaching for IIT-JEE and NEET aspirants at our Hyderabad campus. We provide online coaching for all kinds of competitive exams such as IIT-JEE, NEET, SAT, ACT, PSAT, Subjective SAT, AP & Olympiads, and Foundation Courses for students of Class 6 to 10 (CBSE, ICSE & State Syllabus).

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