$F o u r space i d e n t i c a l space p a r t i c l e s space o f space m a s s space M space a r e space l o c a t e d space a t space t h e space c o r n e r s space o f space a space s q u a r e space o f s i d e space ‘ a ’. space W h a t space s h o u l d space b e space t h e i r space space s p e e d space i f space e a c h space o f space t h e m space r e v o l v e s space u n d e r space t h e space i n f l u e n c e space o f space o t h e r s space g r a v i t a t i o n a l space f i e l d space i n space a space c i r c u l a r space o r b i t space c i r c u m s c r i b i n g space t h e space s q u a r e space ? space$

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

PhysicsMechanics

Mechanics

Physics

$A space v e r y space l o n g space s o l e n o i d space o f space r e a d i u s space R space i s space c a r r y i n g space c u r r e n t space straight I left parenthesis straight t right parenthesis equals kte to the power of negative alpha straight t end exponent left parenthesis straight k greater than 0 right parenthesis space comma space a s space a space f u n c t i o n space o f space t i m e space left parenthesis t space greater or equal than space 0 right parenthesis. C o u n t e r space c l o c k w i s e space c u r r e n t space i s space t a k e n space t o space b e space p o s i t i v e. space A space c i r c u l a r space c o n d u c t i n g space c o i l space o f space r a d i u s space 2 R space i s space p l a c e d space i n space t h e space e q u a t o r i a l space p l a n e space o f space t h e space s o l e n o i d space a n d space c o n c e n t r i c space w i t h space t h e space s o l e n o i d. space T h e space c u r r e n t space i n d u c e d space i n space t h e space o u t e r space c o i l space i s c o r r e c t l y space d e p i c t e d comma space a s space a space f u n c t i o n space o f space t i m e comma space b y space colon space$

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Mechanics

Physics

$T h e space p o s i t i o n space o f space a space p a r t i c l e space a s space a space f u n c t i o n space o f space t i m e space t comma space i s space g i v e n space b y space space space x left parenthesis t right parenthesis equals a t plus b t squared minus c t cubed w h e r e space a comma space b space a n d space c space a r e space c o n s tan t s. space W h e n space t h e space p a r t i c l e space a t t a i n s space z e r o space a c c e l e r a t i o n comma space t h e n space i t s space v e l o c i t y space w i l l space b e space colon space space$

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Mechanics

Physics

$A space s o l i d space s p h e r e space o f space m a s s space ‘ M ’ space a n d space r a d i u s space ‘ a ’ space i s space s u r r o u n d e d space b y space a space u n i f o r m space c o n c e n t r i c space s p h e r i c a l space s h e l l space o f space t h i c k n e s s 2 a space a n d space m a s s space 2 M. space T h e space g r a v i t a t i o n a l space f i e l d space a t space d i s tan c e space ‘ 3 a ’ space f r o m space t h e space c e n t r e space w i l l space b e space$

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Mechanics

Physics

$A space p a r t i c l e space s t a r t s space f r o m space o r i g i n space O space f r o m space r e s t space a n d space m o v e s space w i t h space a space u n i f o r m space a c c e l e r a t i o n space a l o n g space t h e space p o s i t i v e space x minus a x i s. space I d e n t i f y space a l l space f i g u r e s space t h a t space c o r r e c t l y space r e p r e s e n t space t h e space m o t i o n space q u a l i t a t i v e l y. space left parenthesis a space equals space a c c e l e r a t i o n comma space v equals space v e l o c i t y comma space x equals space d i s p l a c e m e n t comma space t equals space t i m e space right parenthesis$

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Mechanics

Physics

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

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Mechanics

Physics

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

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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

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

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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

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

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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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