physics

mechanics

Easy

Question

$C e r t a i n n e u t r o n s t a r s a r e b e l i e v e d t o b e r o t a t i n g a t a b o u t a subscript t not equal to 0. I f s u c h a s t a r h a s a r a d i u s o f 20 k m comma t h e space a c c e l e r a t i o n space o f space a n o b j e c t o n t h e e q u a t o r o f t h e s t a r w i l l b e$

$\frac{\sqrt{3}}{2}$
$\tan^{- 1} (\frac{1}{5})$
$\tan^{- 1} (\frac{3}{5})$
$\tan^{- 1} (1)$

The correct answer is: $\tan^{- 1} (\frac{3}{5})$

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row cell tan space theta equals fraction numerator v squared over denominator r g end fraction equals fraction numerator left parenthesis 10 right parenthesis squared over denominator 50 cross times 10 end fraction equals 1 fifth end cell row cell therefore straight a equals theta equals tan to the power of negative 1 end exponent left parenthesis 1 divided by 5 right parenthesis end cell end table$

$A space r o a d space i s space 10 space m space w i d e. space I t s space r a d i u s space o f space c u r v a t u r e space i s space 50 space m. space T h e space o u t e r space e d g e space i s space a b o v e space t h e space l o w e r space e d g e space b y space a space d i s tan c e space o f space 1.5 m. space space T h i s space r o a d space i s space m o s t space s u i t e d space f o r space t h e space v e l o c i t y space$

PhysicsMechanics

Mechanics

Physics

$A space m a s s space o f space 100 space g m space i s space t i e d space t o space o n e space e n d space o f space a space s t r i n g space 2 space m space l o n g. space T h e space b o d y space i s space r e v o l v i n g space i n space a space h o r i z o n t a l space c i r c l e space m a k i n g space a space m a x i m u m space o f space 200 space r e v o l u t i o n s space p e r space m i n. space T h e space o t h e r space e n d space o f space t h e space s t r i n g space i s space f i x e d space a t space t h e space c e n t r e space o f space t h e space c i r c l e space o f space r e v o l u t i o n. space T h e space m a x i m u m space t e n s i o n space t h a t space space t h e space s t r i n g space c a n space b e a r space i s space left parenthesis a p p r o x i m a t e l y right parenthesis space$

PhysicsMechanics

Mechanics

Physics

$A c a r i s m o v i n g o n a c i r c u l a r p a t h a n d t a k e s a t u r n. I f m 4 pi squared n squared r equals 4 cross times 10 to the power of left parenthesis minus 13 right parenthesis a n d space n equals 0.08 cross times 10 to the power of 8 c y c l e s divided by s e c. space b e t h e r e a c t i o n s o n t h e i n n e r a n d o u t e r w h e e l s r e s p e c t i v e l y comma t h e n$

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

$T h e space a n g u l a r space s p e e d space o f space a space f l y space w h e e l space m a k i n g space 120 space r e v o l u t i o n s divided by m i n u t e i s space$

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

$A space m o t o r space c y c l i s t space m o v i n g space w i t h space a space v e l o c i t y space o f space 72 space k m divided by h o u r space o n space a space f l a t space r o a d space t a k e s space a space t u r n space o n space t h e space r o a d space a t space a space p o i n t space w h e r e space t h e space r a d i u s space o f space c u r v a t u r e space o f space t h e space r o a d space i s space 20 space m e t e r s. space T h e space a c c e l e r a t i o n space d u e space t o space g r a v i t y space i s space 10 space m divided by s e c 2. space I n space o r d e r space t o space a v o i d space s k i d d i n g comma space h e space m u s t space n o t space b e n d space w i t h space r e s p e c t space t o space t h e space v e r t i c a l space p l a n e space b y space a n space a n g l e space g r e a t e r space t h a n space$

PhysicsMechanics

Mechanics

Physics

$A space p a r t i c l e space i s space m o v i n g space i n space a space h o r i z o n t a l space c i r c l e space w i t h space c o n s tan t space s p e e d. space I t space h a s space c o n s tan t space$

PhysicsMechanics

Mechanics

Physics

$A n space a i r c r a f t space e x e c u t e s space a space h o r i z o n t a l space l o o p space w i t h space a space s p e e d space o f space 150 space m divided by s space w i t h space i t s comma space w i n g s space b a n k e d a t space a n space a n g l e space o f space square root of F m r end root. text The radius of the loop is end text square root of fraction numerator F over denominator m r end fraction end root$

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

$T w o b o d i e s o f m a s s 10 k g a n d 5 k g m o v i n g i n c o n c e n t r i c o r b i t s o f r a d i i 8 pi m rightwards arrow over short leftwards arrow divided by rightwards arrow over short leftwards arrow s squared a n d equals 4 pi squared n squared r equals 4 pi squared left parenthesis 1 half right parenthesis squared cross times 4 equals 4 pi squared s u c h t h a t t h e i r p e r i o d s a r e t h e s a m e. T h e n t h e r a t i o b e t w e e n t h e i r c e n t r i p e t a l a c c e l e r a t i o n i s$

PhysicsMechanics

Mechanics

Physics

$A space c o n v e x space l e n s space o f space f o c a l space l e n g t h space 20 space c m space p r o d u c e s space i m a g e s space o f space t h e space s a m e space m a g n i f i c a t i o n space 2 space w h e n space a n space o b j e c t space i s space k e p t space a t space t w o space d i s tan c e space x subscript 1 space a n d space straight x subscript 2 open parentheses straight x subscript 1 greater than straight x subscript 2 close parentheses space f r o m space t h e space l e n s. space T h e space r a t i o space o f space x subscript 1 space a n d space x subscript 2 space i s space colon$

PhysicsMechanics

Mechanics

Physics

$A space w o o d e n space b l o c k space f l o a t i n g space i n space a space b u c k e t space o f space w a t e r space h a s space space 4 over 5 o f space i t s space v o l u m e space s u b m e r g e d. space W h e n space c e r t a i n space a m o u n t space o f space a n space o i l space i s space p o u r e d space i n t o space t h e space b u c k e t comma i t space i s space f o u n d space t h a t space t h e space b l o c k space i s space j u s t space u n d e r space t h e space o i l space s u r f a c e space w i t h space h a l f space o f space i t s space v o l u m e space u n d e r space w a t e r space a n d space h a l f space i n space o i l. space T h e space d e n s i t y space o f space o i l space r e l a t i v e space t o space t h a t space o f space w a t e r space i s space colon space$

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Can’t find what you’re looking for?

$\frac{\sqrt{3}}{2}$
$\tan^{- 1} (\frac{1}{5})$
$\tan^{- 1} (\frac{3}{5})$
$\tan^{- 1} (1)$

The correct answer is: $\tan^{- 1} (\frac{3}{5})$

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