Physics

Mechanics

Easy

Question

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

$a + \frac{b^{2}}{4 c}$
$a + \frac{b^{2}}{c}$
$a + \frac{b^{2}}{3 c}$
$a + \frac{b^{2}}{2 c}$

The correct answer is: $a plus fraction numerator b squared over denominator 3 c end fraction$

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

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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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

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

PhysicsMechanics

Mechanics

Physics

$A space b o d y space o f space m a s s space 2 k g space m a k e s space a n space e l a s t i c space c o l l i s i o n space w i t h space a space s e c o n d space b o d y space a t space r e s t space a n d space c o n t i n u e s t o space m o v e space i n space t h e space o r i g i n a l space d i r e c t i o n space b u t space w i t h space o n e space f o u r t h space o f space i t s space o r i g i n a l space s p e e d. space W h a t space i s space t h e space m a s s o f space t h e space s e c o n d space b o d y ?$

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Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

$A space u n i f o r m space c a b l e space o f space m a s s space ‘ M ’ space a n d space l e n g t h space ‘ L ’ space i s space p l a c e d space o n space a space h o r i z o n t a l space s u r f a c e space s u c h space t h a t space i t s space space open parentheses 1 over n close parentheses to the power of t h end exponent space space p a r t space i s space h a n g i n g space b e l o w space t h e space e d g e space o f space t h e space s u r f a c e. space T o space l i f t space t h e space h a n g i n g space p a r t space o f space t h e space c a b l e space u p t o space t h e space s u r f a c e comma space t h e space w o r k space d o n e space s h o u l d space b e$

PhysicsMechanics

Mechanics

Physics

$T h e space s t r e a m space o f space a space r i v e r space i s space f l o w i n g space w i t h space a space s p e e d space o f space 2 space k m divided by h. space A space s w i m m e r space c a n space s w i m space a t space a space s p e e d space o f space 4 space k m divided by h. space W h a t space s h o u l d space b e space t h e space d i r e c t i o n space o f space t h e space s w i m m e r space w i t h space r e s p e c t space t o space t h e space f l o w space o f space t h e space r i v e r space t o space c r o s s space t h e space r i v e r space s t r a i g h t space ? space$

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

$A space c a r space s o m e t i m e s space o v e r t u r n s space w h i l e space t a k i n g space a space t u r n. space W h e n space i t space o v e r t u r n s comma space i t space i s$

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

$O n space a space r a i l w a y space c u r v e comma space t h e space o u t s i d e space r a i l space i s space l a i d space h i g h e r space t h a n space t h e space i n s i d e space o n e space s o space t h a t space r e s u l tan t space f o r c e space e x e r t e d space o n space t h e space w h e e l s space o f space t h e space r a i l space c a r space b y space t h e space t o p s space o f space t h e space r a i l s space w i l l$

PhysicsMechanics

Mechanics

Physics

$O n space a space r a i l w a y space c u r v e comma space t h e space o u t s i d e space r a i l space i s space l a i d space h i g h e r space t h a n space t h e space i n s i d e space o n e space s o space t h a t space r e s u l tan t space f o r c e space e x e r t e d space o n space t h e space w h e e l s space o f space t h e space r a i l space c a r space b y space t h e space t o p s space o f space t h e space r a i l s space w i l l$

PhysicsMechanics

Mechanics

Physics

$A space b o d y space o f space m a s s$ $20 square root of 3$ $m o v e s space i n space a space c i r c u l a r space p a t h space w i t h space u n i f o r m space a n g u l a r space v e l o c i t y. space T h e space m o t i o n space o f space t h e space b o d y space h a s space c o n s tan t space$

PhysicsMechanics

Mechanics

Physics

$T w o space p a r t i c l e s space o f space e q u a l space m a s s e s space a r e space r e v o l v i n g space i n space c i r c u l a r space p a t h s space o f space r a d i i$ $r equals fraction numerator 34.3 over denominator 2 pi end fraction$ and $v equals fraction numerator 2 pi r over denominator T end fraction equals fraction numerator 2 pi r over denominator square root of 22 end fraction$ $space space r e s p e c t i v e l y space w i t h space t h e space s a m e space s p e e d. space T h e space r a t i o space o f space t h e i r space c e n t r i p e t a l space f o r c e s space i s$

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