physics

mechanics

Easy

Question

$A space 10 k g space b o y space s tan d i n g space i n space a space 40 k g space b o a t space f l o a t i n g space o n space w a t e r space i s space 20 m space f r o m t h e space s h o r e space o f space t h e space r i v e r. space I f space h e space m o v e s space 8 space m e t r e s space o n space t h e space b o a t space t o w a r d s space t h e space s h o r e comma space t h e n space h o w f a r space i s space h e space f r o m space t h e space s h o r e space n o w ?$

$13.6 m$
$15 m$
$12 m$
$9.6 m$

The correct answer is: $13.6 m$

$text Distance of end text straight c. straight m text of the boat from the shore end text equals left parenthesis 20 minus x right parenthesis straight m text Distance of the boy from the shore end text equals 20 straight m text Distance of end text straight c. straight m text of boat and boy system from the shor end text straight e equals fraction numerator straight m subscript 1 straight x subscript 1 plus straight m subscript 2 straight x subscript 2 over denominator straight m subscript 1 plus straight m subscript 2 end fraction not stretchy rightwards double arrow straight x subscript cm equals fraction numerator 10 cross times 20 plus 40 left parenthesis 20 minus straight x right parenthesis over denominator 50 end fraction straight m text After the boy moved end text 8 straight m text towards the shore, end text straight x subscript cm superscript straight prime equals fraction numerator 10 cross times straight d plus 40 left parenthesis straight d minus straight x plus 8 right parenthesis over denominator 50 end fraction text where end text to the power of straight prime straight d to the power of straight prime text is his new distance from the shore end text text Here end text straight x subscript om equals straight x subscript cm text ' as no external force is acting end text text So, end text 10 cross times 20 plus 40 left parenthesis 20 minus straight x right parenthesis equals 10 cross times straight d plus 40 left parenthesis straight d minus straight x plus 8 right parenthesis not stretchy rightwards double arrow 200 plus 800 minus 40 straight x equals 10 straight d plus 40 straight d minus 40 straight x plus 320 not stretchy rightwards double arrow straight d equals 680 over 50 equals 13 times 6 straight m$

$A space l a d d e r space A P thin space o f space t e n g t h space 5 m space i n c l i n e d space t o space a space v e r t i c a l space w a l l space i s space s l i p p i n g o v e r space a space h o r i z o n t a l space s u r f a c e space w i t h space v e l o c i t y space o f space 2 m divided by s comma space W h e n space A space i s space a t space a space d i s tan c e space 3 m space f r o m space O comma space t h e space v e l o c i t y space o f space C M space a t space t h i s space m o m e n t space i s space$

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Mechanics

Physics

$T w o space b l o c k s space o f space m a s s e s space 10 k g space a r e space p l a c e d space o n space X minus a x i s. space T h e space f i r s t space m a s s space i s m o v e d space o n space t h e space a x i s space b y space a space d i s tan c e space o f space 2 space c m space r i g h t. space B y space w h a t space d i s tan c e space s h o u l d space t h e space s e c o n d m a s s space b e space m o v e d space t o space k e e p space t h e space p o s i t i o n space o f space c e n t r e space o f space m a s s space u n c h a n g e d. space$

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Mechanics

Physics

$T h e space d e n s i t y space o f space a space l i n e a r space r o d space o f space l e n g t h space L space v a r i e s space a s rho equals left parenthesis a minus b x right parenthesis space w h e r e space x space i s space t h e space d i s tan c e space f r o m space t h e space e n d space O. D i s tan c e space o f space c e n t r e space o f space m a s s space o f space t e h space r o d space f r o m space O space i s$

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Mechanics

Physics

$T h r e e space i d e n t i c a l space b r i c k s space e a c h space o f space l e n g t h space L space a r e space p l a c e d space a s T h e space c e n t r e space o f space m a s s space o f space t h e space s y s t e m space i s space f r o m space O space a t space a space d i s tan c e.$

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Mechanics

Physics

$text Two particles of equal mass have velocities end text v with not stretchy rightwards arrow on top subscript 1 equals 4 i with not stretchy hat on top text and end text v with not stretchy rightwards arrow on top subscript 2 equals 4 j with not stretchy hat on top m s to the power of negative 1 end exponent text First particle end text text has an acceleration end text a with not stretchy rightwards arrow on top subscript 1 equals left parenthesis 5 i with not stretchy hat on top plus 5 ȷ with not stretchy hat on top right parenthesis m s to the power of negative 2 end exponent text while the acceleration of the other particle is end text text zero. The centre of mass of the two particles moves in a path of end text$

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Mechanics

Physics

$space Two particles of masses space 100 gm text and end text 300 gm space space have at a given time velocities space left parenthesis 10 i with hat on top minus 7 j with hat on top minus 3 k with hat on top right parenthesis text end text text and end text left parenthesis 7 i with hat on top minus 9 j with hat on top plus 6 k with hat on top right parenthesis cms to the power of negative 1 end exponent text respectively. Then velocity of centre of mass of the system in end text cms to the power of negative 1 end exponent text is end text$

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Mechanics

Physics

$A space 30 k g space p r o j e c t i l e space m o v i n g space h o r i z o n t a l l y space w i t h space a space v e l o c i t y space v with rightwards arrow on top subscript 0 equals left parenthesis 120 m divided by s right parenthesis i with hat on top space e x p l o d e s space i n t o space t w o space f r a g m e n t s space A space a n d space B space o f space m a s s e s space 12 k g space a n d space 18 k g comma space r e s p e c t i v e l y. space T a k i n g space p o i n t space o f space e x p l o s i o n space a s space o r i g i n space a n d space k n o w l e d g e space t h a t space 3 s space l a t e r space t h e space p o s i t i o n space o f space f r a g m e n t space A space i s space left parenthesis 300 m comma space 24 m comma negative 48 m space right parenthesis comma space d e t e r m i n e space t h e space p o s i t i o n space o f space f r a g m e n t space B space a t space t h e space s a m e space i n s tan t. space$

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Mechanics

Physics

$A space b l o c k space i s space r e l e a s e d space o n space t h e space c o n v e x space s u r f a c e space o f space a space h e m i s p h e r i c a l space w e d g e space a s space s h o w n space i n space f i g u r e. space D e t e r m i n e space t h e space d i s p l a c e m e n t space o f space t h e space w e d g e space w h e n space t h e space b l o c k space r e a c h e s space t h e space a n g u l a r space p o s i t i o n space theta.$

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Mechanics

Physics

$A space r i n g space a n d space a space p a r t i c l e space o f space m a s s e s space 2 m space a n d space m space a r e space k e p t space a s space s h o w n space i n space t h e space f i g u r e comma space s u c h space t h a t space t h e space C M space o f space t h e space c o m b i n a t i o n space l i e s space a t space t h e space o r i g i n. space F i n d space x.$

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Mechanics

Physics

$F i g u r e space s h o w s space a space u n i f o r m space d i s c space o f space r a d i u s space R comma space f r o m space w h i c h space a space h o l e space o f space r a d i u s space R divided by 2 space h a s space b e e n space c u t space o u t space f r o m space l e f t o f space t h e space c e n t r e space a n d space i s space p l a c e d space o n space t h e space r i g h t space o f space t h e space c e n t r e space o f space t h e space d i s c. space F i n d space t h e space C M space o f space t h e space r e s u l t i n g space d i s c.$

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