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Physics

Mechanics

Easy

Question

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

$\frac{3}{2}$
$\frac{- 2}{3}$
$- 2$
$- 3$

The correct answer is: $fraction numerator negative 2 over denominator 3 end fraction$

$M a s s space o f space t h e space f i r s t space b l o c k comma m subscript 1 equals 10 k g M a s s space o f space t h e space s e c o n d space b l o c k comma space m subscript 2 equals 30 k g triangle x subscript C M end subscript equals fraction numerator m subscript 1 triangle x subscript 1 plus m subscript 2 triangle x subscript 2 over denominator m subscript 1 plus m subscript 2 end fraction 0 equals fraction numerator 10 cross times 2 plus 30 triangle x subscript 2 over denominator 40 end fraction triangle x subscript 2 equals negative 2 over 3 T h e r e f o r e comma space t h e space s e c o n d space b l o c k space s h o u l d space b e space m o v e d space l e f t space t h r o u g h space a space d i s tan c e space o f space 2 divided by 3 space c m space t o space k e e p space t h e space p o s i t i o n space o f space c e n t r e space o f space m a s s space u n c h a n g e d.$

Related Questions to study

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

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

PhysicsMechanics

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

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

PhysicsMechanics

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

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

PhysicsMechanics

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

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

PhysicsMechanics

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

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

PhysicsMechanics

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

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

PhysicsMechanics

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

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

PhysicsMechanics

$M r. space V e r m a space left parenthesis 50 space k g right parenthesis space a n d space M r. space M a t h u r space left parenthesis 60 space k g right parenthesis space a r e space s i t t i n g space a t space t h e space t w o space e x t r e m e s space o f space a space 4 m space l o n g space b o a t space left parenthesis 40 space k g right parenthesis space s tan d i n g space s t i l l space i n space w a t e r. space T o space d i s c u s s space a space m e c h a n i c s space p r o b l e m comma space t h e y space c o m e space t o space i n space w a t e r. space T o space d i s c u s s space a space m e c h a n i c s space p r o b l e m comma space t h e y space c o m e space t o space t h e space m i d d l e space o f space t h e space b o a t. space N e g l e c t i n g space f r i c t i o n space w i t h space w a t e r comma space h o w space t h e space m i d d l e space o f space t h e space b o a t. space N e g l e c t i n g space f r i c t i o n space w i t h space w a t e r comma space h o w space f a r space d o e s space t h e space b o a t space m o v e space i n space t h e space w a t e r space d u r i n g space t h e space p r o c e s s ?$

$M r. space V e r m a space left parenthesis 50 space k g right parenthesis space a n d space M r. space M a t h u r space left parenthesis 60 space k g right parenthesis space a r e space s i t t i n g space a t space t h e space t w o space e x t r e m e s space o f space a space 4 m space l o n g space b o a t space left parenthesis 40 space k g right parenthesis space s tan d i n g space s t i l l space i n space w a t e r. space T o space d i s c u s s space a space m e c h a n i c s space p r o b l e m comma space t h e y space c o m e space t o space i n space w a t e r. space T o space d i s c u s s space a space m e c h a n i c s space p r o b l e m comma space t h e y space c o m e space t o space t h e space m i d d l e space o f space t h e space b o a t. space N e g l e c t i n g space f r i c t i o n space w i t h space w a t e r comma space h o w space t h e space m i d d l e space o f space t h e space b o a t. space N e g l e c t i n g space f r i c t i o n space w i t h space w a t e r comma space h o w space f a r space d o e s space t h e space b o a t space m o v e space i n space t h e space w a t e r space d u r i n g space t h e space p r o c e s s ?$

PhysicsMechanics

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

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

PhysicsMechanics

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$text There are two masses end text m subscript 1 text and end text m subscript 2 text placed at a distance end text l text apart, let the centre of mass end text text o end text text f this system is at a point named end text C. text If end text m subscript 1 text is displaced by end text l subscript 1 text towards end text C text and end text m subscript 2 text is displaced end text text by end text l subscript 2 space text away from end text C comma text find the distance from end text C text where the new centre of mass will be located. end text$

$text There are two masses end text m subscript 1 text and end text m subscript 2 text placed at a distance end text l text apart, let the centre of mass end text text o end text text f this system is at a point named end text C. text If end text m subscript 1 text is displaced by end text l subscript 1 text towards end text C text and end text m subscript 2 text is displaced end text text by end text l subscript 2 space text away from end text C comma text find the distance from end text C text where the new centre of mass will be located. end text$

PhysicsMechanics

$F i g u r e space s h o w s space a space f i x e d space w e d g e space o n space w h i c h space t w o space b l o c k s space o f space m a s s e s space 2 k g space a n d space 3 k g space a r e space p l a c e d space o n space i t s space s m o o t h space i n c l i n e d space s u r f a c e s. space W h e n space t h e space t w o space b l o c k s space a r e space r e l e a s e d space f r o m space r e s t comma space f i n d space t h e space a c c e l e r a t i o n space o f space c e n t r e space o f space m a s s space o f space t h e space t w o space b l o c k s.$

$F i g u r e space s h o w s space a space f i x e d space w e d g e space o n space w h i c h space t w o space b l o c k s space o f space m a s s e s space 2 k g space a n d space 3 k g space a r e space p l a c e d space o n space i t s space s m o o t h space i n c l i n e d space s u r f a c e s. space W h e n space t h e space t w o space b l o c k s space a r e space r e l e a s e d space f r o m space r e s t comma space f i n d space t h e space a c c e l e r a t i o n space o f space c e n t r e space o f space m a s s space o f space t h e space t w o space b l o c k s.$

PhysicsMechanics

$A space p u l l e y space f i x e d space t o space t h e space c e i l i n g space c a r r i e d space a space t h r e a d space w i t h space b o d i e s space o f space m a s s e s space m subscript 1 space a n d space m subscript 2 space a t t a c h e d space t o space i t s space e n d s. space T h e space m a s s e s space o f space t h e space p u l l e y space a n d space t h e space t h r e a d space a r e space n e g l i g i b l e space a n d space f r i c t i o n space i s space a b s e n t. space F i n d space t h e space a c c e l e r a t i o n space o f space t h e space c e n t r e space o f space m a s s space o f space t h i s space s y s t e m.$

$A space p u l l e y space f i x e d space t o space t h e space c e i l i n g space c a r r i e d space a space t h r e a d space w i t h space b o d i e s space o f space m a s s e s space m subscript 1 space a n d space m subscript 2 space a t t a c h e d space t o space i t s space e n d s. space T h e space m a s s e s space o f space t h e space p u l l e y space a n d space t h e space t h r e a d space a r e space n e g l i g i b l e space a n d space f r i c t i o n space i s space a b s e n t. space F i n d space t h e space a c c e l e r a t i o n space o f space t h e space c e n t r e space o f space m a s s space o f space t h i s space s y s t e m.$

PhysicsMechanics

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$T w o space p a r t i c l e s space o f space m a s s e s space 2 k g space a n d space 4 k g space a r e space a p p r o a c h i n g space t o w a r d s space e a c h space o t h e r space w i t h space a c c e l e r a t i o n s 1 m divided by s squared space a n d space space 2 m divided by s squared comma space r e s p e c t i v e l y comma space o n space a space s m o o t h space h o r i z o n t a l space s u r f a c e. space T h e n space f i n d space t h e space a c c e l e r a t i o n o f space c e n t r e space o f space m a s s space o f space t h e space s y s t e m.$

$T w o space p a r t i c l e s space o f space m a s s e s space 2 k g space a n d space 4 k g space a r e space a p p r o a c h i n g space t o w a r d s space e a c h space o t h e r space w i t h space a c c e l e r a t i o n s 1 m divided by s squared space a n d space space 2 m divided by s squared comma space r e s p e c t i v e l y comma space o n space a space s m o o t h space h o r i z o n t a l space s u r f a c e. space T h e n space f i n d space t h e space a c c e l e r a t i o n o f space c e n t r e space o f space m a s s space o f space t h e space s y s t e m.$

PhysicsMechanics

$T w o space b a l l s space w i t h space m a s s e s space m subscript 1 equals 3 k g space a n d space m subscript 2 equals 5 k g space h a v e space i n i t i a l space v e l o c i t i e s space v subscript 1 equals v subscript 2 equals 5 m divided by s space i n space t h e space d i r e c t i o n s space s h o w n space i n space f i g u r e. space T h e y space c o l l i d e space a t space t h e space o r i g i n. space F i n d space t h e space v e l o c i t y space o f space t h e space C M space 3 s space b e f o r e t h e space c o l l i s i o n.$

Two balls with masses and have initial velocities in the directions shown in figure. They collide at the origin. Find the velocity of the CM 3s before the collision.

$T w o space b a l l s space w i t h space m a s s e s space m subscript 1 equals 3 k g space a n d space m subscript 2 equals 5 k g space h a v e space i n i t i a l space v e l o c i t i e s space v subscript 1 equals v subscript 2 equals 5 m divided by s space i n space t h e space d i r e c t i o n s space s h o w n space i n space f i g u r e. space T h e y space c o l l i d e space a t space t h e space o r i g i n. space F i n d space t h e space v e l o c i t y space o f space t h e space C M space 3 s space b e f o r e t h e space c o l l i s i o n.$

Two balls with masses and have initial velocities in the directions shown in figure. They collide at the origin. Find the velocity of the CM 3s before the collision.

PhysicsMechanics

$A space u n i f o r m space m e t a l space p l a t e space o f space r a d i u s space a comma space f r o m space w h i c h space a space d i s k space o f space d i a m e t e r space a space h a s space b e e n space s t a m p e d space o u t space left parenthesis r e m o v e d right parenthesis space a s space s h o w n space i n space f i g u r e. space L o c a t e space t h e space c e n t r e space o f space m a s s space o f space t h e space r e m a i n i n g space p l a t e. space F i n d space t h e space p o s i t i o n space o f space c e n t r e space o f space m a s s space o f space t h e space p l a t e.$

$A space u n i f o r m space m e t a l space p l a t e space o f space r a d i u s space a comma space f r o m space w h i c h space a space d i s k space o f space d i a m e t e r space a space h a s space b e e n space s t a m p e d space o u t space left parenthesis r e m o v e d right parenthesis space a s space s h o w n space i n space f i g u r e. space L o c a t e space t h e space c e n t r e space o f space m a s s space o f space t h e space r e m a i n i n g space p l a t e. space F i n d space t h e space p o s i t i o n space o f space c e n t r e space o f space m a s s space o f space t h e space p l a t e.$

PhysicsMechanics

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