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      physics
      mechanics
      Easy

      Question

      text  Kinetic energy of a particle is increased by 1%.  Find percentage change in linear momentum.  end text

      1. negative 0.5 straight percent sign
      2. plus 0.5 straight percent sign
      3. plus 0.6 straight percent sign
      4. plus 0.1 straight percent sign

      The correct answer is: plus 0.5 straight percent sign


        p equals square root of 2 K m end root text  or  end text p proportional to square root of K text  or  end text p proportional to K to the power of 1 half end exponent
text  (1) (% change in  end text P text  )  end text equals open parentheses 1 half close parentheses text  (\% change in  end text K text  )  end text
straight percent sign text  change in  end text p equals 1 half left parenthesis 1 straight percent sign right parenthesis equals plus 0.5 straight percent sign

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        text  Kinetic energy of a particle is increased by 50%.  Find percentage change in linear momentum.  end text

        text  Kinetic energy of a particle is increased by 50%.  Find percentage change in linear momentum.  end text

        PhysicsMechanics
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        text  A stone is dropped at  end text t equals 0. text  A second stone, with twice the mass of the first, is dropped from the  end text
text  same point at  end text t equals 100 ms. text  How far below the release point is the centre of mass of the two stones at  end text straight t equals 300 ms text  ?  end text

        text  A stone is dropped at  end text t equals 0. text  A second stone, with twice the mass of the first, is dropped from the  end text
text  same point at  end text t equals 100 ms. text  How far below the release point is the centre of mass of the two stones at  end text straight t equals 300 ms text  ?  end text

        PhysicsMechanics
        Mechanics
        Physics

        text  At one instant, the centre of mass of a system of two particles is located on the  end text x text  -axis at  end text x equals 3.0
straight m text  and has a velocity of  end text left parenthesis 6.0 straight m divided by straight s right parenthesis straight j with not stretchy hat on top text  . One of the particles is at the origin, the other particle has a  end text
text  mass of  end text 0.10 kg text  and is at rest on the  end text x text  -axis at  end text x equals 12.0 straight m text  .  What is the velocity of the particle at the origin?  end text

        text  At one instant, the centre of mass of a system of two particles is located on the  end text x text  -axis at  end text x equals 3.0
straight m text  and has a velocity of  end text left parenthesis 6.0 straight m divided by straight s right parenthesis straight j with not stretchy hat on top text  . One of the particles is at the origin, the other particle has a  end text
text  mass of  end text 0.10 kg text  and is at rest on the  end text x text  -axis at  end text x equals 12.0 straight m text  .  What is the velocity of the particle at the origin?  end text

        PhysicsMechanics
        parallel
        Mechanics
        Physics

        text  At one instant, the centre of mass of a system of two particles is located on the  end text x text  -axis at  end text x equals 3.0
straight m text  and has a velocity of  end text left parenthesis 6.0 straight m divided by straight s right parenthesis straight j with not stretchy hat on top text  . One of the particles is at the origin, the other particle has a  end text
text  mass of  end text 0.10 kg text  and is at rest on the  end text x text  -axis at  end text x equals 12.0 straight m text  .  Calculate the total momentum of this system.  end text

        text  At one instant, the centre of mass of a system of two particles is located on the  end text x text  -axis at  end text x equals 3.0
straight m text  and has a velocity of  end text left parenthesis 6.0 straight m divided by straight s right parenthesis straight j with not stretchy hat on top text  . One of the particles is at the origin, the other particle has a  end text
text  mass of  end text 0.10 kg text  and is at rest on the  end text x text  -axis at  end text x equals 12.0 straight m text  .  Calculate the total momentum of this system.  end text

        PhysicsMechanics
        Mechanics
        Physics

        text  At one instant, the centre of mass of a system of two particles is located on the  end text x text  -axis at  end text x equals 3.0
straight m text  and has a velocity of  end text left parenthesis 6.0 straight m divided by straight s right parenthesis bold j with not stretchy hat on top text  . One of the particles is at the origin, the other particle has a  end text
text  mass of  end text 0.10 kg text  and is at rest on the  end text x text  -axis at  end text x equals 12.0 straight m text  .  What is the mass of the particle at the origin?  end text

        text  At one instant, the centre of mass of a system of two particles is located on the  end text x text  -axis at  end text x equals 3.0
straight m text  and has a velocity of  end text left parenthesis 6.0 straight m divided by straight s right parenthesis bold j with not stretchy hat on top text  . One of the particles is at the origin, the other particle has a  end text
text  mass of  end text 0.10 kg text  and is at rest on the  end text x text  -axis at  end text x equals 12.0 straight m text  .  What is the mass of the particle at the origin?  end text

        PhysicsMechanics
        Mechanics
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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 divided by text  apart. Let the centre of mass of this  end text
text  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 by  end text I subscript 2 text  away  end text
text  from  end text C text  . Find the distance, from  end text C text  where 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 divided by text  apart. Let the centre of mass of this  end text
text  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 by  end text I subscript 2 text  away  end text
text  from  end text C text  . Find the distance, from  end text C text  where new centre of mass will be located.  end text

        PhysicsMechanics
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        Mechanics
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        T w o space b l o c k s space o f space m a s s e s space m subscript 1 space a n d space m subscript 2 space end subscript space c o n n e c t e d space b y space a space m a s s l e s s space
s p r i n g space o f space s p r i n g space c o n s tan t space K 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.
B l o c k space 2 space i s space s h i f t e d space b y space a space s m a l l space d i s tan c e space x space t o space t h e
l e f t space a n d space t h e n space r e l e a s e d. space W h e n space b l o c k space 1 space b r e a k s space o f f space t h e space w a l l comma
v e l o c i t y 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 s y s t e m space i s space

        T w o space b l o c k s space o f space m a s s e s space m subscript 1 space a n d space m subscript 2 space end subscript space c o n n e c t e d space b y space a space m a s s l e s s space
s p r i n g space o f space s p r i n g space c o n s tan t space K 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.
B l o c k space 2 space i s space s h i f t e d space b y space a space s m a l l space d i s tan c e space x space t o space t h e
l e f t space a n d space t h e n space r e l e a s e d. space W h e n space b l o c k space 1 space b r e a k s space o f f space t h e space w a l l comma
v e l o c i t y 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 s y s t e m space i s space

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

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

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        A space b o a t space i s space a space t space r e s t space i n space a space r i v e r space a n d space h a s space a space m a s s space o f space 98 space k g. space A space d o g space o f space m a s s space 2 k g space o n space t h e space
b o a t space f r o m space o n e space e n d space t o space t h e space o t h e r space w i t h space a space v e l o c i t y space 20 m divided by s. space T h e n space v e l o c i t y space o f space b o a t space i n space m divided by s
i s

        A space b o a t space i s space a space t space r e s t space i n space a space r i v e r space a n d space h a s space a space m a s s space o f space 98 space k g. space A space d o g space o f space m a s s space 2 k g space o n space t h e space
b o a t space f r o m space o n e space e n d space t o space t h e space o t h e r space w i t h space a space v e l o c i t y space 20 m divided by s. space T h e n space v e l o c i t y space o f space b o a t space i n space m divided by s
i s

        PhysicsMechanics
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        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 ?

        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 ?

        PhysicsMechanics
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        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

        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
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        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

        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

        PhysicsMechanics
        parallel
        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

        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
        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.

        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
        Mechanics
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        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
        parallel

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