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    Physics
    Mechanics
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    Question

    text  A moving particle of mass  end text m text  collides head-on   with a particle of mass  end text 2 m text  which is  end text 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 blank row cell text  initially at rest. Fraction of kinetic energy retained by  end text m comma text  after the collision  end text end cell end table

    1. 8/9
    2. 1/9
    3. 1/3
    4. 2/3

    The correct answer is: 1/9

      text  Coefficient of restitution  end text e equals 1 not stretchy rightwards double arrow open parentheses v subscript 2 minus v subscript 1 close parentheses equals open parentheses u subscript 1 minus u subscript 2 close parentheses not stretchy rightwards double arrow open parentheses v subscript 2 minus v subscript 1 close parentheses equals u subscript 1 not stretchy rightwards arrow left parenthesis 1 right parenthesis text  From conservation of momentum,  end text m u subscript 1 equals m v subscript 1 plus 2 m v subscript 2
      text  Final  end text KE text  of  end text m text  is  end text 1 half m v subscript 1 superscript 2 equals 1 half m fraction numerator u subscript 1 superscript 2 over denominator 9 end fraction text  Fraction of  end text KE text  retained by  end text straight m text  is  end text 1 divided by 9

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      text  A  end text 1 Kg text  ball moving at  end text 12 ms to the power of negative 1 end exponent text collides with a  end text 2 Kg text  ball moving in the opposite  end text text  direction at  end text 24 ms to the power of negative 1 end exponent text . If the coefficient of restitution is  end text 2 divided by 3 comma text  their velocities after  end text text  impact are  end text

      text  A  end text 1 Kg text  ball moving at  end text 12 ms to the power of negative 1 end exponent text collides with a  end text 2 Kg text  ball moving in the opposite  end text text  direction at  end text 24 ms to the power of negative 1 end exponent text . If the coefficient of restitution is  end text 2 divided by 3 comma text  their velocities after  end text text  impact are  end text

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      text  A railway truck of mass  end text 10 to the power of 4 Kg text  travelling at  end text 1 ms to the power of negative 1 end exponent text collides with another of double its  end text text  mass moving in the opposite direction with velocity of  end text 0.2 ms to the power of negative 1 end exponent text . If the trucks couple  end text text  automatically on collision, their common velocity in  end text ms to the power of negative 1 end exponent text .  end text

      text  A railway truck of mass  end text 10 to the power of 4 Kg text  travelling at  end text 1 ms to the power of negative 1 end exponent text collides with another of double its  end text text  mass moving in the opposite direction with velocity of  end text 0.2 ms to the power of negative 1 end exponent text . If the trucks couple  end text text  automatically on collision, their common velocity in  end text ms to the power of negative 1 end exponent text .  end text

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      text  A moving body with a mass m end text subscript 1 text   strikes a body of mass  end text m subscript 2 text  which is stationary.  end text text  Assuming perfectly elastic impact, the ratio  end text m subscript 1 divided by m subscript 2 text  so as to decrease the velocity of  end text text  first body  end text 1.5 text  times is  end text

      text  A moving body with a mass m end text subscript 1 text   strikes a body of mass  end text m subscript 2 text  which is stationary.  end text text  Assuming perfectly elastic impact, the ratio  end text m subscript 1 divided by m subscript 2 text  so as to decrease the velocity of  end text text  first body  end text 1.5 text  times is  end text

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      text  A body of mass  end text 1 Kg text  undergoes elastic collision  with another body at rest and contin-  end text text  useto move in the original direction with   end text 1 divided by 4 text  th of its initial Mass of the  end text o t h e r space b o d y space text end text

      text  A body of mass  end text 1 Kg text  undergoes elastic collision  with another body at rest and contin-  end text text  useto move in the original direction with   end text 1 divided by 4 text  th of its initial Mass of the  end text o t h e r space b o d y space text end text

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      text  A mass  end text m text  moving horizontally (along the  end text x text  - axis) with velocity  end text v text  collides and sticks  end text text  to a mass of  end text 3 m text  moving vertically upward (along the  end text y minus text  axis) with velocity  end text 2 v. text  The  end text text  final velocity of the combination is  end text

      text  A mass  end text m text  moving horizontally (along the  end text x text  - axis) with velocity  end text v text  collides and sticks  end text text  to a mass of  end text 3 m text  moving vertically upward (along the  end text y minus text  axis) with velocity  end text 2 v. text  The  end text text  final velocity of the combination is  end text

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      text  A bullet of mass  end text m text  is fired with a velocity  end text v subscript 1 text  at a body of mass  end text M text  moving in opposite  end text text  direction with velocity  end text v subscript 2 text  . The bullet penetrates the body and emerges with a velocity  end text v. text  The subsequent velocity of the body is  end text

      text  A bullet of mass  end text m text  is fired with a velocity  end text v subscript 1 text  at a body of mass  end text M text  moving in opposite  end text text  direction with velocity  end text v subscript 2 text  . The bullet penetrates the body and emerges with a velocity  end text v. text  The subsequent velocity of the body is  end text

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      text  Two balls have masses in ratio 2:1.  Their velocities are in the ratio of  end text 1 colon 2 text  .  end text T h e space text  coefficient of restitution is  end text 5 over 6 text  . Then the final velocity of each ball is  end text

      text  Two balls have masses in ratio 2:1.  Their velocities are in the ratio of  end text 1 colon 2 text  .  end text T h e space text  coefficient of restitution is  end text 5 over 6 text  . Then the final velocity of each ball is  end text

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      text  A sphere of mass m moving with constant velocity hits another stationary  end text s p h e r e space o f space text  the same mass. If e is the coefficient of restitution,  then the ratio of the velocities of  end text text  the two spheres after collision will be  end text

      text  A sphere of mass m moving with constant velocity hits another stationary  end text s p h e r e space o f space text  the same mass. If e is the coefficient of restitution,  then the ratio of the velocities of  end text text  the two spheres after collision will be  end text

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      text  A bomb shell explodes into  end text 3 text  pieces having masses  end text 1 Kg comma 2 Kg text  and  end text m Kg text  respectively.  end text T h e space 2 K g space a n d space 1 K g space text  masses fly off with velocities  end text 8 ms to the power of negative 1 end exponent text and  end text 12 ms to the power of negative 1 end exponent text  along  end text Y text  and  end text X text  -axes respectively. The third one flies off with speed of  end text 40 ms to the power of negative 1 end exponent. space text  The total mass of  end text t h e space s h e l l space i s

      text  A bomb shell explodes into  end text 3 text  pieces having masses  end text 1 Kg comma 2 Kg text  and  end text m Kg text  respectively.  end text T h e space 2 K g space a n d space 1 K g space text  masses fly off with velocities  end text 8 ms to the power of negative 1 end exponent text and  end text 12 ms to the power of negative 1 end exponent text  along  end text Y text  and  end text X text  -axes respectively. The third one flies off with speed of  end text 40 ms to the power of negative 1 end exponent. space text  The total mass of  end text t h e space s h e l l space i s

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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 m subscript 1 space a n d space m subscript 2 space a r e space c o n n e c t e d space b y space a space l i g h t space a n d space i n e x t e n s i b l e space s t r i n g space w h i c h space p a s s e s space o v e r space a space f i x e d space p u l l e y. space I n i t i a l l y comma space t h e space p a r t i c l e space m subscript 1 space m o v e s space w i t h space a space v e l o c i t y space v subscript 0 w h e n space t h e space s t r i n g space i s space n o t space t a u t. space N e g l e c t i n g space f r i c t i o n space i n space a l l space c o n t a c t i n g space s u r f a c e s comma space f i n d space t h e space v e l o c i t i e s space o f space t h e space p a r t i c l e s space m subscript 1 space a n d space m subscript 2 space j u s t space a f t e r space t h e space s t r i n g space i s space t a u t.

      T w o space p a r t i c l 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 r e space c o n n e c t e d space b y space a space l i g h t space a n d space i n e x t e n s i b l e space s t r i n g space w h i c h space p a s s e s space o v e r space a space f i x e d space p u l l e y. space I n i t i a l l y comma space t h e space p a r t i c l e space m subscript 1 space m o v e s space w i t h space a space v e l o c i t y space v subscript 0 w h e n space t h e space s t r i n g space i s space n o t space t a u t. space N e g l e c t i n g space f r i c t i o n space i n space a l l space c o n t a c t i n g space s u r f a c e s comma space f i n d space t h e space v e l o c i t i e s space o f space t h e space p a r t i c l e s space m subscript 1 space a n d space m subscript 2 space j u s t space a f t e r space t h e space s t r i n g space i s space t a u t.

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      A space p l a t e space o f space m a s s space M space i s space h e l d space a t space r e s t space b y space f i r i n g space b u l l e t s space f r o m space b e l o w. space E a c h space b u l l e t space h a s space a space m a s s space m space v e l o c i t y space u space left parenthesis u p right parenthesis space j u s t space b e f o r e space h i t t i n g space a n d space s t o p s space a f t e r space h i t t i n g space t h e space p l a t e space f o r space a space m o m e n t space a n d space f a l l s. space D e t e r m i n e space t h e space n u m b e r space o f space b u l l e t s space s t r i k i n g space t h e space p l a t e space p e r space u n i t space t i m e.

      A space p l a t e space o f space m a s s space M space i s space h e l d space a t space r e s t space b y space f i r i n g space b u l l e t s space f r o m space b e l o w. space E a c h space b u l l e t space h a s space a space m a s s space m space v e l o c i t y space u space left parenthesis u p right parenthesis space j u s t space b e f o r e space h i t t i n g space a n d space s t o p s space a f t e r space h i t t i n g space t h e space p l a t e space f o r space a space m o m e n t space a n d space f a l l s. space D e t e r m i n e space t h e space n u m b e r space o f space b u l l e t s space s t r i k i n g space t h e space p l a t e space p e r space u n i t space t i m e.

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      A space m a c h i n e space g u n space c a n space f i r e space b u l l e t s space o f space 50 space g r a m s space a t space a space s p e e d space o f space 2000 space m space s to the power of negative 1 end exponent semicolon space t h e space m a n space h o l d i n g space t h e space g u n space c a n space e x e r t space a n space a v e r a g e space f o r c e space o f space 200 space N space a g a i n s t space t h e space g u n. space C a l c u l a t e space t h e space m a x i m u m space n u m b e r space o f space b u l l e t s space w h i c h space h e space c a n space f i r e space p e r space m i n u t e.

      A space m a c h i n e space g u n space c a n space f i r e space b u l l e t s space o f space 50 space g r a m s space a t space a space s p e e d space o f space 2000 space m space s to the power of negative 1 end exponent semicolon space t h e space m a n space h o l d i n g space t h e space g u n space c a n space e x e r t space a n space a v e r a g e space f o r c e space o f space 200 space N space a g a i n s t space t h e space g u n. space C a l c u l a t e space t h e space m a x i m u m space n u m b e r space o f space b u l l e t s space w h i c h space h e space c a n space f i r e space p e r space m i n u t e.

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      A space 3.00 space k g space s t e e l space b a l l space s t r i k e s space t h e space w a l l space w i t h space a space s p e e d space o f space 10.0 space m space divided by space s space a t space a n space a n g l e space o f 60 to the power of 0 space w i t h space t h e space s u r f a c e. space I t space b o u n c e s space o f f space w i t h space t h e space s a m e space s p e e d space a n d space a n g l e. space I f space t h e space b a l l space i s space i n space c o n t a c t space w i t h space t h e space w a l l space f o r space 0.200 space s comma space w h a t space i s space t h e space a v e r a g e space f o r c e space e x e r t e d space b y space t h e w a l l space o n space t h e space b a l l ?

      A space 3.00 space k g space s t e e l space b a l l space s t r i k e s space t h e space w a l l space w i t h space a space s p e e d space o f space 10.0 space m space divided by space s space a t space a n space a n g l e space o f 60 to the power of 0 space w i t h space t h e space s u r f a c e. space I t space b o u n c e s space o f f space w i t h space t h e space s a m e space s p e e d space a n d space a n g l e. space I f space t h e space b a l l space i s space i n space c o n t a c t space w i t h space t h e space w a l l space f o r space 0.200 space s comma space w h a t space i s space t h e space a v e r a g e space f o r c e space e x e r t e d space b y space t h e w a l l space o n space t h e space b a l l ?

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

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

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      A space m a s s space 2 space m space r e s t s space o n space a space h o r i z o n t a l space t a b l e. space I t space i s space a t t a c h e d space t o space a space l i g h t space i n e x t e n s i b l e space s t r i n g space w h i c h space p a s s e s space o v e r space a space s m o o t h space p u l l e space a n d space c a r r i e s space a space m a s s space m space a t space t h e space o t h e r space e n d. space I f space t h e space m a s s space m space i s space r a i s e d space v e r t i c a l l y space t h r o u g h space a space d i s tan c e space h space a n d space i s space t h e n space d r o p p e d. space w h a t space i s space t h e s p e e d space w i t h space w h i c h space t h e space m a s s space 2 space m space b e g i n s space t o space r i s e ?

      A space m a s s space 2 space m space r e s t s space o n space a space h o r i z o n t a l space t a b l e. space I t space i s space a t t a c h e d space t o space a space l i g h t space i n e x t e n s i b l e space s t r i n g space w h i c h space p a s s e s space o v e r space a space s m o o t h space p u l l e space a n d space c a r r i e s space a space m a s s space m space a t space t h e space o t h e r space e n d. space I f space t h e space m a s s space m space i s space r a i s e d space v e r t i c a l l y space t h r o u g h space a space d i s tan c e space h space a n d space i s space t h e n space d r o p p e d. space w h a t space i s space t h e s p e e d space w i t h space w h i c h space t h e space m a s s space 2 space m space b e g i n s space t o space r i s e ?

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