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    Physics
    Mechanics
    Easy

    Question

    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

    1. 1/25
    2. 1/5
    3. 5
    4. 25

    The correct answer is: 5

      text  From eonservation of momentum,  end text m subscript 1 u subscript 1 equals m subscript 1 v subscript 1 plus m subscript 2 v subscript 2 equals m subscript 1 fraction numerator u subscript 1 over denominator 1 times 5 end fraction plus m subscript 2 v subscript 2 not stretchy rightwards double arrow m subscript 2 v subscript 2 equals m subscript 1 u subscript 1 minus 2 over 3 m subscript 1 u subscript 1 equals m subscript 1 u subscript 1 over 3 not stretchy rightwards arrow e equals fraction numerator v subscript 2 minus v subscript 1 over denominator u subscript 1 minus u subscript 2 end fraction equals 1 v subscript 2 minus 2 over 3 u subscript 1 equals u subscript 1 not stretchy rightwards double arrow v subscript 2 equals 5 over 3 u subscript 1 not stretchy rightwards arrow m subscript 2 fraction numerator 5 u subscript 1 over denominator 3 end fraction equals m subscript 1 u subscript 1 over 3 not stretchy rightwards double arrow m subscript 1 over m subscript 2 equals 5

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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.

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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.

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