Tag: collisions in one dimension

Questions Related to collisions in one dimension

sphere collides with another sphere of identical mass kept at rest. Mier collision, the two spheres move. The collision is perfectly inelastic, then the angle between the directions of motion of the two spheres is

collisions in one dimension collisions work, energy and power mechanics physics

  1. ${ 0 }^{ o }$

  2. ${ 45 }^{ o }$

  3. different from ${ 90 }^{ o }$

  4. ${ 90 }^{ o }$

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Correct Option: A

A smooth sphere A of mass m collides elastically with an identical sphere B at rest. The velocity of A before collision is $8 m/s$ in a direction making $60^{o}$ with the line joining the centres at the time of impact. Which of the following is/are possible:

collisions in one dimension collisions work, energy and power mechanics physics

  1. the sphere a comes to rest after collision

  2. the sphere B will move with a speed of $8 m/s$ after collision

  3. the directions of motion of A and B after collision are at right angles

  4. the speed of B after collision is $2 m/s$

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Correct Option: C

An object is moving towards a mirror with  a velocity v as shown in figure.if the collision between the mirror and the object is perfectly elastic, then the velocity of the image after collision with mirror in vector form is.

collisions in one dimension collisions work, energy and power mechanics physics

  1. $ - v\;\widehat j$

  2. $ - v\;\cos \;2\theta \widehat j + v\;\sin \;2\theta \;\widehat i$

  3. $ - v\widehat i$

  4. $ - v\;\cos \theta \;j - \;v\;\sin \theta \;\widehat i$

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Correct Option: A

A body of mass $m$ moving with velocity $u$ collides elastically with another body of mass $m$ at rest. After collision, they moves in a plane with velocities $V _{1}$ and $V _{2}$ respectively. Then the angle beteen $\vec{V} _{1}$ and $\vec{V} _{2}$ is

collisions in one dimension collisions work, energy and power mechanics physics

  1. $zero$

  2. $60^{o}$

  3. $90^{o}$

  4. $180^{o}$

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Correct Option: D

Two solid balls of rubber $A$ and $B$ whose masses are $200\ gm$ and $400\ gm$ respectively, are moving in mutually opposite directions. if the velocity of ball A is $0.3\ m/s$ and both the ball come to rest after collision, then the velocity of ball $B$ is :

collisions in one dimension collisions work, energy and power mechanics physics

  1. $0.15\ m/s$

  2. $-0.15\ m/s$

  3. $1.5\ m/s$

  4. $None\ of\ these$

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Correct Option: B
Explanation:
Initial linear momentum of system 

$= [{{m} _{A}}{{\vec{v}} _{A}}+{{m} _{B}}{{\vec{v}} _{B}}]$

$= 0.2 \times  0.3 + 0.4 \times  vB$

Finally both balls come to rest \ final linear momentum = 0 

By the law of conservation of linear momenum        

$0.2 \times  0.3 + 0.4 \times  vB = 0$

$[{{v} _{B}}=-\dfrac{0.2\times 0.3}{0.4}=-0.15\ m/s]$

A ball of mass m moving with velocity V makes a head on  elastic collision with a ball of the same mass moving with velocity 2V towards it. Taking direction of V as positive velocities of the two balls after collision are

collisions in one dimension collisions work, energy and power mechanics physics

  1. -V and 2V

  2. 2V and -V

  3. V and -2V

  4. -2V and V

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Correct Option: B

Two billiard balls undergo a head-on collision. Ball 1 is twice as heavy as ball 2. Initially, ball 1 moves with a speed $v$ toward ball $2$ which is at rest. Immediately after collision, ball 1 travels at a speed of $v/3$ in the same direction. What type of collision has occured?

collisions in one dimension collisions work, energy and power mechanics physics

  1. inelastic

  2. elastic

  3. completely inelastic

  4. cannot be determined from the information given

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Correct Option: B
Explanation:

Solving the equation of conservation of momentum give us that the relative velocity of approach is equal to the relative velocity of separation. Hence coefficient of restitution is 1.
Which means collision is elastic. 

The collision of two balls of equal mass takes place at the origin of coordinates. Before collision, the components of velocities are $(V _x = 50 c m s^{-1},  V _{y} = 0)$ and $(V _{x} = -40 c m s^{-1}$ and $V _{y} = 30 c m s^{-1})$. The first ball comes to rest after collision. The velocity (components $V _{x}$ and $V _{y}$ respectively) of the second ball are

collisions in one dimension collisions work, energy and power mechanics physics

  1. 10 and 30 $c m s^{-1}$

  2. 30 and 10 $c m s^{-1}$

  3. 5 and 15 $c m s^{-1}$

  4. 15 and $5 c m s^{-1}$

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Correct Option: C

Which of the following does not hold when two particles of masses $m _1$ and $m _2$ undergo elastic collision?

collisions in one dimension collisions work, energy and power mechanics physics

  1. When $m _1 =m _2$ and $m _2$ is stationary, there is maximum transfer of kinetic energy in head an collision

  2. When $m _1=m _2$ and $m _2$ is stationary , there is maximum transfer of momentum in head on collision

  3. when $m _1 >> m _2$ and $m _2$ is stationary, after head on collision $m _2$ moves with twice the velocity of $m _1$

  4. When the collision is oblique and $m _1=m _2$ with $m _2$ stationary, after the collision the particle move in opposite directions.

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Correct Option: A

Two identical balls A and B collide head on elastically. If velocities of A and B, before the collision are +0.5 m/s and -0.3 m/s respectively, then their velocities, after the collision, are respectively

collisions in one dimension collisions work, energy and power mechanics physics

  1. -0.5 m/s and +0.3 m/s

  2. +0.5 m/s and +0.3 m/s

  3. +0.3 m/s and -0.5 m/s

  4. -0.3 m/s and +0.5 m/s

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Correct Option: C
Explanation:

When identical balls collide $elastically $ they just $exchange$ their $SPEEDS$ and get reversed.

This can be verified by applying the $momentum$ conservation and $energy$ conservation, yes energy remains
 conserved for elastic collisions.
so the exchanged velocities will be following $v _1=0.3m/s$ and $v _2=-0.5m/s$