Tag: modelling collisions

Questions Related to modelling collisions

The co-efficient of restitution e for a perfectly elastic collision is

modelling collisions collisions momentum work, energy and power physics

  1. $1$

  2. $0$

  3. $-1$

  4. infinity

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Correct Option: A
Explanation:

The co-efficient of restitution for a perfectly elastic collision is $e = 1$

The co-efficient of restitution for a perfectly inelastic collision is $e = 0$
The co-efficient of restitution for rest of the collisions is $0<e < 1$

Two spheres of different masses moving in the same direction undergo perfect head on elastic collision.
Then,
a) Their velocities are interchanged if they are of same mass

b) If the heavier sphere were at rest before collision. it continues to be at rest after collision and the lighter sphere retraces its path with the same velocity

c) If the lighter sphere were at rest before collision, it moves with the velocity of the heavier sphere and the heavier sphere continues to move with its original velocity after collision.

d) If the lighter sphere were at rest before collision, it moves with double the velocity of the heavier sphere and the heavier sphere continues to move with its original velocity, after collision.

modelling collisions collisions momentum work, energy and power physics

  1. a,b,c are correct

  2. a,b are correct

  3. b,c are correct

  4. a,b,d are correct

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Correct Option: D
Explanation:

A) Common result.
B) e.g Ball hitting a wall
C) $e= \dfrac{O-V}{V-V^{1}} = 1$
$V^{1} = 2V$
D) As in C

 Assertion (A) : When a ball hits a floor obliquely and gets reflected after inelastic collision, only the vertical component of its velocity gets changed.
Reason (R) : During collision the floor exerts a force on the ball only along the normal but not parallel to the surface

modelling collisions collisions momentum work, energy and power physics

  1. Both Assertion (A) and Reason (R) are correct and R is the correct explanation

  2. Both Assertion (A) and Reason (R) are correct but the reason does not give the correct explanation

  3. A is true but R is false

  4. A is false but R is true

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Correct Option: A
Explanation:

During an oblique collision of ball with floor , the only force considered is normal reaction force which is always perpendicular to surface until clearly given rough surface no force parallel to surface is taken into account.

A $90\ gm$ ball moving at $100 \ cm/s$ collide head on with a stationary $10\ gm$ ball. The coefficient of restitution is $0.5$. The collision is :

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  1. elastic

  2. inelastic

  3. perfect inelastic

  4. none

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Correct Option: B
Explanation:

If $e = 1$, then the collision is called perfectly elastic.
If $0 < e <1$, the collision is called inelastic.
If $e = 0$,  the collision is called perfectly inelastic.

A body dropped freely from a height h on to a horizontal plane, bounces up and down and finally comes to rest.The coefficient of restitution is e. The ratio of velocities at the beginning and after two rebounds is 

modelling collisions collisions momentum work, energy and power physics

  1. 1 : e

  2. e : 1

  3. $1 : e^3$

  4. $e^2 : 1 $

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Correct Option: D
Explanation:

Let initial velocity is v at time of collision. $v = \sqrt { 2gh } $

after first re bound velocity ${v} _{1} = ev$
after second rebound velocity ${v} _{2} = e{v} _{1} = {e}^{2}v$
ratio $=\dfrac { { v } _{ 2 } }{ v } =\dfrac { { e }^{ 2 }v }{ v } $
$ ={ e }^{ 2 }:1$

Two bodies of equal masses moving with equal speeds makes a perfectly inelastic collision. If the speed after the collision is reduced to half, the velocities of approach is 

modelling collisions collisions momentum work, energy and power physics

  1. $30 ^ { \circ }$

  2. $60 ^ { \circ }$

  3. $90 ^ { \circ }$

  4. $120 ^ { \circ }$

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Correct Option: C

Two small spheres of equal mass, and heading towards each other with equal speeds, undergo a headon collision (no external force acts on system of two spheres). Then which of the following statement is correct?

modelling collisions collisions momentum work, energy and power physics

  1. Their final velocities must be zero

  2. Their final velocities may be zero

  3. Each must have a final velocity equal to the others initial velocity

  4. Their velocities must be reduced in magnitude

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Correct Option: B
Explanation:

Nothing is mentioned about coefficient of restitution. 

Hence the only true statement is 'their final velocities may be zero.'