Tag: collisions

Questions Related to collisions

During an "elastic collision " , 
a) there is no loss of kinetic energy
b) the bodies are perfectly elastic
c) temporarily some of the kinetic energy is used to deform the bodies
d) after collision the bodies regain the original shape keeping the total energy constant

modelling collisions collisions momentum work, energy and power physics

  1. only "a" is true

  2. a, c, d are true

  3. b, c, d are true

  4. a, b, c ,d are true

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Correct Option: D
Explanation:

In an elastic collision, e is equal to 1. Therefore, the kinetic energy used in causing deformation of the bodies is recovered completely in the reformation since the reformation is complete. So no energy is lost. 

Identify the correct statements from the following :

a) The collisions between the nuclei and fundamental particles are considered as elastic collisions.
b) Emission of an alpha particle by $U^{235}$ is an "elastic collision".
c) The collision between two ivory balls is considered as " elastic collision".
d) A running man jumps into a train. It is an "elastic collision".

modelling collisions collisions momentum work, energy and power physics

  1. Only a & b are true

  2. Only b & c are true

  3. a, b & c are true

  4. b, c & d are true

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Correct Option: C
Explanation:

A collision is considered elastic collision if the kinetic energy before collision is equal to the kinetic energy after collision.

In collision of nuclei and fundamental particles, unless there is emission of gamma rays, kinetic energy of the system remains constant.

In Alpha particle emission, energy is not being released in any other form. Hence kinetic energy of the system will remain same before and after the emission.

In collision of two ivory balls, the balls being extremely hard, no deformation happens and for most practical purposes energy is assumed to not being converted into any other form such as heat(which happens when there is friction or deformation).

In the case of a running man jumping on to the train, friction and deformation happens in order for the man to continue moving along with the train. Thus energy was converted into other forms. Hence, it is an example of inelastic.

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 :

modelling collisions collisions momentum work, energy and power physics

  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.'

A particle of mass $1\ g$ moving with a velocity $\vec {v _{1}} = 3\hat {i} - 2\hat {j} ms^{-1}$ experiences a perfectly in elastic collision with another particle of mass $2\ g$ and velocity $\vec {v _{2}} = 4\hat {j} - 6\hat {k} ms^{-1}$. The velocity of the particle is:

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

  1. $2.3\ ms^{-1}$

  2. $4.6\ ms^{-1}$

  3. $9.2\ ms^{-1}$

  4. $6\ ms^{-1}$

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Correct Option: B
Explanation:

From conservation of momentum
$m _{1}\vec {v _{1}} + m _{2}\vec {v _{2}} = (m _{1} + m _{2})\vec {v}$


$1\times (3\hat {i} - 2\hat {j}) + 2\times (4\hat {j} - 6\hat {k}) = (1 + 2)\vec {v}$

$\Rightarrow 3\hat {i} + 6\hat {j} - 12\hat {k} = 3\vec {v} $

$\Rightarrow \vec {v} = \hat {i} + 2\hat {j} - 4\hat {k}$


$v = |\vec {v}| = \sqrt {1 + 4 + 16} = 4.6\ ms^{-1}$.