Physics · Science General

Collisions, Momentum and Kinetic Energy

385 Questions

Collisions, momentum, and kinetic energy questions analyze the principles of elastic and inelastic impacts. They require calculating mass, velocity, and conserved energy during physical interactions. These foundational physics topics are essential for most government engineering and general science examinations.

Elastic collisionsInelastic collisionsMomentum calculationKinetic energy principlesVelocity after impact

Collisions, Momentum and Kinetic Energy Questions

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

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

  1. $1$
  2. $0$
  3. lies in between $0$ and $1$

  4. infinity
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The coefficient of restitution is defined as the ratio of the relative velocity of separation to that of approach, in a situation of two objects colliding with each other. 

The relative velocity of approach is the difference between the individual velocities of the two bodies before the collision.
The relative velocity of separation is that after the collision.
In a perfectly elastic collision, the two relative velocities are exactly equal. Hence the coefficient becomes $= 1$

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

A lighter body moving with a velocity $v$ collides with a heavier body at rest. Then :

  1. the lighter body rebounces with twice the velocity of bigger body

  2. the lighter body retraces its path with the same velocity in magnitude

  3. the heavier body does not move practically

  4. both (2) and (3)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In a collision system where $m _1$ moves with $u _1$ initially and $m _2$ is at rest with $m _2 >>> m _1$.
Let the final velocity of $m _1$ be $v _1$ and $m _2$ be $v _2$.
Assumption: Let the collision be elastic. Using linear momentum conservation and equation for coefficient of restitution,
$ m _1u _1 = m _2v _2 + m _1v _1 $
$ v _2 - v _1 = u _1 $


We get $ v _1 = \dfrac {m _1 - m _2 }{m _1 + m _2} u _1 $

$ v _2 = \dfrac {2m _1}{m _1 + m _2} u _1 $

Using  $m _2 >>>  m _1,$  we get $ v _1 = -u _1 $ and $ v _2 = 0 $.  

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

Two identical bodies moving in opposite direction with same speed, collided with each other. If the collision is perfectly elastic then

  1. after the collision both comes to rest

  2. after the collision first comes to rest and second moves in the same direction with a speed 2v

  3. after collision they recoil with same speed

  4. all the above are possible
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$mv+m(-v)=m{ v } _{ 1 }+m{ v } _{ 2 }=0\Rightarrow { v } _{ 1 }+{ v } _{ 2 }=0\$
$ \dfrac { { v } _{ 1 }-{ v } _{ 2 } }{ v-(-v) } =1\Rightarrow { v } _{ 1 }-{ v } _{ 2 }=2v\ $

$thus,\quad { v } _{ 1 }=v\ { v } _{ 2 }=-v$

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

 A 6 kg mass travelling at $2.5 ms^{-1}$ collides head on with a stationary 4 kg mass. After the collision the 6 kg mass travels in its original direction with a speed of $1 ms^{-1}$. The coefficient of restitution is

  1. $1/4$
  2. $1/2$
  3. $3/4$
  4. $5/8$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$e=\dfrac{v-1}{2.5}$

$=\dfrac{1.25}{2.5}=\dfrac{1}{2}$

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

A particle of mass m is attached to one end of a massless spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time $t=0$ with an initial velocity $u _0$. When the speed of the particle is $0.5 u _0$. It collides elastically with a rigid wall. After this collision.

  1. The speed of the particle when it returns to its equilibrium position is $u _0$
  2. The time at which the particle passes through the equilibrium position for the first time is $t=\pi\sqrt{\dfrac{m}{k}}$
  3. The time at which the maximum compression of the spring occurs is $t=\dfrac{4\pi}{3}\sqrt{\dfrac{m}{k}}$
  4. The time at which the particle passes through the equilibrium position for the second time is $t=\dfrac{5\pi}{3}\sqrt{\dfrac{m}{k}}$
Reveal answer Fill a bubble to check yourself
A,D Correct answer
Explanation

$\cfrac{1}{2}mv _o^2=\cfrac{1}{2}Kx^2+\cfrac{1}{2}\times m(0.25)v _o^2\quad equation (1)$

After elastic collision, black speed $=v _o$
So, when, it comes back to equilibrium point its speed is $u _o$.
Amplitude, $A=\cfrac {u _o}{\sqrt{K}}$
From equation $(1)$
$x=\cfrac{\sqrt {3}u _o}{2}\sqrt {\cfrac{m}{K}}$
$\therefore t _1=\cfrac {\pi}{3\omega}=\cfrac {\pi\sqrt{m}}{3\sqrt {K}}$
Time to reach the equilibrium position for the first time $=\cfrac{2\pi}{3} \sqrt {\cfrac{m}{K}}$
Second time, it will reach at time
$=\cfrac{2\pi}{3}\sqrt {\cfrac{m}{K}}+\cfrac {T}{2}$
$=\cfrac{2\pi}{3}\sqrt{\cfrac{m}{K}}+\cfrac {2\pi\sqrt {m}}{\sqrt {K}\pi 2}$
$=\cfrac {5\pi}{3}\sqrt {\cfrac {m}{K}}$

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

Two balls of equal mass undergo head on collision while each was moving with speed $6\ m/s$. If the coefficient of restitution is $\dfrac{1}{3}$, the speed of each ball after impact will be

  1. $18\ m/s$
  2. $2\ m/s$
  3. $6\ m/s$
  4. $4\ m/s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speed of balls are $v _1$ and $v _2$.

There is no external force acting, momentum will be conserved. 
$m _1u _1+ m _2u _2= m _1v _1+m _2v _2$
$\Rightarrow m\times 6-m\times 6=mv _1+ mv _2$
$\Rightarrow v _1=-v _2$
Coefficient , $e=-\dfrac{v _1-v _2}{u _1-u _2}$  $\Rightarrow \dfrac{1}{3}= -\dfrac{v _1-v _2}{6+6}$  $\Rightarrow v _1=-2 m/s$

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

Two particles of masses ${m} _{1}$ and ${m} _{2}$ in projectile motion have velocities ${v} _{1}$ and ${v} _{2}$ respectively at time $t=0$. They collide at time ${t} _{0}$. Their velocities become ${v'} _{1}$ and ${v'} _{2}$ at time $2{t} _{0}$ while still moving in air. The value of $\left[ \left( { m } _{ 1 }{ v' } _{ 1 }+{ m } _{ 2 }{ v' } _{ 2 } \right) -\left( { m } _{ 1 }{ v } _{ 1 }+{ m } _{ 2 }{ v } _{ 2 } \right)  \right] $

  1. zero
  2. $({m} _{1}+{m} _{2})g{t} _{0}$
  3. $2({m} _{1}+{m} _{2})g{t} _{0}$
  4. $\cfrac{1}{2}({m} _{1}+{m} _{2})g{t} _{0}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

External force = $F _{ext}=\dfrac{\Delta p}{\Delta t}=((m _{1}v _{1}^{'}+m _{2}v _{2}^{'})-(m _{1}v _{1}+m _{2}v _{2}))/2t _{0}-0$

$((m _{1}v _{1}^{'}+m _{2}v _{2}^{'})-(m _{1}v _{1}+m _{2}v _{2})=2t _{0}F _{ext}=2to(m _{1}+m _{2})g$

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

In a one dimensional collision between two identical particles A and B, B is stationary and A has momentum P before impact. During impact B gives an impulse J to A. Then coefficient of restitution between the two is

  1. $\dfrac { 2J }{ P } +1$
  2. $\dfrac { 2J }{ P } -1$
  3. $\dfrac { J }{ P } +1$
  4. $\dfrac { J }{ P } -1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$p=mu$
$u=\dfrac{P}{m}$
$p-J$
$=V _A=\dfrac{P-J}{m}$     $V _B=\dfrac{J}{m}$

$\therefore \dfrac{v _{sep}}{V _{app}=\dfrac{V _B-V _A}{u}}$

$=\dfrac{\left(\dfrac{J}{m}\right)-\left(\dfrac{P-J}{m}\right)}{\dfrac{P}{m}}$

$=\dfrac{2J-P}{P}$

$=\dfrac{2J}{P}-1$
Multiple choice collisions in one dimension collisions work, energy and power mechanics physics

A particle of mass m, is attached to one end of a massless spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0, with an initial velocity $u _0$. When the speed of the particle is $0.5\, u _0$, it collides elastically with a rigid walk. After this collision:

  1. The speed of the particle when it returns to its equilibrium position is $u _0$
  2. The time at which the particle passes through the equilibrium position for the first time is $t = \pi \sqrt{\dfrac{m}{k}}$
  3. The time at which the maximum compression of the spring occurs is $t = \dfrac{4\pi}{3}\sqrt{\dfrac{m}{k}}$
  4. The time at which the particle passes througout the equilibrium position for the second time is $t= \dfrac{4\pi}{3}\sqrt{\dfrac{m}{k}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In an elastic collision with a rigid wall, the particle reverses its velocity. Since the spring potential energy is conserved and the collision is elastic, the total energy remains constant. The particle will return to the equilibrium position with the same speed u0 it had initially.

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

A ball hits the floor and rebounds after an elastic collision. In this case:

  1. the momentum of the ball just after the collision is same as that just before the collision.

  2. the kinetic energy of the ball remains same during collision.

  3. the total momentum of the ball and the earth is conserved.

  4. the total energy of the ball and the earth remains the same.
Reveal answer Fill a bubble to check yourself
C,D Correct answer
Explanation

Since the velocity before and after the collision change hence momentum of the ball will change. So (a) is not true.  


Since the collision is inelastic a part of the mechanical energy is lost hence (b) is not true.  

Taking earth and the ball as a system there is no external force on the system. Hence the total momentum of the ball and the earth is conserved. So (c) is true.  

From the conservation principle of the energy, the total energy of the ball and the earth remains the same. Hence (d) is true.

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

Two identical spheres move in opposite direction with speed $v _1$ and $v _2$ and pass behind an opaque screen, where they may either cross without touching ( Event 1) or make an elastic head-on collision ( Event 2)

  1. We can never make out which events has occured
  2. We cannot make out which event has occured only if $v _1= v _2$

  3. We can always make out which event has occured

  4. We can make out which event has occured only if
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For identical spheres colliding elastically, they exchange velocities. If they cross without touching, they continue with their original velocities. If they collide, they also end up with the same final velocities as if they had passed through each other. Thus, the final state is indistinguishable.

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

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

  1. ${ 0 }^{ o }$
  2. ${ 45 }^{ o }$
  3. different from ${ 90 }^{ o }$
  4. ${ 90 }^{ o }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a perfectly inelastic collision between identical masses, the spheres stick together and move with a common velocity after collision. Since they combine and move as one object, they travel in the same direction, making the angle between their motion directions 0°.

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

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:

  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 $2 m/s$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For an elastic collision between identical masses where one is at rest, the particles move at 90 degrees to each other after the collision, provided the collision is not head-on.

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

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.

  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$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice collisions in one dimension collisions work, energy and power mechanics physics

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

  1. $zero$
  2. $60^{o}$
  3. $90^{o}$
  4. $180^{o}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In a head-on elastic collision between two bodies of equal mass, they exchange velocities. If the second body was at rest, the first body comes to rest and the second moves with the initial velocity of the first. The angle between them is 180 degrees if we consider the path of the first body after it stops (which is not applicable) or 0 degrees. However, in general 2D elastic collisions of equal masses, they move at 90 degrees. The option 180 degrees is likely a distractor or refers to a specific 1D case.