Physics · Science General

Collisions, Momentum and Kinetic Energy

331 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

A steel ball moving with a velocity $\overline{v}$ collides with an identical ball originally at  rest. The velocity of the first ball after the collision is :

  1. $\left(-\dfrac{1}{2}\right)\overline{v}$
  2. $-\overline{v}$
  3. $\overline{v}$

  4. zero
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Here, a steel ball moving with a velocity $\bar v$ collides with an identical ball originally at  rest. hence, masses of two steel balls are equal. For a head-on collision with a stationary object of equal mass, the projectile will come to rest and the target will move off with equal velocity, thus, the velocity of the first ball after the collision is zero.

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

In the elastic collision of heavy vehicle moving with a velocity 10 ms$^{-1}$ and a small stone at rest, the stone will fly away with a velocity equal to : 

  1. 40 ms$^{-1}$
  2. 20 ms$^{-1}$
  3. 10 ms$^{-1}$
  4. 5 ms$^{-1}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In the elastic collision between a heavy object and a very light object at rest, the velocity of particles after collision is 
for heavy particle, $v _1 = u _1$
for light particle, $v _2 = 2u _1 - u _2$
since, $u _2 = 0$ hence, 
$v _2 = 2u _1$
Therefore, the stone will fly away with a velocity equal to 
$v _2 = 2u _1 = 2(10) = 20 ms^{-1}$

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

Two particles of masses $ {m} _{1}, {m} _{2} $ movie with initial velocities $ u _{1} \text { and } u _{2} $.On collision, one of the particles get excited to higher level, after absorbing energy If final velocities of particles be $  v _{1}  $ and $  v _{2}  $ then we must have :

  1. $
    \dfrac{1}{2} m _{1} u _{1}^{2}+\dfrac{1}{2} m _{2} u _{2}^{2}=\dfrac{1}{2} m _{1} v _{1}^{2}+\dfrac{1}{2} m _{2} v _{2}^{2}-\varepsilon
    $
  2. $
    \dfrac{1}{2} m _{1} u _{1}^{2}+\dfrac{1}{2} m _{2} u _{2}^{2}+\varepsilon=\dfrac{1}{2} m _{1} v _{1}^{2}+\dfrac{1}{2} m _{2} v _{2}^{2}
    $
  3. $
    \dfrac{1}{2} m _{1}^{2} u _{1}^{2}+\dfrac{1}{2} m _{2}^{2} u _{2}^{2}-\varepsilon=\dfrac{1}{2} m _{1}^{2} v _{1}^{2}+\dfrac{1}{2} m _{2}^{2} v _{2}^{2}
    $
  4. $
    m _{1}^{2} u _{1}+m _{2}^{2} u _{2}-\varepsilon=m _{1}^{2} v _{1}+m _{2}^{2} v _{2}
    $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\begin{array}{l} Total\, \, initial\, \, energy\, \, of\, \, two\, \, particles \ =\frac { 1 }{ 2 } { m _{ 1 } }{ u _{ 1 } }^{ 2 }+\frac { 1 }{ 2 } { m _{ 2 } }{ u _{ 2 } }^{ 2 } \ Total\, \, final\, \, energy\, \, of\, \, two\, particles \ =\frac { 1 }{ 2 } { m _{ 1 } }{ v _{ 1 } }^{ 2 }+\frac { 1 }{ 2 } { m _{ 2 } }{ v _{ 2 } }^{ 2 }+\in  \ U\sin  g\, \, energy\, \, conservation\, \, principle, \ \frac { 1 }{ 2 } { m _{ 1 } }{ u _{ 1 } }^{ 2 }+\frac { 1 }{ 2 } { m _{ 2 } }{ u _{ 2 } }^{ 2 }=\frac { 1 }{ 2 } { m _{ 1 } }{ v _{ 1 } }^{ 2 }+\frac { 1 }{ 2 } { m _{ 2 } }{ v _{ 2 } }^{ 2 }+\in  \ \therefore \frac { 1 }{ 2 } { m _{ 1 } }{ u _{ 1 } }^{ 2 }+\frac { 1 }{ 2 } { m _{ 2 } }{ u _{ 2 } }^{ 2 }-\in =\frac { 1 }{ 2 } { m _{ 1 } }{ v _{ 1 } }^{ 2 }+\frac { 1 }{ 2 } { m _{ 2 } }{ v _{ 2 } }^{ 2 } \end{array}$

Hence,
option $(C)$ is correct answer.

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

A moving sphere of mass m suffer a perfect elastic collision (not head on) with an  equally massive stationary sphere. after collision both fly off at angle $\theta $ value of which is :

  1. 0
  2. $\pi $

  3. indeterminate
  4. $\pi /2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For an elastic collision between two equal masses where one is initially at rest, the angle between the final velocity vectors is always 90 degrees (pi/2).

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

 A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly- elastic collision with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg ball is 6 J. The possible value of m is/are :

  1. 1 kg only

  2. 1 kg , 9kg

  3. 1 kg, 6kg

  4. 6kg only
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial kinetic energy of the 3 kg ball is (1/2)3(4)^2 = 24 J. After an elastic collision, its kinetic energy is 6 J. Using the conservation of kinetic energy and momentum for an elastic collision in 1D, the final speed of the 3 kg mass can be found, leading to possible mass values of m = 1 kg or m = 9 kg.

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

In an elastic collision the K.E of one body decreases by $100 J$. If the masses colliding bodies are in the ratio 3:4 the K.E of the other body increase by 

  1. $\dfrac{400}{3} J$
  2. $\dfrac{500}{3} J$
  3. $100 J$
  4. $0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In any isolated system undergoing an elastic collision, total kinetic energy is conserved. Thus, the decrease in kinetic energy of one body must equal the increase in kinetic energy of the other body. Since one body loses 100 J, the other body gains exactly 100 J, regardless of their mass ratio.

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

Two identical balls  $A$  and  $B$  having velocities of  $0.5\mathrm { m } / \mathrm { s }$  and  $- 0.3 \mathrm { m } / \mathrm { s }$  respectively collide elastically in one dimension. The velocities of  $B$  and  $\mathrm { A }$  after the collision respectively will be

  1. $0.3 \mathrm { m } / \mathrm { s } \text { and } 0.5 \mathrm { m } / \mathrm { s }$
  2. $- 0.5 \mathrm { m } / \mathrm { s } \text { and } 0.3 \mathrm { m } / \mathrm { s }$
  3. $0.5 \mathrm { m } / \mathrm { s } \text { and } - 0.3 \mathrm { m } / \mathrm { s }$
  4. $- 0.3 \mathrm { m } / \mathrm { s } \text { and } 0.5 \mathrm { m } / \mathrm { s }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When two identical masses collide elastically in one dimension, they simply exchange their velocities. Since A starts at 0.5 m/s and B at -0.3 m/s, after the collision, A will have -0.3 m/s and B will have 0.5 m/s.

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

A particle of mass $ m _1 $ hits another particle of mass $ m _2 $ at rest with a velocity $ \overrightarrow { u }  $. The collision is head-on and elastic.If $ m _1 >> m _2 $, then after collision, the velocity of $ m _2 $ will be-

  1. $ \overrightarrow { u } $
  2. $ - \overrightarrow { u } $
  3. $ 2 \overrightarrow { u } $
  4. $ -2 \overrightarrow { u } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a head-on elastic collision where a very massive body (m1) hits a stationary light body (m2), the velocity of the light body after the collision is twice the velocity of the incident massive body.

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

Which of the following does no undergo elastic collision?

  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 $ is stationary,there is minimum transfer of momentum in head on collision
  3. When $ m _1 >> 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.
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 sphere P of mass m and  velocity $\underset{V _{1}}{\rightarrow}$  undergoes an oblique and perfectly elastic collision with an identical sphere Q initially at rest.  The  angle $\Theta $  between the velocites of the spheres after the collision shall be

  1. 0
  2. $45^{\circ}$
  3. $90^{\circ}$
  4. $180^{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a perfectly elastic collision between two identical masses where one is initially at rest, the two bodies will move at an angle of 90 degrees to each other after the collision, provided the collision is oblique.

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

A neutron collides head-on with a stationary hydrogen atom $( _1H^1)$ in ground state, then choose the correct statement (assume that mass of neutron and mass of $( _1H^1)$ atom is same)

  1. If kinetic energy of the neutron is less than $13.6eV$, collision must be elastic
  2. If kinetic energy of the neutron is less than $13.6eV$, collision must be inelastic
  3. Inelastic collision may take place only when initial kinetic energy of neutron is greater than $13.6eV$

  4. Perfectly inelastic collisin cannot take place.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If the kinetic energy of the neutron is less than the excitation energy of the hydrogen atom (13.6 eV), the collision cannot result in internal energy changes, so it must be elastic to conserve energy and momentum.

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

Choose the correct statements from the following :

  1. the general form of Newton's second law of motion is $\vec{F} _{ext} = \vec m a$.

  2. a body can have energy and get no momentum.

  3. a body having momentum must necessarily have kinetic energy.

  4. the relative velocity of two bodies in a head-on elastic collision remains unchanged in magnitude and direction.
Reveal answer Fill a bubble to check yourself
B,C Correct answer
Explanation

General form of 2nd law is $\vec { { F } _{ ext } } =m\vec { { a } _{ COM } } $
A body can have potential energy.
$KE=\dfrac { { p }^{ 2 } }{ 2m } $, so if a body has momentum it must have KE
its a fact that relative velocity in any type of collision changes in direction.

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

A point mass $M$ moving with a certain velocity collides with a stationary point mass $\dfrac{M}{2}$. The collision is elastic and one dimension. Let the ratio of the final velocities of $M$ and $\dfrac{M}{2}$ be $x$. The value of $x$ is :

  1. $2$
  2. $3$
  3. $\dfrac{1}{2}$
  4. $\dfrac{1}{4}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$v _1=\dfrac{\left(M-\dfrac{M}{2}\right)}{\left(M+\dfrac{M}{2}\right)}u _1=\dfrac{u _1}{3}$


$\therefore v _2=\dfrac{4u _1}{3}$


$\therefore \dfrac{v _1}{v _2}=\dfrac{1}{4}$