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

In Newton's formula, mass is a measure of the

  1. amount of matter in an object

  2. speed at which an object travels

  3. food a plant or animal must take in

  4. shape of a planet's path around the sun
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In physics, mass is defined as the measure of the amount of matter in an object, which is also related to its inertia.

Multiple choice chemistry matter in our surroundings diffusion in different states of matter properties of solids, liquid, and gas particle theory of matter

Elastic collisions transfer:

  1. a lot of energy

  2. moderate energy between particles

  3. no energy between particles

  4. none of above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

All collisions between the particles of matter are perfectly elastic. Elastic collisions transfer no energy between particles. Each particle has exactly the same energy after the collision as before.

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

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:

  1. $2.3\ ms^{-1}$
  2. $4.6\ ms^{-1}$
  3. $9.2\ ms^{-1}$
  4. $6\ ms^{-1}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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} $

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


$v = |\vec {v}| = \sqrt {1 + 4 + 16} = 4.6\ ms^{-1}$.
Multiple choice collisions in one dimension collisions work, energy and power mechanics physics

A ball P moving with a speed of $v \ ms^{-1}$ collides directly with another identical ball Q moving with a speed $10\ ms^{-1}$ in the opposite direction. P comes to rest after the collision. If the coefficient of restitution is 0.6, the value of $v$ is:

  1. $30\ ms^{-1}$
  2. $40\ ms^{-1}$
  3. $50\ ms^{-1}$
  4. $60\ ms^{-1}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation


As momentum is conserved, we can say,

$m(v-10)=mv _2$

$v _2=(v-10)$

$e=\dfrac{v _2-v _1}{u _1+u _2}=\dfrac{(v-10)-0}{(v+10)}$

$0.6=\dfrac{v-10}{v+10}$

$0.6v+6=v-10$

$0.4v=16$ 

$v=40\ ms^{-1}$

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

A particle of mass m moving with velocity ${u} _{1}$ collides elastically with particle of same mass moving with velocity ${u} _{2}$ in the same direction. After collision their speeds are ${v} _{1}$ and ${v} _{2}$ respectively then-
(A) ${ u } _{ 1 }+{ v } _{ 1 }={ v } _{ 2 }+{ u } _{ 2 }$
(B)${ u } _{ 1 }-{ v } _{ 1 }={ v } _{ 2 }+{ u } _{ 2 }$

  1. Both the equations A and B are correct

  2. Both the equations A and B are incorrect

  3. Equation A is correct but not B

  4. Equation B is correct but not A
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a 1D elastic collision between particles of equal mass, the particles simply exchange velocities. Thus, v1 = u2 and v2 = u1. Equation A (u1 + v1 = v2 + u2) becomes u1 + u2 = u1 + u2, which is correct. Equation B (u1 - v1 = v2 + u2) becomes u1 - u2 = u1 + u2, which is incorrect unless u2 = 0.

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

A particle of mass $1\ kg$ moving with a velocity of $(4\hat {i}-3\hat {j})m/s$ collides with a fixed surface. After the collision velocity of the particle is $(4\hat {i}-3\hat {j})m/s$. Collision is

  1. Elastic

  2. Ineleastic

  3. Perfectly inelastic

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

The velocity vector before collision is (4i - 3j) and after is (4i - 3j). Since the velocity vector is unchanged, the particle did not actually collide with the surface in a way that changed its motion. However, if the question implies the velocity component normal to the surface was reversed, it would be elastic. Given the options, elastic is the only one where kinetic energy is conserved.

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

Two masses $m _{1}$ and $m _{2}$, approaches each other with equal speeds and collide elastically. After collision $m _{2}$ comes to rest. Then $m _{1}$/$m _{2}$ is

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

For an elastic collision where m2 is at rest, the final velocity of m2 is v2' = (2*m1*u1)/(m1+m2). Since m1 and m2 approach with equal speeds u, the relative velocity is 2u. After collision, m2 is at rest, so v2' = 0. This implies m1 must have been moving in a way that cancels out, but for elastic collisions, m1/m2 = 1/2 is the standard result for specific energy transfer conditions.

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

Two identical balls each of mass in are moving in opposite direction with a speed v. if they collide elastically maximum potentail energy stored in the ball is :

  1. 0
  2. $\dfrac { 1 }{ 2 } { mv }^{ 2 }$
  3. ${ mv }^{ 2 }$
  4. $2{ mv }^{ 2 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Net momentum before collision will be $mv+(-mv)=0$, $negative$ because from $opposite $ direction.

so after the collision they will get stopped to make the net momentum again $zero$ and whole energy will be get stored
 as $PE$. ($inelastic $ $ collision$)

There is one other possibility too that is they $exchange$ their velocities so that again the net momentum will become
 $zero.$ $elastic$ $ collision$ .
In elastic collision there is no loss in $KE$  so $no$ storage of $PE.$


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

Two particles moving initially in the same direction undergo a one dimensional,elastic collision. Their relative velocities before and after the collision are $\overrightarrow { { v } _{ 1 } } $ and $\overrightarrow { { v } _{ 2 } } $. Then:

  1. $\left| \overrightarrow { { v } _{ 1 } } \right| = \left| \overrightarrow { { v } _{ 2 } } \right| $
  2. $\overrightarrow { { v } _{ 1 } } = - \overrightarrow { { v } _{ 2 } }$ only if the two are of equal mass.
  3. $\overrightarrow { { v } _{ 1 } } = -\overrightarrow { { v } _{ 2 } } = {\left| \overrightarrow { { v } _{ 1 } } \right|}^{2}$
  4. $\left| \overrightarrow { { v } _{ 1 }} . \overrightarrow { { v } _{ 2 }} \right| = - {\left| \overrightarrow { { v } _{ 1 } } \right|}^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In an elastic collision, the relative velocity of separation is equal to the negative of the relative velocity of approach. Thus, v_rel_after = -v_rel_before. This is expressed as the dot product of the relative velocity vectors being the negative square of the magnitude of the initial relative velocity.

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

The coefficient of restitution of a perfectly elastic collision is :

  1. $1$
  2. $0$
  3. $\infty$
  4. $-1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Coefficent of Restitution is a measure of the "bounciness" of a collision between two objects: how much of the kinetic energy remains for the objects to rebound from one another vs. how much is lost as heat, or work done deforming the objects.

The coefficient, e is defined as the ratio of relative speeds after and before an impact, taken along the line of the impact:
$e=\dfrac { Speed\quad of\quad separation }{ Speed\quad of\quad approach } $

(i)   For perfectly elastic collision $e = 1$
(ii)  For perfectly inelastic collision $e = 0$
(iii) For other collision $0 \lt e \lt 1$

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

A ball moving with a velocity v strikes a wall moving toward the ball with a velocity u. An elastic impact lasts for t sec. Then the mean elastic force acting on the ball is 

  1. $\displaystyle \frac { 2mv }{ t } $
  2. $\displaystyle \frac { 2m\left( \upsilon +u \right) }{ t } $
  3. $\displaystyle \frac { 2m\left( \upsilon +2u \right) }{ t } $
  4. $\displaystyle \frac { m\left( 2\upsilon +u \right) }{ t } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Relative speed of the ball $\displaystyle =\left( \upsilon +u \right) $
Speed after rebouncing $\displaystyle =-\left( \upsilon +u \right) $
Now, $\displaystyle F=m\frac { \Delta \upsilon  }{ \Delta t } =\frac { m }{ t } \left[ \left( \upsilon +u \right)  \right] -[-\left[ \left( \upsilon +u \right)  \right]] $
$\displaystyle =\frac { 2m }{ t } \left( \upsilon +u \right) $

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

A ball with mass m and speed $V _0$ hit a wall and rebounds back with same speed.
Calculate the change in the object's kinetic energy.

  1. $-mv _0 ^2$
  2. $- \frac{1}{2}mv _0 ^2$

  3. Zero
  4. $ \frac{1}{2}mv _0 ^2$
  5. $mv _0 ^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The speed of the ball remains the same $v _0$ before and after the collision with wall.

Thus the kinetic energy remains $\dfrac{1}{2}mv _0^2$.
Since kinetic energy is a scalar quantity, the change in it is zero.

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

 A body of mass $m$ moving at a constant velocity $v$ hits another body of the same mass moving at the same velocity but in the opposite direction and sticks to it. The common velocity after collision is

  1. $v$
  2. $0$
  3. $2v$
  4. $\dfrac{v}{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the collision is inelastic, applying momentum conservation for inelastic collisions,
$ mv + m(-v) = (m+m)V $
$ V = 0 $.