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 modelling collisions collisions momentum work, energy and power physics

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 :

  1. elastic

  2. inelastic

  3. perfect inelastic

  4. none
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

Multiple choice modelling collisions collisions momentum work, energy and power physics

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 

  1. 1 : e

  2. e : 1
  3. $1 : e^3$
  4. $e^2 : 1 $
Reveal answer Fill a bubble to check yourself
D Correct answer
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$

Multiple choice modelling collisions collisions momentum work, energy and power physics

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 

  1. $30 ^ { \circ }$
  2. $60 ^ { \circ }$
  3. $90 ^ { \circ }$
  4. $120 ^ { \circ }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a perfectly inelastic collision of equal masses m, m*v1 + m*v2 = 2*m*v_final. If v_final = v/2, then v1 + v2 = v. This implies the angle between the initial velocity vectors must be 90 degrees.

Multiple choice modelling collisions collisions momentum work, energy and power physics

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?

  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
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Nothing is mentioned about coefficient of restitution. 

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

Multiple choice evs - i substances, objects and energy renewable resources alternative fuels and energy sources alternative sources of energy

A 200 gm mass has velocity of $(3\hat i+4\hat j)$m/s at certain instant. Find its kinetic energy. 

  1. $2.5 J$
  2. $0.5 J$
  3. $0.8 J$
  4. $1.5 J$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

First we will calculate the Magnitude of velocity  so $v=\sqrt{3^2+4^2}=5\ m/s$

Now m=200 gm or 0.2 kg

So $KE=\dfrac{mv^2}{2}=\dfrac{0.2\times 5^2}{2}$

so $KE=2.5\ J$

Multiple choice physics along with motion what forces can do? force and it's unit force and its effects

Choose the wrong statement:

  1. 1 kg wt = 9.8 N

  2. Momentum is a vector quantity.

  3. Force is always conserved.

  4. Momentum is conserved in the absence of an external force.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$ 1kg-wt = 1 \times 9.8 N $ 

$ momentum = mass \times velocity $ As velocity is vector, momentum is vector.
Friction is non conservative force.
According to Newton's second law, rate of change of momentum is directly proportional to applied force.
So,if force is zero, momentum is conserved.
So wrong statement is option C.

Multiple choice physics along with motion what forces can do? force and it's unit force and its effects

Two bodies of masses ${m} _{1}$ and ${m} _{2}$ are acted upon by a constant force $F$ for a time $t$. They start from rest and acquire kinetic energies ${E} _{1}$ and ${E} _{2}$ respectively. Then $\dfrac{{E} _{1}}{{E} _{2}}$ is

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

Bodies of mass $m _1$ and $m _2$ acted on by force F (say) for time t. Acceleration in mass $m _1$= $\dfrac{F}{m _1}$
Acceleration in mass $m _2$= $\dfrac{F}{m _2}$
Velocity acquired during this time for mass $m _1$
$v _1=\dfrac{F}{m _1} t$
Velocity acquired during this time for mass $m _2$
$v _2=\dfrac{F}{m _2} t$

Ratio of kinetic energy acquired
$\dfrac{E _1}{E _2}=\dfrac{\dfrac{1}{2}m _1v _1^2}{\dfrac{1}{2}m _2v _2^2}$
$\dfrac{E _1}{E _2}=\dfrac{m _1\times (\dfrac{F}{m _1} t)^2}{m _2\times (\dfrac{F}{m _2} t)^2}$
$\dfrac{E _1}{E _2}=\dfrac{m _2}{m _1}$

Multiple choice physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

 Two bodies of different masses have same K.E. The one having more momentum is

  1. Heavier body

  2. lighter body

  3. both none

  4. both
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$K.E.$ for a given momentum is inversely proportional to the mass$.$

So$,$ the lighter mass has greater kinetic energy$.$ For two bodies having same kinetic energy$,$ the heavier one has greater momentum$.$
Hence,
option $(B)$ is correct answer.  

Multiple choice physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

A stationary body explodes into two fragments of masses ${m} _{1}$ and ${m} _{2}$. If momentum of one fragment is $p$, the minimum energy of explosion is

  1. $\cfrac { { p }^{ 2 } }{ 2\left( { m } _{ 1 }+{ m } _{ 2 } \right) } $
  2. $\cfrac { { p }^{ 2 } }{ 2\left( \sqrt { { m } _{ 1 }{ m } _{ 2 } } \right) } $
  3. $\cfrac { { p }^{ 2 }\left( { m } _{ 1 }+{ m } _{ 2 } \right) }{ 2{ m } _{ 1 }{ m } _{ 2 } } $
  4. $\cfrac { { p }^{ 2 } }{ 2\left( { m } _{ 1 }-{ m } _{ 2 } \right) } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initially body is stationary (zero velocity)

using conservation of momentum
$\left( A \right) O=P+{ P _{ 2 } },{ P _{ 2 } }$ is momentum of mass ${m _2}$ after explosion
$\begin{array}{l} { P _{ 2 } }=-P \ Energy={ E _{ 1 } }\Rightarrow \dfrac { { { P^{ 2 } } } }{ { 2{ m _{ 1 } } } } d{ E _{ 2 } }=\dfrac { { { { \left( { -P } \right)  }^{ 2 } } } }{ { 2{ m _{ 2 } } } }  \ net\, \, energy\Rightarrow { E _{ 1 } }+{ E _{ 2 } }=\dfrac { { { P^{ 2 } } } }{ { 2{ m _{ 2 } } } } +\dfrac { { { P^{ 2 } } } }{ { 2{ m _{ 2 } } } } \Rightarrow \dfrac { { { P^{ 2 } } } }{ { 2\left( { { m _{ 1 } }+{ m _{ 2 } } } \right)  } }  \end{array}$

Multiple choice physics the essence of change different forms of energy energy conversions energy transformations and energy transfers

A body off mass $5kg$ falls from a height of $30metre$. If its all mechanical energy is changed into heat, then heat produced will be 

  1. $ \text{350 cal} $
  2. $ \text{150 cal} $
  3. $ \text{60 cal} $
  4. $ \text{6 cal} $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Potential energy = mgh = 5 * 9.8 * 30 = 1470 Joules. Since 1 calorie is approximately 4.2 Joules, 1470 / 4.2 = 350 calories.

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

Using $E = m{c}^{2}$, find out the energy released, when $2  u$ of mass is destroyed completely.
Take $1  u = 1.66 \times {10}^{-27}  kg$.

  1. $4.65 MeV$
  2. $3627 MeV$
  3. $91.5 MeV$
  4. $1865 MeV$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
When $2u$ of mass is destroyed completely then
$\triangle m=2u\\ E=\triangle m{ c }^{ 2 }\\ E=2\times 931MeV\\ \therefore 1u=931Mev/{ c }^{ 2 }\\ So,E=1863MeV\approx 1865MeV$
So, (D) is correct option.
Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

Energy released if mass of $2\ amu$ is converted into energy is :

  1. $1.5 \times 10^{-10}\ J$
  2. $3 \times 10^{-10}\ J$
  3. $1863\ J$
  4. $931.5 \Mev$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$ E = \Delta m c^{2}$
    $ = (2 \times 1.67 \times 10^{-27}  kg) \times (3 \times 10^{8} \frac{m}{s})^{2} $
    $ = 3 \times 10^{-10}  J$