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

In one - dimensional head on collision, the relative velocity of approach before collision is equal to :

  1. relative velocity of separation after collision
  2. $e$ times relative velocity of separation after collision
  3. $1/e$ times relative velocity of separation after collision

  4. sum of the velocities after collision
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Coefficient of restitution is given by,

$e = \dfrac{\text{velocity of separation along line of impact}}{\text{Velocity of approach line of impact}}$

$\therefore e = \dfrac{v _2-v _1}{u _1- u _2}$

$\therefore u-1 - u _2 = \dfrac{1}{e} (v _2-v _1)$

$\therefore$ option C is correct.

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

A body of mass 'm' moving with certain velocity collides with another identical body at rest. If the collision is perfectly elastic and after the collision, if both the bodies move, they can move

  1. in the same direction

  2. in opposite direction

  3. in perpendicular direction
  4. making $45^o$ to each other
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Make your co-ordinate axes such that 1 is along the line joining the centres of the 2 just at time on collision and one, tangential. Now consider the velocity of the coming ball in 2 components of the coordinate axes we just assumed, say vn and vt(v-normal and v-tangential). Now during collision, v-tangential can't change as there is no impact along this direction. And collision along normal is just like collision in 1-D. The equations are exactly same. Hence the 1st particle will have 0 velocity along normal and second will move along normal. Hence, they'll move perpendicular to each other. 

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

 A marble going at a speed of $12 ms^{-1}$ hits another marble of equal mass at rest. If the collision is perfectly elastic. Find the velocity of the first after collision.

  1. $4$
  2. $0$
  3. $2$
  4. $3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$m(12)+m(0)=m{ v } _{ 1 }+m{ v } _{ 2 }=0\Rightarrow { v } _{ 1 }+{ v } _{ 2 }=12\ $
$-\dfrac { { v } _{ 1 }-{ v } _{ 2 } }{ 12-(0) } =1\Rightarrow { v } _{ 1 }-{ v } _{ 2 }=-12\ $
$thus,\quad { v } _{ 1 }=0\ { v } _{ 2 }=12,\quad so\quad velocity\quad of\quad first\quad after\quad collision\quad is\quad 0.$

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

N identical balls are placed on a smooth horizontal surface. Another ball of same mass collides elastically with velocity $u$ with first ball of N balls. A process of collision is thus started in which first ball collides with second ball and the second ball with the third ball and so on. The coefficient of resulting for each collision is $e$. Find speed of Nth ball :

  1. $(1+e)^{N}u$
  2. $u(1+e)^{N-1}$
  3. $\cfrac{u(1+e)^{N-1}}{2^{N-1}}$
  4. $u^{N}(1+e)^{N-1}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a series of collisions, the velocity of the nth ball is multiplied by a factor related to the coefficient of restitution e for each collision.

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

A neutron moving with velocity u collides with a stationary $\alpha -particle$ The velocity of the neutron after collision is 

  1. $-\dfrac { 3\cup }{ 5 } $
  2. $\dfrac { 3\cup }{ 5 } $
  3. $\dfrac { 2\cup }{ 5 } $
  4. $-\dfrac { 2\cup }{ 5 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Mass of alpha particle is $4$ times to neutron 
according to the condition alpha paticle is at rest so its velocity is zero
now the final velocity of neutron is calculated from this formula
$U' = (m-1-m _2÷ m _1+m _2) U^1$
by putting$,$ 
$U' = (1-4÷1+4) $
$= -3U/5 $
Negative sign shows reverse direction of neutro$.$
Hence,
option $(A)$ is correct answer.

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

The principle of conservation of linear momentum can be strictly applied during a collision between two particles provided the time of impact is

  1. Extremely small

  2. Moderately small

  3. Extremely large

  4. Depends on a particular case
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The principle of conservation of linear momentum can be strictly applied during a collision between two particles provided the time of impact is  $Moderately\,\,small.$

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

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The percentage error in the measurement of mass and speed are 2% and 3% respectively. The maximum percentage error in the estimation of kinetic energy of a body will be:

  1. 11%

  2. 8%

  3. 5%

  4. 1%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$K.E = \dfrac{1}{2}mv^{2}$


$ \dfrac{\triangle K.E}{K.E} =

\dfrac{\triangle m}{m} + 2 \dfrac{\triangle v}{v}$

              $ = 2+2(3) = 8$%

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

If the error in measurement of momentum of a particle is $10$% and mass is known exactly,the permissible error in the determination of kinetic energy is

  1. $20$%
  2. $5$%
  3. $21$%
  4. $10$%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Kinetic energy K = p^2 / (2m). Since mass is constant, dK/K = 2 * dp/p. With dp/p = 10%, dK/K = 2 * 10% = 20%.

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The speed of a body is measured with a positive error of 30%. If the mass of the body is known exactly, the kinetic energy is calculated with an error of

  1. $60$%
  2. $30$%
  3. $69$%
  4. $39$%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Kinetic energy K = (1/2)mv^2. Since mass is constant, dK/K = 2 * dv/v. Given dv/v = 30%, dK/K = 2 * 30% = 60%.

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

Percentage error in the measurement of mass and speed are 2% and 3% respectively. The error in the estimate of kinetic energy obtained by measuring mass and need will be

  1. 12%

  2. 10%

  3. 8%

  4. 2%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given percentage errors in mass and velocity = $2$% and $3$% respectively


The kinetic energy of the particle is given by 


$KE$ = $\dfrac { m{ v }^{ 2 } }{ 2 } $

The percentage error in kinetic energy will be

$\dfrac { \Delta m }{ m } \times 100\quad +\quad 2\dfrac { \Delta v }{ v } \times 100$

= $2 + 6$

= $8$% 

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

A body of mass $m =3.513\ kg$ is moving along the x-axis with a speed of $5.00{ ms }^{ -1 }$. The magnitude of its momentum is recorded as :

  1. $17.56\ kg{ ms }^{ -1 }$
  2. $17.57\ kg{ ms }^{ -1 }$
  3. $17.6\ kg{ ms }^{ -1 }$
  4. $17.565\ kg{ ms }^{ -1 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Momentum$=mv=3.513\times 5.00=17.565\approx 17.57$
$\approx 17.6 kg m/s$
(Since 5.00 contains  least no. of significant figures i.e. 3)

Multiple choice

The coefficient of restitution is a measure of the:

  1. Elasticity of a collision

  2. Inelasticity of a collision

  3. Momentum of a collision
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The coefficient of restitution is a dimensionless quantity that measures the elasticity of a collision. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach of the colliding objects. A coefficient of restitution of 1 indicates a perfectly elastic collision, while a coefficient of restitution of 0 indicates a perfectly inelastic collision.

Multiple choice

What is the formula for the kinetic energy of an object?

  1. \(KE = \frac{1}{2} mv^2\)
  2. \(KE = mv\)
  3. \(KE = \frac{1}{2} m^2v\)
  4. \(KE = \frac{1}{2} v^2\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for the kinetic energy of an object is (KE = \frac{1}{2} mv^2), where (m) is the mass of the object and (v) is its velocity.

Multiple choice

What is the formula for calculating kinetic energy?

  1. $KE = rac{1}{2}mv^2$
  2. $KE = mv$
  3. $KE = m^2v$
  4. $KE = rac{1}{2}m^2v^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Kinetic energy (KE) is calculated using the formula $KE = rac{1}{2}mv^2$, where 'm' is the mass of the object and 'v' is its velocity.