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

A bullet of mass m is fired into a large block of wood of mass M with velocity v. The final velocity of the system is?

  1. $\left(\dfrac{m}{M-m}\right)v$

  2. $\left(\dfrac{m+M}{M}\right)v$

  3. $\left(\dfrac{M-m}{M}\right)v$

  4. $\left(\dfrac{m}{m+M}\right)v$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

u is initial velocity 

v is finall velocity 
m1 is m 
m2 is M 
u1 is v 
u2 is 0 
${ v } _{ 1 }={ v } _{ 2 }={ v } _{ 3 }$
$total\quad initial\quad momentum=finall\quad momentum$
${ m } _{ 1 }{ u } _{ 1 }+{ m } _{ 2 }{ u } _{ 2 }={ m } _{ 1 }{ v } _{ 1 }+{ m } _{ 2 }{ v } _{ 2 }$
$mv+M\times 0=m{ v } _{ 3 }+{ Mv } _{ 3 }$
$mv=\left( m+M \right) { v } _{ 3 }$
${ v } _{ 3 }=\dfrac { mv\quad  }{ m+M } $

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.

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

Two solid balls of rubber $A$ and $B$ whose masses are $200\ gm$ and $400\ gm$ respectively, are moving in mutually opposite directions. if the velocity of ball A is $0.3\ m/s$ and both the ball come to rest after collision, then the velocity of ball $B$ is :

  1. $0.15\ m/s$

  2. $-0.15\ m/s$

  3. $1.5\ m/s$

  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Initial linear momentum of system 

$= [{{m} _{A}}{{\vec{v}} _{A}}+{{m} _{B}}{{\vec{v}} _{B}}]$

$= 0.2 \times  0.3 + 0.4 \times  vB$

Finally both balls come to rest \ final linear momentum = 0 

By the law of conservation of linear momenum        

$0.2 \times  0.3 + 0.4 \times  vB = 0$

$[{{v} _{B}}=-\dfrac{0.2\times 0.3}{0.4}=-0.15\ m/s]$
Multiple choice collisions in one dimension collisions work, energy and power mechanics physics

Two billiard balls undergo a head-on collision. Ball 1 is twice as heavy as ball 2. Initially, ball 1 moves with a speed $v$ toward ball $2$ which is at rest. Immediately after collision, ball 1 travels at a speed of $v/3$ in the same direction. What type of collision has occured?

  1. inelastic

  2. elastic

  3. completely inelastic

  4. cannot be determined from the information given
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solving the equation of conservation of momentum give us that the relative velocity of approach is equal to the relative velocity of separation. Hence coefficient of restitution is 1.
Which means collision is elastic. 

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

The collision of two balls of equal mass takes place at the origin of coordinates. Before collision, the components of velocities are $(V _x = 50 c m s^{-1},  V _{y} = 0)$ and $(V _{x} = -40 c m s^{-1}$ and $V _{y} = 30 c m s^{-1})$. The first ball comes to rest after collision. The velocity (components $V _{x}$ and $V _{y}$ respectively) of the second ball are

  1. 10 and 30 $c m s^{-1}$

  2. 30 and 10 $c m s^{-1}$

  3. 5 and 15 $c m s^{-1}$

  4. 15 and $5 c m s^{-1}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice collisions in one dimension collisions work, energy and power mechanics physics

Which of the following does not hold when two particles of masses $m _1$ and $m _2$ 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 $m _1=m _2$ and $m _2$ is stationary , there is maximum transfer of momentum in head on collision

  3. when $m _1 >> m _2$ and $m _2$ 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
Explanation

When m1 = m2 and m2 is stationary, the first particle transfers all its kinetic energy to the second particle in a head-on collision. This is the maximum possible transfer.