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

A ball of mass $m$ moving with velocity $v$ collides elastically with another ball of identical mass coming from opposite direction with velocity $2v$. Their velocities after collision will be :

  1. $-v,2v$

  2. $-2v,v$

  3. $v,-2v$

  4. $2v,-v$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$mv-2mv=mv _{1}+mv _{2}$
$-v=v _{1}+v _{2}$...........(1)

and $\dfrac{v _{2}-v _{1}}{v+2v}=1\Rightarrow v _{2}-v _{1}=3v$............(2)
Solving eqs. $(i)$ and $(ii)$,
$v _{2}-v _{1}=3v$
$\dfrac{v _{2}+v _{1}=-v}{2v _{2}=2v}$
$\therefore v _{2}=v$ and $-v _{1}=2v\therefore v _{1}=-2v$

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

Two solid rubber balls $A$ and $B$ having masses $200\ g$ and $400\ g$ respectively are moving in the opposite direction. A velocity of $A$ which is equal to $0.3\ m/s$. After the collision the two balls come to rest when the velocity of $B$ is 

  1. $0.15\ m/s$

  2. $1.5\ m/s$

  3. $-0.15\ m/s$

  4. $none\ of\ these$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From conservation of linear momentum:

               $P _i=P _f$                  $(P _f=0)$

$m _{A}v _{A}+m _{B}v _{B}=0$
$v _{B}=-\dfrac{m _{A}v _{A}}{m _{B}}=-\dfrac{200\times 10^{-3}\times 0.3}{400\times 10^{-3}}$
$V _B=-\dfrac{60}{400}=-0.15$

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

A ball of mass m moving with velocity v collides elastically with another ball of identical mass coming from the opposite direction with velocity 2v. Their velocities after collision are :

  1. $-v,:2v$

  2. $-2v,:v$

  3. $v,:-2v$

  4. $2v,:-v$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When bodies of same mass collide head on elastically then after collision they exchange their velocities.

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

A sphere $'P'$ of mass $'m'$ moving with velocity $'u'$ collides head-on with another sphere $'Q'$ of mass $'m'$ which is at rest. The ratio of final velocity of $'Q'$ to initial velocity of $'P'$ is
($e =$ coefficient of restitution)

  1. $\dfrac{e-1}{2}$

  2. ${\left[\dfrac{e+1}{2}\right]}^{{1}/{2}}$

  3. $\dfrac{e+1}{2}$

  4. ${\left[\dfrac{e+1}{2}\right]}^{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Here,  ${m} _{1} = {m} _{2} = m$,     ${u} _{1} = u$,    ${u} _{2} = 0$
Let ${v} _{1},   {v} _{2}$ be their velocities after collision.
According to principle of conservation of linear momentum
$mu + 0 = m\left({v} _{1}+{v} _{2}\right)$
or   ${v} _{1} + {v} _{2} = v$       ....(i)
By definition,   $e = \dfrac{{v} _{2} - {v} _{1}}{u-0}$
or   ${v} _{2} - {v} _{1} = eu$      .....(ii)
Adding equations (i) and (ii), we get
${v} _{2} = \dfrac{u\left(1+e\right)}{2}    \Rightarrow    \dfrac{{v} _{2}}{u} = \dfrac{1+e}{2}$

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

If two balls each of mass 0.06 kg moving in opposite directions with speed of $4\, m\, s^{-4}$ collide and rebound with same speed, then the impulse imparted to each ball due to other is:

  1. $0.48\, kg\, m\,s^{-1}$

  2. $0.53\, kg\, m\,s^{-1}$

  3. $0.8\, kg\, m\,s^{-1}$

  4. $0.92\, kg\, m\,s^{-1}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mass = $0.06kg$


Velocity= $4 m/s$

Rebound velocity = $-4 m/s$

Impulse = change in momentum 

Impulse = $m (u) – m (v)$

Impulse = $0.06 \times 4 – (0.06 \times -4) $

Impulse = $0.24 – (-0.24)$

Impulse = $0.24+0.24$


Impulse = $0.48kgm/s$

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

 A ball of mass '$M$' moving with a velocity $\overrightarrow{V}$ collides head on elastically with another body of the same mass    '$M$' moving with a velocity $-\overrightarrow{V}$ in the opposite direction. After the collision :

  1. The velocities are exchanged by the two balls

  2. Both the balls come to rest

  3. Both of them move at right angles to the original line of motion

  4. One ball comes to rest and the other ball travels back with a velocity $2v$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since the collision is elastic, we know that when two bodies of same mass have an elastic collision their velocities get interchanged.
$m _1u _1+m _2u _2=m _1v _1+m _2v _2$


But $m _1=m _2=M,   u _1=V,   u _2=-V$

$\Rightarrow MV-MV=Mv _1+Mv _2$

$\Rightarrow v _1+v _2=0$.............(1)

The coefficient of restitution $(e)$ is given by,

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


But for elastic collision,  $e=1$

$-\dfrac{v _1-v _2}{V+V}=1$

$\Rightarrow v _2-v _1=2V$..............(2)

From (1) and (2), we get,
$v _2=V$
$v _1=-V$

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

 A heavy steel ball of mass greater than 1 kg moving with a speed of 2m/ s collides head on with a stationary ping pong ball of mass less than 0.1 g. The collision is elastic. After the collision the ping pong ball moves approximately with a speed

  1. $ 2 m / s $

  2. $4 m/ s$

  3. $2\times10^{4}m / s$

  4. $2\times10^{3}m / s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the body is much heavy these won't be much change in velocity
& $e = 1$


i.e., $\dfrac{v-2}{0-2} = -1$

$\Rightarrow v = 4 m/s$

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

Consider the following statements A and B. Identify the correct choice in the given answer

 A : In a one - dimensional perfectly elastic collision between two moving bodies of equal masses, the  bodies merely exchange their velocities after collision

 B : If a lighter body at rest suffers perfectly elastic collision with a very heavy body moving with a certain velocity, after collision both travel with same velocity

  1. A and B are correct

  2. Both A and B are wrong

  3. A is correct B is wrong

  4. A is wrong B is correct
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A : Only possible case.
B : Since masses are not same velocities can't be same.

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

 Consider the following statements A and B and identify the correct answer:
$A :$ In an elastic collision, if a body suffers a head on collision with another of same mass at rest, the first body comes to rest while the other starts moving with the velocity of the first one.
$B :$ Two bodies of equal masses suffering a head-on elastic collision merely exchanges their velocities.

  1. A and B are true

  2. A and B are false

  3. A is true but B is false

  4. A is false but B is true
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For an elastic collision $($ using momentum conservation and coefficient of restitiution $)$,


$ v _1 = \dfrac{m _1-m _2}{m _1+m _2}u$

$ v _2 = \dfrac{2m _1}{m _1+m _2}u$.

If $m _1=m _2,$ then$, v _1 = 0 ,v _2 = u$.
In general, the velocities of the bodies just get interchanged in an elastic collision if their masses are equal.