Tag: work, energy and power

Questions Related to work, energy and power

A ball moving with a certain velocity hits another identical ball at rest. If the plane is frictionless and collision is elastic, the angle between the directions in which the balls move after collision, will be

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

  1. $30^{o}$

  2. $60^{o}$

  3. $90^{o}$

  4. $120^{o}$

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Correct Option: C

Two perfectly elastic objects $A$ and $B$ of identical mass are moving with velocities $15\ m/s$ and $10\ m/s$ respectively collide along the direction of line joining them. Their velocities after collision are respectively:

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

  1. $10\ m/s, 15\ m/s$

  2. $20\ m/s, 5\ m/s$

  3. $0\ m/s, 25\ m/s$

  4. $5\ m/s, 20\ m/s$

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Correct Option: A
Explanation:

$15m+10m=mv _1+mv _2$

$25=v _1+v _2$...............(i)
and $\dfrac{v _2-v _1}{u _1-u _2}=1$
$\Rightarrow \dfrac{v _2-v _1}{15-10}=1$
$\Rightarrow v _2-v _1=5$............(ii)
$v _1+v _2=25$
$\dfrac{v _2-v _1=5}{2v _2=30}$
$\therefore v _2=15m/s,v _1=10m/s$

A body of mass $8\ kg$ collides elastically with a stationary mass of $2\ kg$. If initial $KE$ of moving mass be $E$, the kinetic energy left with it after the collision will be:

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

  1. $0.80\ E$

  2. $0.64\ E$`

  3. $0.36\ E$

  4. $0.08\ E$

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Correct Option: C

If two bodies $A$ and $B$ of definite shape (dimensions of bodies are not ignored) $A$ is moving with speed of $10\ m/s$ and $B$ is in rest. They collide elastically. Then;

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

  1. body $A$ comes to rest and $B$ moves with speed of $10\ ms$

  2. they may move perpendicular to each other

  3. $A$ and $B$ may come to rest

  4. they must move perpendicular to each other

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Correct Option: B

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 :

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

  1. $-v,2v$

  2. $-2v,v$

  3. $v,-2v$

  4. $2v,-v$

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Correct Option: B
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 $-v _{1}=2v\therefore v _{1}=-2v$

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 

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

  1. $0.15\ m/s$

  2. $1.5\ m/s$

  3. $-0.15\ m/s$

  4. $none\ of\ these$

Show answer
Correct Option: C
Explanation:

From conservation of linear momentum:

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

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

A ball of mass $m _{1}$ is moving with velocity $v$. It collides head on elastically with a stationary ball of mass $m _{2}$. The velocity of ball becomes $\dfrac{v}{3}$ after collision, then the value of the ratio $\dfrac{m _{2}}{m _{1}}$ is:

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

  1. $1$

  2. $2$

  3. $3$

  4. $4$

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Correct Option: B

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 :

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

  1. $-v,:2v$

  2. $-2v,:v$

  3. $v,:-2v$

  4. $2v,:-v$

Show answer
Correct Option: B
Explanation:

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

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)

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

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

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

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

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

Show answer
Correct Option: C
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
${v} _{2} = \dfrac{u\left(1+e\right)}{2}    \Rightarrow    \dfrac{{v} _{2}}{u} = \dfrac{1+e}{2}$

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:

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

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

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

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

  4. $0.92\, kg\, m\,s^{-1}$

Show answer
Correct Option: A
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 = $0.48kgm/s$