Tag: work, energy and power

Quizzes (16) Questions (235)

Questions Related to work, energy and power

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

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

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

For an elastic collision between two identical masses where one is initially at rest, the angle between the final velocities is 90 degrees.

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

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:

  1. $10\ m/s, 15\ m/s$
  2. $20\ m/s, 5\ m/s$
  3. $0\ m/s, 25\ m/s$
  4. $5\ m/s, 20\ m/s$
Reveal answer Fill a bubble to check yourself
A Correct answer
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)
$v _1+v _2=25$
$\dfrac{v _2-v _1=5}{2v _2=30}$
$\therefore v _2=15m/s,v _1=10m/s$

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

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:

  1. $0.80\ E$
  2. $0.64\ E$`
  3. $0.36\ E$
  4. $0.08\ E$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The fraction of kinetic energy retained by the incident mass m1 after an elastic collision with stationary mass m2 is ((m1 - m2)/(m1 + m2))^2. Here, m1=8, m2=2, so the fraction is ((8-2)/(8+2))^2 = (6/10)^2 = 0.36.

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

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;

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

In a general elastic collision between two bodies, the conservation of momentum and energy allows for various scattering angles depending on the impact parameter. They do not necessarily move perpendicular to each other unless the masses are equal and one is at rest.

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 = $0.48kgm/s$