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Multiple choice modelling collisions collisions momentum work, energy and power physics

A mass $m$ moves with velocity $v$ and collides inelastically with another identical mass. After collision, the 1st mass moves with velocity $\frac { v }{ \sqrt { 3 }  } $ in a direction perpendicualr to the initial direction of motion. find the speed of the second mass after collision.

  1. $v$
  2. $\sqrt { 3v } $
  3. $\frac { 2 }{ \sqrt { 3 } } v$
  4. $\frac { v }{ \sqrt { 3 } } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Conservation of momentum: m*v*i = m*v1*j + m*v2*cos(theta)*i + m*v2*sin(theta)*j. Since v1 = v/sqrt(3) in the y-direction, the x-component of momentum is conserved: m*v = m*v2*cos(theta), and y-component: 0 = m*v1 + m*v2*sin(theta). Solving these gives v2 = 2*v/sqrt(3).

Multiple choice modelling collisions collisions momentum work, energy and power physics

A body of mass 2.0 kg makes an elastic collision with another body at rest and continues to move in the original direction but with one-fourth of its original speed v. What is the mass of other body and the speed of the center of mass of two bodies ?

  1. $ 1.0 kg and \frac {2}{3}v $
  2. $ 1.2 kg and \frac{5}{8} $
  3. $ 1.4 kg and \frac {10}{17} v $
  4. $ 1.5 kg and \frac {4}{7} v $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$m _{1}=2\ kg$
$u _{1}=4\ m/s$
$v _{1}=\dfrac {u _{1}}{4}=\dfrac {4}{4}=1\ m/s$
$u _{2}=0$
since nothing is given so we would take it as elastic collision. 
hence conservation of momentum is given by:
$m _{1}u _{1}+m _{2}u _{2}=m _{1}v _{1}+m _{2}v _{2}$
$2\times 4+0=2\times 1+m _{2}v _{2}$
$m _{2}v _{2}=6$
according to the conservation kinetic energy:
$\dfrac {1}{2}m _{1}u _{1}^{2}+\dfrac {1}{2}m _{2}u _{2}^{2}=\dfrac {1}{2}m _{1}v _{1}^{2}+\dfrac {1}{2}m _{2}v _{2}^{2}$
$2\times 16+0=2\times 1+m _{2}v _{2}^{2}$
$m _{2}v _{2}^{2}=30$
$\dfrac {m _{2}v _{2}^{2}}{m _{2}v _{2}}=\dfrac {30}{6}$
$v _{2}=5\ m/s$
$m _{2}=1.2\ kg$


Multiple choice modelling collisions collisions momentum work, energy and power physics

Two objects of mass 3 kg and 2 kg move along x and y ais with $ 4 m/s^2 $ and $ 3 m/s ^2 $ respectively on a horizontal smooth table.after collision the bodies stick together.then :

  1. Heat generated in the process is 15 joules

  2. Heat generated in the process is 18 joules
  3. direction of motion x-axis after collision is $ 60^0 $
  4. direction of x-axis after collision is $ tan{-1} \left( \frac { 1 }{ 3 } \right) $
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice modelling collisions collisions momentum work, energy and power physics

$n$ balls each of mass $m$ impinge elastically each second on a surface with velocity $u$. The average force experienced by the surface will be

  1. $mnu$
  2. $2\ mnu$
  3. $4\ mnu$
  4. $mnu/2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
  • Elastically means the balls get bounced with $same$ speed i.e $u$
  • so the change in momentum will be $P _2-P _1=-mu-mu=-2mu$
  • so the momentum tranferred to the surface will be $-(-2mu)=2mu$
  • thus the total momentum transferred by $n$ balls will be $2mnu$
  • force $F=\dfrac{Momentum}{time}=\dfrac{2mnu}{1sec}=2mnu$
Multiple choice modelling collisions collisions momentum work, energy and power physics

A body moving towards a finite body at rest collides with it. It is possible that :

  1. both the bodies come to rest

  2. both the bodies move after collision

  3. the moving body comes to rest and stationary body starts moving

  4. the stationary body remain stationary and moving body changes its direction
Reveal answer Fill a bubble to check yourself
B,C Correct answer
Explanation

If a body moving towards a finite body at rest collides with it then momentum will be conserved and hence, the velocities after collision are may be in inverse proportion to their masses or may get interchanged. Hence, both the bodies move after collision or the moving body comes to rest and stationary body starts moving.

Multiple choice modelling collisions collisions momentum work, energy and power physics

A body moving towards a finite body at rest collides with it. It is possible that:

  1. both the bodies come to rest

  2. both the bodies moves after collision

  3. the moving body comes to rest and the stationary body starts moving

  4. the stationary body remains stationary, the moving body changes its velocity
Reveal answer Fill a bubble to check yourself
B,C Correct answer
Explanation

both bodies cannot come to rest as  it will violate the law of conservation of momentum.
Option (D) will also violate conservation of momentum.

Multiple choice modelling collisions collisions momentum work, energy and power physics

A mass $m _1$ moves with a great velocity. It strikes another mass $m _2$ at rest in a head on collision and comes back along its path with a low speed after collision. Then :

  1. $m _1 > m _2$
  2. $m _1 = m _2$
  3. $m _1 < m _2$
  4. there is relation between $m _1$ and $m _2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a head-on elastic collision between a small projectile and a more massive target, the projectile will bounce back with low speed and the massive target will be given a very small velocity. Hence, $m _1 < m _2$

Multiple choice modelling collisions collisions momentum work, energy and power physics

A body moving towards a body of finite mass at rest collides with it. It is possible that :

  1. both bodies come to rest

  2. the stationary body remains stationary and the moving body rebounds.

  3. the moving body stop and the body at rest start moving.

  4. all of the above are correct.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From the very fundamental law of collision we know that in a collision momentum of the system is conserved .
Therefore the only possible option is C.

Multiple choice modelling collisions collisions momentum work, energy and power physics
Collision is a physical process in which two or more objects, either particle masses or rigid bodies, experience very high force of interaction for a very small duration. It is not essential for the objects to physically touch each other for collision to occur. Irrespective of the nature of interactive force and the nature of colliding bodies, Newton's second law holds good on the system. Hence, momentum of the system before and after the collision remains conserved if no appreciable external force acts on the system during collision.
The amount of energy loss during collision, if at all, is indeed dependent on the nature of colliding objects. The energy loss is observed to be maximum when objects stick together after collision. The terminology is to define collision as 'elastic' if no energy loss takes place and to define collision as 'plastic' for maximum energy loss. The behaviour of system after collision depends on the position of colliding objects as well. A unidirectional motion of colliding objects before collision can turn into two dimensional after collision if the line joining the centre of mass of the two colliding objects is not parallel to the direction of velocity of each particle before collision. Such type of collision is referred to as oblique collision which may be either two or three dimensional.

Which of the following collision is one-dimensional?

  1. Head on collision

  2. Perfectly elastic collisions

  3. Perfectly inelastic collisions

  4. Oblique collisions
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Head-on collision is always one dimensional the centre of mass of each body move in the same direction after collision as they were moving before collision.