Perfectly Inelastic Collision

Q.

The principle of conservation of linear momentum can be strictly applied during a collision between two particles provided the time of impact is

1. Extremely small

2. Moderately small

3. Extremely large

4. Depends on a particular case

Q.

A ${}^{238}U$ nucleus decays by emitting an alpha particle of speed ${}^{\prime }{v}^{\prime }m{s}^{-1}$. The recoil speed of the residual nucleus (in $m{s}^{-1}$ ) is:

1. $\frac{-4v}{234}$

2. $\frac{v}{4}$

3. $\frac{-4v}{238}$

4. $\frac{4v}{238}$

Q. A ball hanging from a support by an inextensible string of length $l$ is strucked perfectly inelastically by an identical ball of mass $m$ moving with horizontal velocity of $u=\sqrt{2gl}$. Assuming the balls execute circular motion just after collision, find the tension in the string just after collision.

1. $mg$
2. $3mg$
3. $2mg$
4. $0$

Q. A completely inelastic collision is one in which the two colliding particles after collision.

1. are separated
2. remain together
3. split into fragments

Q.

A moving body of mass m and velocity 3 km/h collides with a body at rest of mass 2m and sticks to it. Now the combined mass starts to move. What will be the combined velocity

1. 3 km/h

2. 2 km/h

3. 1 km/h

4. 4 km/h

Q. A body of mass $m$ moves with speed $2v$ and a body of mass $2m$ moves with speed $v$ on a smooth horizontal surface, both along positive $x$ axis. After some time, they collide and stick together. What is the speed of the system after they stick together?

1. $\frac{2v}{3}$
2. $\frac{v}{3}$
3. $\frac{4v}{3}$
4. $\frac{5v}{3}$

Q.

A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragments with equal masses fly in mutually perpendicular directions with speeds of 21 m/s. The velocity of the heaviest fragment will be

1. 11.5 m/s

2. 14.0 m/s

3. 7.0 m/s

4. 9.9 m/s

Q.

A shell is fired from a cannon with velocity 'v' m/s at an angle '$\theta$' with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon then the speed of the other piece immediately after the explosion is

1. $3vcos\theta$

2. $2vcos\theta$

3. $\frac{3}{2}vcos\theta$

4. $\frac{\sqrt{3}}{2}vcos\theta$

Q.

A body of mass 40 kg having velocity 4 m/s collides with another body of mass 60 kg having velocity 2 m/s. If the collision is inelastic, then loss in kinetic energy will be

1. 440 J

2. 392 J

3. 48 J

4. 144 J

Q.

When two bodies stick together after collision, the collision is said to be

1. Partially elastic

2. Total elastic

3. Total inelastic

4. None of the above

Q. A body of mass m moving with a speed v suffers an inelastic collision with another body of M at rest and sticks to it. The speed of the composite body will be

1. $\left(\frac{m+M}{m}\right)v$
2. $\left(\frac{m}{m+M}\right)v$
3. $\left(\frac{M}{m+M}\right)v$
4. $\left(\frac{m+M}{M}\right)v$

Q. A particle of mass $m$ moving in the $x-$ direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y-$ direction with speed $v$. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

1. $50\%$
2. $56\%$
3. $62\%$
4. $42\%$

Q. A ball of mass 'm' moving horizontally at a speed 'v' collides with the bob of a simple pendulum at rest. The mass of the bob is also 'm'. If the collision is perfectly inelastic, the height to which the two balls rise after the collision will be given by

1. $\frac{v^2}{g}$
2. $\frac{v^2}{2g}$
3. $\frac{v^2}{4g}$
4. $\frac{v^2}{8g}$

Q. A particle of mass $m$ moving in the $x-$ direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y-$ direction with speed $v$. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

1. $50\%$
2. $56\%$
3. $62\%$
4. $42\%$

Q. A bullet of mass $50\text{gm}$ is fired with a velocity of $90\text{m/s}$ towards a ball of mass $500\text{gm}$, initially at rest. When the bullet strikes the ball, it gets embedded into it and the system starts moving. What is the ratio of the kinetic energy of the bullet to the kinetic energy of the $\text{(bullet + ball)}$ system?

1. $10.5$
2. $11$
3. $8$
4. $14$

Q. A body of mass $m$ moves with speed $2v$ and a body of mass $2m$ moves with speed $v$ on a smooth horizontal surface, both along positive $x$ axis. After some time, they collide and stick together. What is the speed of the system after they stick together?

1. $\frac{2v}{3}$
2. $\frac{v}{3}$
3. $\frac{4v}{3}$
4. $\frac{5v}{3}$

Q.

A particle (a mud pallet) of mass 'm' strikes a smooth stationary wedge of mass $M$ with a velocity $v_0$, at an angle $\theta$ with horizontal. If the collision is perfectly inelastic, find the velocity of the wedge just after the collision.

1. $\frac{m{v}_{0}sin\theta }{m+M}$

2. $\frac{m{v}_{0}tan\theta }{m+M}$

3. $\frac{m{v}_{0}cos\theta }{m+M}$

4. $\frac{M{v}_{0}cos\theta }{m+M}$

Q.

Two particles of equal masses moving the same speed collide perfectly in-elastically. After the collision the combined mass moves with half of the speed of the individual masses. The angle between the initial momenta of individual particle is

1. ${60}^{\circ }$

2. ${90}^{\circ }$

3. ${120}^{\circ }$

4. ${45}^{\circ }$

Q.

In the arrangements shown in figure, masses of each ball are 1 kg and mass of trolley is 4 kg. In the figure shell of mass 1 kg moving horizontally with velocity v = 6 m/sec collides with the ball and get stuck to it .It's maximum deflection of the thread (length 1.5 m) with vertical is:

1. ${53}^{\circ }$

2. ${37}^{\circ }$

3. ${30}^{\circ }$

4. ${60}^{\circ }$

Q. A box of mass $2\text{kg}$ slides from a height of $8\text{m}$ on the inclined plane and struck the ball. After collision, the ball sticks on the box. If mass of the ball is $200\text{g}$, then what will be the velocity of the box after collision? Assuming all surfaces are frictionless and initially the ball is at rest. (take $g=10m/s^2)$

1. $2.3\text{m/s}$
2. $4.5\text{m/s}$
3. $8.5\text{m/s}$
4. $11.5\text{m/s}$

Q.

A body of mass $m_1$ is moving with a velocity 'v'. It collides with another stationary body of mass $m_2$. They get embedded. At the point of collision, the velocity of the system is

1. Increases

2. Decreases but does not become zero

3. Remains same

4. Become zero

Q. For perfectly inelastic collision of two particles, choose the correct statement.

1. Relative velocity of both particle with respect to each other will be zero after collision.
2. Kinetic energy of both particle will remain same before and after collision.
3. Momentum of system will not remain conserved.
4. None of these

Q. Two bodies of mass $0.4\text{kg}$ and $0.8\text{kg}$ move towards each other with initial velocities $5\text{m/s}$ and $2\text{m/s}$ respectively. After the collision, they stick together. Then, find the distance travelled by the combined mass, $12\text{sec}$ after the collision.

1. $3\text{m}$
2. $12\text{m}$
3. $8\text{m}$
4. $4\text{m}$

Q.

A body of mass 2 kg moving with a velocity of 3 m/sec collides head on with a body of mass 1 kg moving in opposite direction with a velocity of 4 m/sec. After collision, two bodies stick together and move with a common velocity which in m/sec is equal to

1. $\frac{1}{4}$

2. $\frac{1}{3}$

3. 
   $\frac{2}{3}$

4. $\frac{3}{4}$

Q. A magnet with a mass of $0.25\text{kg}$ moving with a velocity of $10\text{m/s}$ strikes a metal block of mass $20\text{kg}$ moving with a velocity of $5\text{m/s}$. Both magnet and block are moving in the same direction initially. The magnet sticks to the metal block after the collision. What is the final velocity of the system ?

1. $8.5\text{m/s}$
2. $10\text{m/s}$
3. $7.5\text{m/s}$
4. $5.06\text{m/s}$

Q.

Two identical blocks each of mass 10 kg are moving with a speed of 4m/s towards each other along a frictionless horizontal surface. The two blocks collide, stick together and come to rest. Consider the two blocks as a system, work done by external force is

1. Zero

2. 160 J

3. 80 J

4. 40 J

Q.

A U shaped tube of mass '2m' is placed on a smooth horizontal surface. Two identical spherical balls each of mass 'm' and of diameter slightly less than the inner diameter of tube enters into the tube with a velocity u as shown. (Assume no loss of energy anywhere and all collisions to be elastic).

Speed of each spherical ball, just before their collision is

1. $\frac{u}{\sqrt{3}},\frac{u}{\sqrt{3}}$

2. $\frac{2u}{3\sqrt{3}},\frac{u}{\sqrt{3}}$

3. $\frac{\sqrt{3}u}{2},\frac{\sqrt{3}u}{2}$

4. $\frac{u}{2},\frac{\sqrt{3}u}{2}$