Perfectly Inelastic Collision

Q.

How is the elastic collision equation derived?

Q. What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of $5$ times its mass?

(Assume the collision to be head-on elastic collision)

Q. An explosion breaks a rock into three parts, in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $1\text{kg}$ moves with a speed of $12{\text{ms}}^{-1}$ and the second part of mass $2\text{kg}$ moves with $8{\text{ms}}^{-1}$ speed. If the third part files off with $4{\text{ms}}^{-1}$ speed, then its mass is-

1. $17\text{kg}$
2. $3\text{kg}$
3. $5\text{kg}$
4. $7\text{kg}$

Q. In a one-dimensional collision, a particle of mass $2m$ collides with a particle of mass $m$ at rest. If the particles stick together after the collision, what fraction of the initial kinetic energy is lost in the collision?

1. $\frac{1}{4}$
   
2. None
   
3. $\frac{1}{2}$
   
4. $\frac{1}{3}$
   

Q. After a perfectly inelastic collision between two identical balls moving with the same speed in different directions, the speed of the combined mass becomes half of their initial speed. The angle between the velocities of the two balls just before collision is

1. ${90}^{\circ }$
2. ${60}^{\circ }$
3. ${120}^{\circ }$
4. ${30}^{\circ }$

Q.

A block of mass $M$ moving on the frictionless horizontal surface collides with the spring of the spring constant $K$ and compresses it by length $L$. The maximum momentum of the block after the collision is?

1. $0$

2. $\frac{M{L}^2}{K}$

3. $L\sqrt{MK}$

4. $\frac{K{L}^2}{2M}$

Q.

A particle of mass m moving eastward with a speed v collides with another particle of the same mass m and moving northward with the same speed v. The two particles coalesce on collision. The new particle of mass 2m will move in the north-easterly direction with a velocity

1. v/2

2. 2v

3. 

4. v

Q.

A bag (mass M) hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined (bag + bullet) system

1. 

2. 

3. 

4. 

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. 
2. 
3. 
4. 

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. 392 J

2. 144 J

3. 48 J

4. 440 J

Q.

A bullet is fired from a rifle. If the rifle recoils freely, then the kinetic energy of the rifle is

1. Less than that of the bullet

2. More than that of the bullet

3. Same as that of the bullet

4. Equal or less than that of the bullet

Q. When $u^{238}$ nucleus, originally at rest, decays by emitting an alpha particle having a speed u, the recoil speed of the residual nucleus is

1. $\frac{-4u}{234}$
2. $-\frac{4u}{238}$
3. $\frac{4u}{234}$
4. $\frac{4u}{238}$

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 BULLET OF MASS 10 G IS HORIZONTALLY FIRED WITH A VELOCITY 100 M/S FROM A GUN OF MASS 10 KG . THE GUN WILL MOVE BACKWARD WITH LINEAR MOMENTUM

Q.

Initially the nucleus of radium – 226 is at rest. It decays due to which and a particle and the nucleus of radon are created. The released energy during the decay is 4.87 Mev, which appears as the kinetic energy of the two resulted particles. $[m_{\alpha }=4.002amu,m_{Rn}=222.017amu]$

What is the linear momentum of the a – particle?

1. $2.01\times {10}^{-19}kgm{s}^{-1}$

2. $1.01\times {10}^{-19}kgm{s}^{-1}$

3. $4.01\times {10}^{-19}kgm{s}^{-1}$

4. $8.01\times {10}^{-19}kgm{s}^{-1}$

Q.

A body of mass 'm' moving with a constant velocity 'v' hits another body of the same mass moving with the same velocity 'v' but in the opposite direction and sticks to it. The velocity of the compound body after collision is

1. v

2. 2v

3. Zero

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

Q.

A neutron moving witha speed v strikes a hydrogen atom in ground state towards it with the same speed. Find the minimum speed of the neutron for which inelastic (completly or partially) collision may take place. The mass of neutron = mass of hydrogen = $1.67\times {10}^{-27}kg$

Q.

In an elastic collision of two bodies

1. Total momentum of the system remains conserved

2. Total energy of the system remains conserved

3. The kinetic energy before collision is equal to kinetic energy after collision

4. The kinetic energy changes during collision stage

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

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

Q.

Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed V. If the collision is elastic, which of the following figure is a possible result after collision?

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. 

2. 

3. 

4. 

Q. A particle is thrown up with a certain velocity and at an angle $\theta$ with the horizontal . The variation of kinetic energy $\left(E\right)$ with time $\left(t\right)$ is given by

1. 
2. 
3. 
4. 

Q. In an inelastic collision of two bodies, which of the following quantities do not change before and after the collision?

1. Total kinetic energy
2. Total linear momentum
3. Total energy
4. Total angular momentum

Q.

What is momentum? Write its SI unit. Interpret force in terms of momentum. Represent the following graphically (a) momentum versus velocity when mass is fixed. (b) momentum versus mass when velocity is constant.

Q. The position vector of a particle of mass 2 kg is given as function $\overrightarrow{r}=30t\hat{i}+(40t-5t^2)\hat{j}$. The angular momentum of the particle about the origin at t = 4 s is

1. 4800 $\frac{kg.m^2}{s}$
2. 3600 $\frac{kg.m^2}{s}$
3. 1200 $\frac{kg.m^2}{s}$
4. 2400 $\frac{kg.m^2}{s}$

Q. Two identical 5kg block are moving with same speed of 2m/s towards each other along friction less horizontal surface. The two blocks collide, stick together and come to rest. Consider the two blocks as a system. Calculate work done by internal forces.

Q.

A bomb of mass $3.0kg$ explodes in air into two pieces of masses $2.0kg$ and $1.0kg$. The smaller mass goes at a speed of $80m/s$. The total energy imparted to the two fragments in $kJ$ is

1. $1.07$

2. $2.14$

3. $2.4$

4. $4.8$

Q.

A bullet hits and gets embedded in a solid block resting on a horizontal frictionless table. What is conserved ?

1. Momentum alone

2. Momentum and kinetic energy

3. Kinetic energy alone

4. Neither momentum nor kinetic energy

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 bomb of mass $3mkg$ explodes into two pieces of mass $mkg$ and $2mkg$. If the velocity of $mkg$ mass is $16m/s$. The total kinetic energy released in the explosion in $J$ is

1. $192mJ$

2. $96mJ$

3. $384mJ$

4. $768mJ$