Com in Perfectly Inelastic Collision

Q. A spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is $2.0N{m}^{-1}$ and the mass of the block is $2.0kg$. Ignore the mass of the spring. Initially, the spring is in an unstretched condition. Another block of mass $1.0kg$ moving with a speed of $2.0m{s}^{-1}$ collides elastically with the first block. The collision is such that the $2.0kg$ block does not hit the wall. The distance in metres between the two blocks when the spring returns to its unstretched position for the first time after the collision is

Q.

A ball moving with a velocity of 9 m/sec collides with another similar stationary ball. After the collision both the balls move in directions making an angle of 30° with the initial direction. After the collision, their speed will be:-

Q.

A bullet of mass m leaves a gun of mass M kept on a smooth horizontal surface. If speed of the bullet relative to the gun is v, then recoil speed of the gun will be:

1. 

2. 

3. 

4. 

Q.

A person of mass $m$ is standing on one end of a plank of mass $M$ and length $L$ and floating in the water. The person moves from one end to another and stops. The displacement of the plank is

1. $\frac{Lm}{(m+M)}$

2. $\frac{L(M+m)}{m}$

3. $\frac{(M+m)}{Lm}$

4. $\frac{LM}{(m+M)}$

Q.

A bullet of mass $20g$ is fired horizontally with a velocity of $150m/s$ from a pistol of mass $2Kg$. Find the recoil velocity of the pistol.

Q. a car of mass 1000 kg moving with a speed of 30 m/s collides with a back of a stationary bidy of mass 9 tonnes. Calculate the speed of vehicle immediately after collision if they remain together

Q. A ball of mass $m$ moving with uniform speed, collides elastically with another stationary ball. The incident ball will lose maximum kinetic energy, when the mass of the stationary ball is,

1. $m$
2. $2m$
3. $4m$
4. infinity

Q. A ball is projected upwards from a height h above the surface of the earth with velocity v. The time at which the ball strikes the ground is

1. 
2. 
3. 
4. 

Q.

A wooden block of mass M rests on a horizontal surface. A bullet of mass m moving in the horizontal direction strikes and gets embedded in it. The combined system covers a distance x on the surface. If the coefficient of friction between wood and the surface is $\mu$, the speed of the bullet at the time of striking the block is (where m is mass of the bullet)

1. 

2. 

3. 

4. 

Q. A sphere carrying charge is just at rest without falling down touching a vertical wall, by applying a horizontal electric feld 100 $N{C}_{-1}$. The charge on the ball is 0.01 C. If the coefficient of friction between wall and sphere is 0.2, mass of the sphere is (g = 10 $m/s^2$)

1. 2 kg
2. 20 gm
3. 0.2 kg
4. 2g

Q.

A 2 kg mass moving with a velocity of $10m{s}^{-1}$ collides with another 6 kg mass moving in opposite direction with a velocity of $20m{s}^{-1}$. After the collision, they stick and move together. Find their common velocity and the momentum.

1. 

2. 

3. 

4. 

Q.

A 5 kg rifle fires a 10 g bullet at a velocity of 500 m/s. Find the recoil velocity of the rifle.

Q. A space vehicle is traveling at 4300Kmph relative to earth when the exhausted motor (mass 4m) is disengaged and sent back ward with a velocity 82Kmph relative to the command module (mass m) . What is the speed of the command module relative to earth just after separation

Q. A $15\text{g}$ bullet is fired horizontally at a speed of $350\text{m/s}$ into $1.2\text{kg}$ block that hangs by a vertical string as shown below. The bullet remains embedded in the block. Find the speed of the bullet and the block.

1. $10\text{m/s}$
2. $22.5\text{m/s}$
3. $350\text{m/s}$
4. $4.32\text{m/s}$

Q.

A body of mass m moving with a velocity v in the x-direction collides and sticks with another body of mass M moving with a velocity V in the y-direction. The magnitude of the momentum of the composite body is

1. $(m+M)(v+V)$

2. $\sqrt{{\left(mv\right)}^2+{\left(MV\right)}^2}$

3. $(Mv+mV)$

4. $(mv+MV)$

Q. Two identical particles collide in the air in an perfectly inelastic manner. Before collision, one moves horizontally and the other moves in vertical direction with equal speed. After collision, the fractional loss in kinetic energy of the system of particles is

1. $\frac{1}{2}$
2. $\frac{1}{\sqrt{2}}$
3. $\frac{\sqrt{3}}{2}$
4. $0$

Q. A bullet of mass $200\text{g}$ fired with a velocity of $200\text{m/s}$, hits a block of mass $2\text{kg}$ moving with a velocity of $10\text{m/s}$. After hitting the block, the bullet lodges into it. What is the velocity of the combined system? Assume that the collision is perfectly inelastic.

1. $20\text{m/s}$
2. $54.54\text{m/s}$
3. $27.27\text{m/s}$
4. $36.36\text{m/s}$

Q. A bullet of mass 10g is fired horizontally into a 5kg wooden block, at rest on horizontal surface. The coefficient of kinetic friction between the block and the surface is 0.1 Calculate the speed of the bullet striking the block, if the combination moves 20m before coming to rest.

Q.

A bullet of mass 20g travelling horizontally with a speed of 500 m/s passes through a wooden block of mass 10.0 kg initially at rest on a level surface. The bullet emerges with a speed of 100 m/s and the block slides 20 cm on the surface before coming to rest. The friction coefficient between the block and the surface is $g=10m{s}^{-2}$

1. 0.50

2. 0.24

3. 0.16

4. 0.32

Q.

A 10gm bullet is fired from a 5kg rifle horizontally with a velocity of 500 m/s .Find the recoil velocity of the rifle.

Q.

If the kinetic energy of a particle is doubled, de Broglie wavelength becomes:

1. $2$ times

2. $4$ times

3. $\sqrt{2}$ times

4. $\frac{1}{\sqrt{2}}$ times

Q. Object $A$ of mass $m$, is moving at a velocity $v_1$ to the right. It collides and sticks to object $B$ of mass $m_2$ moving in the same direction as object $A$ with velocity $v_2$. After collision, both the objects have the same velocity $\frac{1}{2}(v_1+v_2)$. What is the relationship between $m_1$ and $m_2$? [$v_1$ and $v_2$ are not equal]

1. $m_1=m_2$
2. $m_1=2m_2$
3. $m_1=4m_2$
4. $m_1=m_2/2$

Q.

A set of 'n' identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is L. The block at one end is given a speed 'v' towards the next one at time, t = 0. All collisions are completely inelastic, then

1. The last block starts moving at

2. The last block starts moving at

3. The centre of mass of the system will have a final speed v

4. The centre of mass of the system will have a final speed

Q. A ball of mass $m$ moving with speed $u$ undergoes a head on collision with a stationary ball of mass $3m$. If collision is perfectly inelastic, find the loss of kinetic energy.

1. $\frac{1}{16}m{u}^2$
2. $\frac{1}{4}m{u}^2$
3. $\frac{1}{8}m{u}^2$
4. $\frac{3}{8}m{u}^2$

Q.

A ball A moving with a certain velocity collides, with another ball B of the same mads at rrsr.If the coefficient of restitution is e, the ratio of the velocities of A and B just after collision is

Q. The velocity of a body of mass $2kg$ changes from $v_1=2\hat{i}+3\hat{j}-\hat{k}m/s$ to $v_2=-3\hat{i}+2\hat{j}+3\hat{k}m/s$ in $3sec$ under the influence of a external force. Find the magnitude of the force applied ?

1. 5.1 N
2. 4.8 N
3. 4.3 N
4. 4 N

Q. A $15\text{g}$ bullet is fired horizontally at a speed of $350\text{m/s}$ into $1.2\text{kg}$ block that hangs by a vertical string as shown below. The bullet remains embedded in the block. Find the speed of the bullet and the block.

1. $10\text{m/s}$
2. $22.5\text{m/s}$
3. $350\text{m/s}$
4. $4.32\text{m/s}$

Q.

Two balls of masses 2 kg and 4 kg are moving towards each other with velocities $4m{s}^{-1}$ and $2m{s}^{-1}$ respectively on a frictionless surface. After the collision, the 2 kg ball returns back with a velocity of $2m{s}^{-1}$.

Determine (a) the velocity of 4 kg block after the collision. (b) the loss in kinetic energy in collision (c) coefficient of restitution.

Q.

An empty truck of mass $1000kg$ moving at a speed of $36km{h}^{-1}$. It is loaded with $500kg$material on its way and again moves with the same speed. Will the momentum of the truck remain the same after loading?. If not find the momentum of the truck after loaded.

Q.

A ball of mass $m$ travelling with velocity $5v$ collides with and sticks to a ball of mass $5m$ travelling in the same direction with velocity $v$ .Their common velocity after the collision is

1. $v$

2. $\frac{6v}{5}$

3. $\frac{8v}{10}$

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