Law of Conservation of Mometum

Q.

Calculate the recoil velocity of a gun having mass equal to 5 kg, if a bullet of 25 g acquires the velocity of $500m{s}^{-1}$ after firing from the gun.

1. $10m{s}^{-1}$

2. $25m{s}^{-1}$

3. $2.5m{s}^{-1}$
4. $5m{s}^{-1}$

Q. A body of mass $300g$ kept at rest breaks into two parts due to internal forces. One part of mass $200g$ is found to move at a velocity of $12m{s}^{-1}$ towards east. The velocity of the other part is:

1. $24m{s}^{-1}$ towards west
2. $14m{s}^{-1}$ towards east
3. $24m{s}^{-1}$ towards east
4. $54m{s}^{-1}$ towards south

Q. Ball A of mass 6 kg moving with a velocity of 20 $m{s}^{-1}$ collides with another ball B of mass 2 kg moving in the opposite direction with a velocity of 10 $m{s}^{-1}$. After the collision, ball A comes to rest. Find the speed of ball B after collision.

1. 10 $m{s}^{-1}$
2. 20 $m{s}^{-1}$
3. 30 $m{s}^{-1}$
4. 50 $m{s}^{-1}$

Q. A boy is running with a velocity of $2m{s}^{-1}$. He jumps over a stationary cart of $2kg$ while running. If the mass of the boy is of $20kg$, find the velocity at which the cart moves after he jumps over the cart. (Neglect friction between the cart and ground)

1. $1.81m{s}^{-1}$
2. $1.3m{s}^{-1}$
3. $1.92m{s}^{-1}$
4. $2.44m{s}^{-1}$

Q. 2 plastic balls have masses of $100g$ and $200g$. The $100g$ ball is moving at $3m{s}^{-1}$ and hits the $200g$ stationary ball. They collide with each other and after the collision, the $100g$ ball moves with a velocity of $1.5m{s}^{-1}$ in the same direction. Calculate the velocity of the other ball after collision.

Q. 2 plastic balls have masses of $100g$ and $200g$. The $100g$ ball is moving at $3m{s}^{-1}$ and hits the $200g$ stationary ball. They collide with each other and after the collision, the $100g$ ball moves with a velocity of $1.5m{s}^{-1}$ in the same direction. Calculate the velocity of the other ball after collision.

1. $0.75m{s}^{-1}$
2. $0.75km{s}^{-1}$
3. $0.75cm{s}^{-1}$
4. $0.57m{s}^{-1}$

Q.

From a rifle of mass $4kg$, a bullet of mass $50g$ is fired with an initial velocity of $35m{s}^{-1}$ with respect to the ground. Calculate the initial recoil velocity of the rifle.

1. 0.4375 m/s

2. 0.4 m/s

3. 0 m/s

4. 0.3375 m/s

Q.

Ball A of mass $5kg$ travelling at $6m{s}^{-1}$collides with another ball B of mass $2kg$ travelling at $2m{s}^{-1}$ in the same direction. After collision, the velocity of ball A reduces to $2m{s}^{-1}$. Calculate the velocity of ball B after the collision.

1. $10m{s}^{-1}$

2. $12m{s}^{-1}$

3. $6m{s}^{-1}$

4. $8m{s}^{-1}$

Q.

The total momentum of a system always remains unchanged before and after the collision.

1. True
2. False

Q. A massive ball moving with speed v collides head-on with a tiny ball at rest having a very small mass as compared to the first ball. If the collision is elastic, then immediately after the impact, the second ball will move with a speed approximately equal to

1. v
2. 2v
3. v/2
4. $\infty$

Q. 2 plastic balls have masses of $100g$ and $200g$. The $100g$ ball is moving at $3m{s}^{-1}$ and hits the $200g$ stationary ball. They collide with each other and after the collision, the $100g$ ball moves with a velocity of $1.5m{s}^{-1}$ in the same direction. Calculate the velocity of the other ball after collision.

Q. A bullet of 5 g is fired from a pistol of 1.5 kg. If the recoil velocity of pistol is $1.5m{s}^{-1}$, what is the final momentum of the pistol?

1. $10kgm{s}^{-1}$
2. $1.5kgm{s}^{-1}$
3. $2.25kgm{s}^{-1}$
4. $2.5kgm{s}^{-1}$

Q.

A bullet of mass $20g$ moving with a velocity of $100m{s}^{-1}$ strikes a wooden block of mass $80g$ at rest and gets embedded into it. Calculate the velocity of the combined system.

1. 10 ms^-1

2. 30 ms^-1

3. 20 ms^-1

4. 5 ms^-1

Q.

Explain how the law of conservtion of momentum can be used to explain
(i) recoil of a gun
(ii) motion of a rocket. [3 MARKS]

Q.

A bullet was fired from a gun. Choose the correct option for the situation assuming that no external force is acting on the gun-bullet system.

1. Since the mass of bullet is very less than the mass of the gun, the momentum of bullet is not equal to the momentum of gun.

2. The magnitude of momentum of gun is equal to that of bullet.

3. During firing, the law of conservation of momentum does not hold true.

4. The momentum of gun is twice the momentum of bullet.

Q. A bullet having a mass of $10g$ and moving with a speed of $1.5m{s}^{-1}$ penetrates a thick wooden plank of mass $90g$. The plank was initially at rest. The bullet gets embedded in the plank and both move together. Determine their velocity.

1. $0.10m{s}^{-1}$

2. $0.35m{s}^{-1}$
3. $0.15m{s}^{-1}$
4. $0.25m{s}^{-1}$

Q. A bullet of mass $‘m^{\prime }$, moving with a speed $‘v^{\prime }$ strikes a wooden block of mass $M$ kept at rest and gets embedded in it. The speed of this embedded block will be:

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

Q. A gun weighing $4kg$ fires a bullet of $40g$ with a velocity of $500m{s}^{-1}$. The velocity with which gun recoils is

1. $5m{s}^{-1}$
2. $10m{s}^{-1}$
3. $20m{s}^{-1}$
4. $4m{s}^{-1}$

Q.

Ball A of mass $5kg$ travelling at $6m{s}^{-1}$collides with another ball B of mass $2kg$ travelling at $2m{s}^{-1}$ in the same direction. After collision, the velocity of ball A reduces to $2m{s}^{-1}$. Calculate the velocity of ball B after the collision.

1. $10m{s}^{-1}$

2. $12m{s}^{-1}$

3. $6m{s}^{-1}$

4. $8m{s}^{-1}$

Q. Two masses ${\text{m}}_1$ and ${\text{m}}_2$ collide with each other. Before the collision, the velocities are ${\text{u}}_1$ and ${\text{u}}_2$ respectively. After the collision, the velocities are ${\text{v}}_1$ and ${\text{v}}_2$ respectively. The total final momentum after collision is given by:

1. ${\text{m}}_1{\text{v}}_2+{\text{m}}_2{\text{v}}_1$
2. ${\text{m}}_1{\text{u}}_2+{\text{m}}_2{\text{u}}_1$
3. ${\text{m}}_1{\text{u}}_1+{\text{m}}_2{\text{u}}_2$
4. ${\text{m}}_1{\text{u}}_1+{\text{m}}_2{\text{v}}_2$

Q. Two small glass spheres of masses 10 g and 20 g are moving in a straight line in the same direction with velocities of $3m{s}^{-1}$ and $2m{s}^{-1}$ respectively. They collide with each other. After collision, glass sphere of mass 10 g moves with a velocity of $2.5m{s}^{-1}$. Find the velocity of the second ball after collision.

1. $5.5m{s}^{-1}$
2. $2.25m{s}^{-1}$
3. $2.75m{s}^{-1}$
4. $7.5m{s}^{-1}$

Q. If a bomb at rest explodes and splits into two equal fragments, the fragments will move in

1. one direction and with equal velocities.
2. opposite directions with equal velocities.
3. opposite directions with different velocities.
4. one direction with different velocities.