**Law of conservation of linear momentum**

The second and third laws of motion lead to one of the most important and fundamental principles of physics, called the **law of conservation of linear momentum. **

*It can be stated as follows:*

When no external force acts on a system of several interacting particles, the total linear momentum of the system is conserved. The total linear momentum is the vector sum of the linear momenta of all the particles of the system.

### Numerical Problems Based on Class 11 Physics Conservation of Linear Momentum

Q.1. A 40 kg shell is flying at a speed of 72 kmh^{-1}. It explodes into two pieces. One of the two pieces of mass 15 kg stops. Calculate the speed of the other.

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Answer: 32 ms^{-1}

Q.2. A bullet of mass 7 g is fired into a block of metal weighing 7 kg. The block is free to move. After the impact, the velocity of the bullet and the block is 70cms^{-1}. What is the initial velocity of the bullet?

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Answer: 700.7 ms^{-1}

Q.3. A man weighing 60 kg runs along the rails with a velocity of 18 kmh^{-1} and jumps into a car of mass 1 quintal standing on the rails. Calculate the velocity with which the car will start travelling along the rails.

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Answer: 1.88 ms^{-1}

Q.4. A machine gun of mass 10 kg fires 20 g bullets at the rate of 10 bullets per second with a speed of 500 ms^{-1}. What force is required to hold the gun in position? (Ans. 100 N)

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Answer: 100 N
Q.5. A truck of mass 2Ã—10^{4}kg travelling at 0.5 ms^{-1} collides with another truck of half its mass moving in the opposite direction with a velocity of 0.4 ms^{-1}, if the trucks couple automatically on collision, calculate the common velocity with which they move. (Ans. 0.2 ms^{-1})

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Answer: 0.2 ms^{-1}