Question

Car A has a mass of 1,200 kg and is traveling at a rate of 22 km/hr. It collides with car B. Car B has a mass of 1,900 kg and is traveling in the same direction at 25 km/hr. Which of the following statements is true?
A) The momentum before the collision is equal to the momentum after the collision.

B) The momentum before the collision is greater than the momentum after the collision.

C) The momentum before the collision is less than the momentum after the collision.

Answer 1

The car A has a mass of 1200 kg.

The car B has the mass of 1900 kg.

It is given that velocity of car  A is given as 22 Km/hr

The car B has the velocity of 25 Km/hr.

Let the mass of two bodies are denoted as  $m_{1} \ and\ m_{2}$

Let the velocity of cars A and B are denoted as $v_{1} \ and\ v_{2}$

The momentum before collision is-

                                                  $p_{i} =m_{1} v_{1} +m_{2} v_{2}$

[Here p stand for momentum.]

We are asked to calculate the final momentum of the system after collision.

The answer of the question is based law of conservation of  linear momentum.

As per law of conservation of linear momentum the sum total linear momentum for an isolated system is always constant.Hence irrespective of the type of collision[elastic and inelastic],the momentum of the system is always constant which is a universal truth.

Let after the collision the velocity of A and B are $v'_{1} \ and\ v'_{2}$

Hence the final momentum of the system is-

                                                        $p_{f} = m_{1} v'_{1} +m_{2} v'_{2}$

As per the law of conservation of linear momentum, the initial and final momentum must be equal i.e      

                              $p_{i} =p_{f}$

                               $m_{1} v_{1} +m_{2}v_{2} =m_{1} v'_{1} +m_{2} v'_{2}$

Hence the option A  is right.

Answer 2

A
This principle is known as the law of conservation of momentum.