Question

The sum of the product of the masses and the velocities of the two moving bodies before and after the collision remain the same
A) Law of the conservation of the mass
B) Law of conservation of the velocity
C) Law of conservation of the energy
D) Law of conservation of the momentum

Answer 1

Hint
As according to the question the sum of the product of the masses and the velocities of the two moving bodies before and after the collision remain the same. Hence in the equation there must be involvement of the product of the mass and the velocity.

Complete answer:
Let’s consider the all the above option one by one-
Considering the option one; Here in the question, it asked us that the sum of the product of the masses and the velocities of the two moving bodies before and after the collision remains the same.
But in option one (A) it is considering only mass. So option one is not correct.
Considering the second case, In this case it is talking about only velocity. So the second option is also incorrect.
Now about the third case, it is talking about the energy but as we know that energy is of two types: Potential energy and the kinetic energy. Kinetic energy is dependent on the mass and the velocity but potential energy depends only on the position. So this option is also incorrect.
In the last option as we know that, Momentum is the product of the mass and the velocity
Numerically it can written as-
$P = mv$
And according to Newton's second law of motion the sum of the Momentum of the body remains the same before and after the collision.
Hence option (D) is correct.

Note
Newton's second law of the motion states that the change in the velocity divided by the change in time gives the value of the acceleration.