Momentum And Kinetic Energy In Collisions

To solve the problem of finding the ratio of linear momenta for three bodies with equal kinetic energies, we start by considering the relationship between kinetic energy and momentum.

The kinetic energy ( ) of a body is given by the formula:

where is the mass and is the velocity of the body.

The linear momentum ( ) of a body is given by:

We are told that the kinetic energies of bodies A, B, and C are equal. Therefore, for each body:

Since the kinetic energies are equal, we can write:

Now, we can express the momentum for each body in terms of its velocity:

, ,

Then, the momentum for each body is:

, ,

Simplifying further, we find the momentum expressions:

, ,

Given masses are g, kg, and kg. Converting to kg, we have kg.

Using these masses to find the ratio of their momentum:

Momentum ratio:

Solving for the combined ratio gives:

Thus, the correct option is .