If two objects a and b have the same kinetic energy but a has three times the momentum of b, what is the ratio of their inertias?

Explanation:

First of all, let's remind that:

- The kinetic energy of an object is given by , where m is the mass and v is the speed

- The momentum of an object is given by

- The inertia of an object is proportional to its mass, so we can write , where k just indicates a constant of proportionality

In this problem, we have:

- (the two objects have same kinetic energy)

- (A has three times the momentum of B)

Re-writing both equation we have:

If we divide first equation by second one we get

And if we substitute it into the first equation we get

So, B has 9 times more mass than A, and so B has 9 times more inertia than A, and their ratio is: