Two marbles, one twice as massive as the other, are dropped from the same height. When they strike the ground, how does the kinetic energy of the more massive marble compare to that of the other marble

The more massive one will have larger kinetic energy.

Explanation:

We know that when we drop an object, the acceleration of the object will be equal to the gravitational acceleration.

a(t) = -9.8m/s^2

And to get the velocity, we need to integrate over time, to get:

v(t) = (-9.8m/s^)*t + v0

Where v0 is the initial speed of the object.

You can see that the mass of the object does not affect the velocity of it.

Then when we drop two marbles of different masses from the same height, we know that the final velocity of them will be equal.

Now, we also know that the kinetic energy can be written as:

K = (m/2)*v^2

where m is the mass, and v is the velocity.

Then the kinetic energy of the marble with less mass can be written as:

k = (m/2)*v^2

And the kinetic energy for the more massive one is:

K = (M/2)*v^2

And we know that both of them have the same velocity, and M is larger than m, then we can conclude that the marble with larger mass will have larger kinetic energy.