Imagine a game of swing ball, where the rope is 1m long, and the ball weighs 1kg. How do you calculate the weight that the pole has to be so it does not get pulled over, assuming it is not burried in the ground?
In order to maintain stability, the center of mass (COM) of an object must not go over the pivot from which it is rotating:
So you need to account for weight and geometry. Assuming that you have a cylindrical pole, you will have a figure similar to the image above (quite thinner, obviously), and if we also assume that the weight of the rope and ball does not change the COM, then you know the position of it.
Now you can measure the angle needed for the COM to be just over your pivot. Now you need to calculate how much energy do you need to make this rotation and compare it with the kinetic energy that the ball has.
The weight of the pole will affect how much energy you need to lift the COM over the pivot.
Reading the question again, I may have misunderstood it. Are you going to fix the pole to the ground? Like with bolts and so? Then the weight of the pole is not as important as the feature that you use to fix it to the ground.