How does increasing the density of a ruler affect its balance?

[NasuSama]

Homework Statement

In procedure 3, you balance the ruler. If the density of the ruler increases without changing its dimensions, the ruler will...

→still be balanced
→be unbalanced, but the direction depends on the hanging mass, the mass of the ruler, and distances
→tip away from m
→tip toward m

In my lab report, it says that I need to balance the ruler at the 40 cm mark and then, adjust the mass to the left to make the ruler balanced.

2. The attempt at a solution

I said that the ruler will tip away from m, contrast to the ruler hung at the center 50 cm mark, but I'm not sure if that is true.

 

[CWatters]

Replace the ruler with massless ruler and an equivalent mass hanging from its center of gravity.

 

[Basic_Physics]

The centre of gravity will not move to another point when its density is increased - look at the formula for calculating the coordinates of the centre of gravity - this is what CWatters suggests in effect just worded differently.