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It lowers proportionally to the decrease in the mass.

Since potential energy = mgh, changing the "m" would completely change the potential energy.

For instance if we look at g as 10 m/s^2 and h as 10m:

The original mass is 10kg. (10kg)*(10m/s^2)*(10m)= 1000J

If we cut the mass in half. (5kg)*(10m/s^2)*(10m)= 500J

The potential energy is cut in half.

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