If it’s properly weighted, I think it will show you the slope. Imagine a circle on a sloped line, weighed at the bottom. If the circle is upright, so the weight is at the bottom, the point of contact is a bit above the bottom of the circle.
The direct distance from the point of contact to the bottom of the circle has to be less than along the perimeter; also the angle to the circle’s bottom has to be shallower than that of the slope.
Therefore, if the circle rolls down until the weight (that used to be the bottom) is now the point of contact, the point of contact travels a distance along the slope equal to that arc (perimeter) of the circle. The new point of contact must therefore now be lower than the bottom of the circle was before.
So the circle will come to rest with the weight at the point of contact (or above?), i.e. the circle is now tilted. Similarly, the ball with a weight near the bottom will sit tilted on a sloped surface.
It can show you if there is a slope, maybe. If it is properly weighted then it wouldn’t even do that.
If it’s properly weighted, I think it will show you the slope. Imagine a circle on a sloped line, weighed at the bottom. If the circle is upright, so the weight is at the bottom, the point of contact is a bit above the bottom of the circle.
The direct distance from the point of contact to the bottom of the circle has to be less than along the perimeter; also the angle to the circle’s bottom has to be shallower than that of the slope.
Therefore, if the circle rolls down until the weight (that used to be the bottom) is now the point of contact, the point of contact travels a distance along the slope equal to that arc (perimeter) of the circle. The new point of contact must therefore now be lower than the bottom of the circle was before.
So the circle will come to rest with the weight at the point of contact (or above?), i.e. the circle is now tilted. Similarly, the ball with a weight near the bottom will sit tilted on a sloped surface.