A man has to measure his suitcase's mass, but he can't just put it on a scale and measure it as the suitcase is too big. Instead, he measures himself as having a mass of $100$ kg and decides to hold the suitcase in one hand and step on the scale, subtracting $100$ kg from what the scale reads. However, having abnormally long arms, he holds the suitcase so that its centre of mass is $l$ m away from his body's centre of mass.
The man wonders whether/how the value of $l$ will affect his reading.
Thanks!
In order not to fall off the scale, he must position himself so that a vertical line through the centre of mass of the combined system (him + suitcase) meets the convex hull of the region where his feet contact the scale. But as long as he succeeds in doing that, and holds himself and the suitcase motionless, he should get an accurate reading.
This assuming, of course, that $l$ is small compared to the radius of the Earth.