Centroid Question: Understanding & Measuring Distance

[Ry122]

I'm having trouble understanding what this question is actually asking for. Is it assuming the centroid to be the origin and asking how far the bottom of the shape extends downwards for the origin to be the centroid?

 

[Fightfish]

I'm having trouble understanding what this question is actually asking for. Is it assuming the centroid to be the origin and asking how far the bottom of the shape extends downwards for the origin to be the centroid?

No, I don't think so. To the best of my interpretation of the question, it contains two parts:
(1) Given this shape, find out the position of the centre of mass (in terms of L).
(2) From that answer, determine the range of values of L such that the centre of mass lies in the shape itself (i.e. $L \leq y_{c} \leq 0$)

 

[haruspex]

I'm having trouble understanding what this question is actually asking for. Is it assuming the centroid to be the origin and asking how far the bottom of the shape extends downwards for the origin to be the centroid?

Not exactly that, but if you were to answer that question it would be a short step to answering the last part of the given question. Wouldn't help so much with the first part though, so address that first.

 

[HallsofIvy]

The figure is described completely and you are asked to find the centroid. So, no, the problem does not assume the centroid is at the origin! The centroid of a region always lies within it convex hull but for some values of L, the centroid might lie just above the origin, outside the figure itself.