Assuming a solid rectangular plate, hinged along one edge. How does one calculate the mass of the plate if the force necessary to lift the opposite edge is known?
This is blatantly a homework question, so we're only allowed to discuss methods, and not give you the answer. With any problem like this the very first thing to do is draw a diagram. From the limited information in your question I think the situation loks like this:
You know the force $F$ that you're using to lift the end of the plate, and you want to know the force $mg$, where $m$ is the mass of the plate and $g$ is the acceleration due to gravity.
You find $mg$ by taking moments about the hinge. The distance from the hinge to the end of the plater where you're applying the force is $l$, and if the plate is a rectangle the force $mg$ acts from the centre of mass, which is $l/2$ away from the hinge.
The rest is up to you!