Is there a way to give specific mass to a solid body?

For simulation purposes I need to control and have specific mass on certain solid bodies. So the question is, is it possible to add a mass to a solid with random dimension

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It would probably be easier to create a custom material and vary the density of that material until you get the mass you need.

 
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Usually in your CAD system you can determine the volume of the part. If you have a specific weight that you are working with, you can divide that into the volume and determine the density that you'd need to apply in order to have the model weight = your target weight.
If you use properties of your model, you could put that into a design table and do the calculations that way.

 
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