Solving Two Physics Problems: Weighing Rocks and Steel Barbells

[SnowOwl18]

Alright, these two problems are driving me nuts:

1. ---To verify her suspicion that a rock specimen is hollow, a geologist weighs the specimen in air and in water. She finds that the specimen weighs twice as much in air as it does in water. The solid part of the specimen has a density of 5.10×103kg/m3. What fraction of the specimen's apparent volume is solid?----

I think that this involves Archimede's Principle because she floats the rock in water to find displacement... the equation is (magnitude of buoyant force)= (weight of displaced fluid) ...but I don't see how I can use that equation..

Also this problem:
----A bodybuilder is holding a 29.9kg steel barbell above her head. How much force would she have to exert if the barbell were lifted underwater?---

It doesn't seem like much information to work with...maybe i'd need to use archimede's principle here as well, to find the weight displacement...but again, I'm not sure how to do that.

Thanks for any help on these problems :)

 

[Tide]

HINT: The mass of an object is the product of its density and volume.

 

[SnowOwl18]

hmm so mass= density x volume. For the first problem I know the density and that the weight in air is twice that of in water...how do I use that equation if I don't actually know the mass though? Thanks for you're help so far :)

 

[Tide]

Does this help?

$$Submerged \ Weight = Dry \ Weight - \rho_{water} \ g Volume_{hollow}$$

$$Dry \ Weight = \rho_{rock} \ g \ Volume_{rock}$$