If we have two objects with the same mass but different densities (lets assume object 1 is denser, therefore volume is lower relative to object 2).assume both objects have a lower density than water. now if we put both in water, both will float. since they float, buoynacy force is equal to the weight of the object, so buoynacy force in 1 and 2 should be equal .however if we use f(boyancy)=pvg--> then becuase the submerged v is less for the denser object and p fluid is the same, then we can conclude that f bouynacy are not the same for both objects. true or false?

take the volume that is submerged. That's the volume of water displaced.

but the volume of submerged is different in those two

so buoyancy force is different in those two

weights are the same

probably. since the densities* are different.

In question it says wights are the same and diffferent volumes

so it seems that the one with more density should have a lower buyonacy force

but you said that when an object floats the buoyancy force equals weight,so since both objects have the same weight,then buoynacy force should be equal in those two

The more dense object will float with a greater percentage of its volume immersed, not less.

2) If they have the same MASS, the more dense one will have less VOLUME