A metal object of mass 8kg which has an internal cavity is attached to a inflattend rubber spherical balloon of negligible mass by an inextensible massless string.the system just floats on water of relative density 1.the specific gravity of metal is 8.find the volume of the cavity in the metal

What do you mean with "just floats on water"? Is it "does not sink but it is entirely immersed"?

If yes, then use the following argument:

It has mass 8kg, density 8 thus volume 1l. To receive enough hydrostatic force to avoid sinking it must displace 8kg of water (which having density 1, translates to 8l of water). As the body has volume 1l, it needs additional 7l, thus the cavity must have volume 7l.