Why will solids float in liquids of greater density but sink in liquids of lesser density?
Greater the liquid density, greater is the [buoyant] upward force for relatively small volume of displaced liquid. It floats, when the weight of the solid equals the weight of the displaced liquid. Lesser the liquid density, lesser is the [buoyant] upward force for relatively larger volume of displaced liquid. Even after the whole solid is immersed into the liquid, the upward force of the displaced liquid is not enough to balance the weight of the solid. The solid goes on into the liquid by the resultant downward force.