I have 2 questions, the second question is based on the answer of the first question
1.)When an object floats, is the volume of the object submerged and displaced water equal?
2.)So if volume displaced become equal to volume of object, According to the formula, volume and gravity get cancelled on both sides leaving densities equal. This is not possible because if the density of object is less it floats.
V(object)p(density of the object)g=Buoyant force=V(displaced liquid)p(density of the liquid)g
Best Answer
When an object floats, not all of the object is submerged. There is some portion that remains above the surface.
This means that the total volume of the object is greater than the volume of the object that is submerged. Since, as you said, the volume of the object that is submerged is equal to the volume of displaced water, this means that the total volume of the object is greater than the volume of displaced water.
This is what makes the equality in your question possible - the density of the floating object is less than water, but its total volume is greater than the volume of displaced water. This also means that the closer an object's density is to the density of displaced water, the lower in the water it will float (for example, ice is only slightly less dense than water, so most of an iceberg is submerged - a fact that has led many ships to their demise).