# Force required to pull a floating object under water relative to mass and volume

Let's say you have multiple objects with the same density floating on top of the water but they have different volumes and masses. Does it take any more force to pull the different objects under the water that say, more mass or volume ? Or does the only thing that matter is the density?

There is similar question asked here: Changes in force required to push buoyant object under liquid/water but I am unable to think through it when applied to different objects. I am not sure if they have the same density that would imply that the same volume of water is being displaced.

• The reactionary force that is created by water purely depends on the volume of the water displaced. The net force depends on the difference in the densities of the object and the water. So, taking an iron and a wooden nail of same dimensions and hence different masses, the iron nail sinks while the wooden nail floats.( Even though the reactionary force by the water is same for both). You should draw a free body diagram , label the forces and write down the net force on that object. Do this for multiple objects and see. May 28, 2021 at 13:04
• In case I wasn't clear in my question, I am talking about the force required for say a human being to pull the object under the water. Not just simply why something sinks or floats. May 28, 2021 at 13:22
• If something floats, you find the buoyant force. The human has to apply a force of magnitude atleast equal to the buoyant force. For this, you have to necessarily do the above process I say. May 28, 2021 at 13:24

The force required depends upon two factors, the volume of the object and its weight.

The volume determines how much water is displaced when the object is pulled under the water- the greater the volume, the more force you have to apply.

The weight of the object gives you a helping hand, since gravity will act to pull the object down.

The density tells you the ratio of the two factors- ie the extent to which the weight is going to help you pull the object under. If the density is greater than the density of water, the object will sink all by itself. If the density is less, you will have to exert a force, and the magnitude of the force will increase directly with the volume of the object.

Density = mass / volume

buoyant force = weight of displaced fluid

For example 3 different objects with the same density:

Object 1: 100 mass units / 10 volume units
Object 2: 200 mass units / 20 volume units
Object 3: 60 mass units / 6 volume units


As more and more of the object is being submerged into the water it takes more force to submerge it as the buoyant force is increasing. So even though Object 3 and Object 2 have the same density, it will always more force to submerge Object 2 just based on the volume. If you have objects with different densities that are buoyant they will come to rest with a different percentage already submerged, however to fully submerge the object you will always have to contend with the volume of the entire object, there the force required to pull an already floating object underwater will always be greater for larger volume objects regardless of density.