Why do we need to apply more force to push a submerged object deeper? If the buoyant force acting on a body submerged in a liquid,say water, does not depend on depth, why does it become increasingly difficult to push an object deeper and deeper.
I know that the buoyant force is just the pressure difference between the bottom and the top of an object, and since the only forces acting are the force F( which you are applying on the body to push it) , the buoyant force and the weight of the object and also since the latter 2 are constant shouldn't F also be constant?
Could someone please point out to me where i am going wrong?
 A: Well, firstly, I'm not a physics pro but here is a possible explanation.. When you talk about pushing a bucket into water.. I guess initially YOU were not submerged so there was no buoyant force on your body. However, as you pushed the bucket deeper, you would have stepped into the water so you yourself would experience an upward  buoyant force. This would make it difficult for you to push the bucket deeper down. Or it might have something to do with the portion of the bucket submerged.. as the answer above this explains..
A: The force required to push an object into water increases as the object submerges, i.e. as the amount of water the object displaces steadily increases. But  I think if you do the experiment carefully you will find that, once the object is fully submerged, the force required should be almost constant.
Thereafter, many objects get easier to push down with increasing depth, as the water pressure crushes them and they therefore displace less water. Wetsuits, for example, become greatly less buoyant with depth for this reason, which is why divers usually wear a buoyancy compensator. 
At extreme depths, if something is less compressible than water, it will become harder to push down owing to the increasing density of water with depth. Factors such as this are important in the design of deep sea submersibles and bathyscaphes such as Alvin and the Trieste.
A: I believe that were you are "going wrong" is on your statement, "Why do you need to apply more force to push a submerged object deeper?"
As you state, "the buoyancy force is the result of the difference in pressure between the bottom and top of the object." Therefore, as you submerge the object deeper, even though the density of the liquid increases, it increases for both, the bottom and the top - equally.  Thus, the difference in pressure remains the same!
If you are obtaining a different result than this, you probably are doing something wrong, or there are other variables that you have not disclosed. 
A: I believe the question is taken from class 9th NCERT, page 140 ,activity 10.4.
You read the half part that The upward force exerted by the water goes on increasing as the bottle is pushed deeper then you missed the next few words - till it is completely immersed.
A: I'm not sure but it's probably because the density of water gets bigger as we go deeper due to the weight of the liquid above, changing the force of buoyoncy.
