I just did the another solution. I will attach here. Got the same as you again.
In the first photo I calculated the force due the liquid 2
In the second one the force due the liquid 1 (taking into account the pressure that liquid 2 keeps exerting)
The last one I found the resultant
I think now...
I will try to do it by integrating too. I realized now that I really made a simple mistake and the resultant force is what you found. But now I am a little bit confused, the total force does not depend of 𝜌2 . Isnt that weird ? What should the answer for 𝜌2 be ?
Yeah. P is the pressure at the bottom of the tank. F' is the force that acts on that area due the pressure P. E is the buoyancy force(the famous one E = density of liquid x gravity x volume of body submersed), but here is the main problem of this kind of situation : We cannot just say that E is...
Yeah. This problem is from the Ibero-American Physics Olympiad 2017 but they did not share the solution/answer. I will attach here what I did, sorry for not doing this before.