There is a cuboidal box which is filled with liquid of density . Let & be the force applied by the liquid on and , respectively.
Find .
Bonus: Solve this problem without using calculus.
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There is a property that the total force on an area inside any fluid is equal to the pressure applied by that fluid at the center of the area × total area
now let a r e a o f Δ A B C = a r e a Δ A D C = Δ
and when we calculate the depth of the center of both the triangle we will sea that the depth of the center of Δ A D C is twice the depth of the center of Δ A B C
so F 2 F 1 = δ × g × 2 h × Δ δ × g × h × Δ = 0 . 5
where δ = d e n s i t y g i v e n l i q u i d
h = d e p t h o f c e n t e r o f Δ A B C
g = a c c e l e r a t i o n d u e t o g r a v i t y