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A cuboidal container of dimensions a x a x 2a (height 2a) is filled with two immiscible liquids: the lower half (height a) has density 2*rho and the upper half (height a) has density rho. Neglecting atmospheric pressure, find the ratio of the force on the base to the force on a side wall of the cuboid.
- 2: 3
- 1: 3
- 5: 6
- 6: 5
Correct answer: 6: 5
Solution
The base experiences the full hydrostatic pressure of both layers. The side wall force requires integrating pressure over height, accounting for the two different density regions (upper region pressure grows with rho, lower region starts at rho*g*a and grows with 2*rho).
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