A homogeneous body with a volume of 300 cm3 floats in a liquid whose density is 5 times

| February 16, 2021 | education

A homogeneous body with a volume of 300 cm3 floats in a liquid whose density is 5 times higher than the density of the body’s substance. Determine the volume of the body part above the surface of the liquid.

Let p be the density of the substance of the body, expressed in g / cm ^ 3. Then 5p is the density of the fluid in which the body floats.

Body weight, expressed in grams, is 300 rubles. If x is the volume of that part of the body that is immersed in liquid, then the mass of the liquid in this volume is 5p * x. According to Archimedes’ law, the equality

5p * x = 300p, and canceling by p we get

5x = 300, whence

x = 60 cm ^ 3.

Since x is the volume of the immersed part of the body, we get that the volume of the non-immersed part is 300 – 60 = 240 cm ^ 3.



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