A 400 cm3 ball floats in the liquid, plunging into the liquid by 3/8 of its volume. The density of the liquid is 2 times

| January 28, 2021 | education

A 400 cm3 ball floats in the liquid, plunging into the liquid by 3/8 of its volume. The density of the liquid is 2 times the density of the ball material. What is the volume of the cavity inside the ball?

To find the value of the volume of the cavity inside the specified ball, we use the equality: Ft = Fa; m * g = ρl * g * Vp; ρsh * (V – Vpol) * g = ρl * g * Vp, whence we can express: V – Vpol = ρl * g * Vp / (ρsh * g) and Vpol = V – ρl * Vp / ρsh.

Constants and variables: V (volume of the specified sphere) = 400 cm3; ρl (fluid density) = ρsh (ball material density); Vp (volume of the immersed part) = 3/8 V.

Calculation: Vpol = V – ρl * Vp / ρsh = 400 – 2ρsh * 3/8 * 400 / ρsh = 400 – 300 = 100 cm3.

Answer: The cavity inside the specified ball has a volume of 100 cm3.



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