A hydrometer is made of a tube of diameter 2.3cm.The mass of the tube and it’s content is 80g. If it floats in a liquid density

Question

A hydrometer is made of a tube of diameter 2.3cm.The mass of the tube and it’s content is 80g. If it floats in a liquid density 800kg|m, calculate the depth to whc it sinks

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Minh Khuê 6 months 2021-07-27T15:41:27+00:00 1 Answers 31 views 0

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    2021-07-27T15:42:27+00:00

    Answer:

    The depth to which the hydrometer sinks is approximately 24.07 cm

    Explanation:

    The given parameters are;

    The diameter of the hydrometer tube, d = 2.3 cm

    The mass of the content of the tube, m = 80 g

    The density of the liquid in which the tube floats, ρ = 800 kg/m³

    By Archimedes’ principle, the up thrust (buoyancy) force acting on the hydrometer = The weight of the displaced liquid

    When the hydrometer floats, the up-thrust is equal to the weight of the hydrometer which by Archimedes’ principle, is equal to the weight of the volume of the liquid displaced by the hydrometer

    Therefore;

    The weight of the liquid displaced = The weight of the hydrometer, W = m·g

    Where;

    g = The acceleration due to gravity ≈ 9.81 m/s²

    ∴ W = 80 g × g

    The volume of the liquid that has a mass of 80 g (0.08 kg), V = m/ρ

    V = 0.08 kg/(800 kg/m³) = 0.0001 m³ = 0.0001 m³ × 1 × 10⁶ cm³/m³ = 100 cm³

    The volume of the liquid displaced = 100 cm³ = The volume of the hydrometer submerged, V_h

    V_h = A × h

    Where;

    A = The cross-sectional area of the tube = π·d²/4

    h = The depth to which the hydrometer sinks

    h = V_h/A

    ∴ h = 100 cm³/( π × 2.3²/4 cm²) ≈ 24.07 cm

    The depth to which the tube sinks, h ≈ 24.07 cm.

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