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5 October, 15:05

An object weighing 335 N in air is immersed in water after being tied to a string connected to a balance. The scale now reads 250 N. Immersed in oil, the object appears to weigh 290 N. (a) Find the density of the object. (b) Find the density of the oil.

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  1. 5 October, 15:17
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    (a.) Density of the object = 3.941 * 10³ kg/m³ = 3941 kg/m³

    (b.) Density of oil = 529 kg/m³

    Explanation:

    Relative density = Density of a substance / density of water.

    According to Archimedes's principal: It states that when a body is wholly or partly immersed in a liquid or fluid, it experience a loss in weight which is equal to the upthrust.

    According to Archimedes's principal,

    Relative density = weight in air (N) / Apparent loss of weight under water (N).

    ∴ Density of a object / Density of water = Weight of object in air/apparent loss of weight under water (Upthrust in water).

    (a.)

    where, Density of water = 1000kg/m³, weight of object in air = 335 N

    Apparent loss of weight under water (upthrust in water) = 335 - 250 = 85N

    ∴ Density of the object = (weight of object in air/loss of weight under water) * density of water.

    Density of the object = (335/85) * 1000 = 3.941 * 10³ kg/m³.

    Density of the object = 3.941 * 10³ kg/m³.

    (b.) Relative density of oil = Density of oil/Density of water.

    From Archimedes's principal,

    Relative density = Upthrust of the body in oil / Upthrust of the body in water.

    Upthrust in oil = 335 - 290 = 45 N,

    Upthrust in water = 85 N.,

    Density of water = 1000 kg/m³

    ∴ Density of oil = (upthrust in oil / upthrust in water) * density of water

    Density of oil = (45/85) * 1000 = 0.529 * 1000

    Density of oil = 529 kg/m³
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