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23 May, 20:21

A solid sphere of mass 8.6 kg, made of metal whose density is 3400 kg/m^3, hangs by a cord. When the sphere is immeresed in a liquid of unknown density, the tension in the cord is 38N. What is the density of the liquid?

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  1. 23 May, 20:35
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    1868.58 kg/m³

    Explanation:

    From Archimedes principle,

    R. d = Density of object / density of liquid = Weight in air / Upthrust.

    D/D' = W/U ... Equation 1

    Where D = density of the solid sphere, D' = density of liquid, W = weight of solid sphere in air, U = upthrust of solid sphere in liquid.

    Making D' the subject of the equation,

    D' = D (U/W) ... Equation 2

    Recall,

    U = W-T ... Equation 3

    Where m = mass of the solid sphere, g = acceleration due to gravity.

    W = mg ... Equation 4

    Where T = tension in the cord.

    Given: m = 8.6 kg

    constant: g = 9.81 m/s²,

    Substitute into equation 4

    W = 8.6 (9.81)

    W = 84.366 N.

    Also given: T = 38 N

    Substitute into equation 3

    U = 84.366-38

    U = 46.366 N.

    Finally, substituting into equation 2,

    given that D = 3400 kg/m³

    D' = 3400 (46.366/84.366)

    D' = 1868.56 kg/m³

    Hence the density of the liquid = 1868.58 kg/m³
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