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13 September, 16:10

A frog in a hemispherical pod finds that he just floatswithout

sinking in a fluid of density 1.25 g/cm3. If the pod has

a radius of3.00 cm and negligible mass, what isthe mass of the

frog?

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Answers (1)
  1. 13 September, 17:54
    0
    The mass of the frog = 70.72 g

    Explanation:

    From the law of flotation,

    Weight of the frog = weight of the fluid displaced

    Wₓ = Wₐ ... Equation 1

    Where Wₓ Weight of the frog, Wₐ = weight of the fluid displaced.

    But,

    Wₓ = mₓg ... Equation 2

    Wₐ = ρVg ... Equation 3

    Where mₓ = mass of frog, V = volume of fluid displaced, ρ = density of fluid, g = acceleration due to gravity.

    Substituting both equation 2 and 3 into equation 1

    mₓg = ρVg

    Equation g from both side of the equation,

    mₓ = ρV ... Equation 4

    Given: ρ = 1.25 g/cm³, and V = volume of a hemisphere = 2/3πr³

    Where r = radius of the pod = 3.00 cm³, π = 3.143

    V = 2/3 (3.143) (3) ³

    V = 2*3.143*9

    V = 56.574 cm³

    Substituting these values into equation 4,

    mₓ = 1.25*56.574

    mₓ = 70.7175 g

    mₓ ≈ 70.72 g

    Thus the mass of the frog = 70.72 g
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