Question

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?

Answer 1

The mass of the frog = 70.72 g

Step-by-step 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