A frog in a hemispherical pod(see fig) just floats without sinking into sea water with density $1.35 g / c m^{3}$ . If the pod has radius $6$ cm and negligible mass, what is the mass of the frog?

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Solution

Buoyancy is an upward force exerted by a fluid that opposes the weight of an immersed object.
In terms of Volume, Height and area, It is given by $F_{b} = ρ g V = ρ g h A$
where,
$ρ$ is the density of the fluid,
$g$ is the gravity,
$V$ is volume of the immersed part of the body in the fluid.
$h$ is the height of immersed part and
$A$ is the area.
In this case, the density of the liquid is $1.35 g / c m^{3}$ , $g = 10 m / s^{2}$ and the area of the hemisphere is given as $\frac{4}{6} π r^{2} = 452.16 {c m}^{3}$ .
Therefore, $F_{b} = ρ g V = 1.35 \times 1 \times 452.16 = 610.4 g$ .
Hence, the mass of the frog is $610.4 g$

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A frog in a hemispherical pod(see fig) just floats without sinking into sea water with density 1.35g/cm3. If the pod has radius 6cm and negligible mass, what is the mass of the frog?

A frog in a hemispherical pod(see fig) just floats without sinking into sea water with density $1.35 g / c m^{3}$ . If the pod has radius $6$ cm and negligible mass, what is the mass of the frog?