Q12E

Question

You are preparing some apparatus for a visit to a newly discovered planet Caasi having oceans of glycerin and a surface acceleration due to gravity of 5.40 m/s2 . If your apparatus floats in the oceans on earth with 25.0% of its volume submerged, what percentage will be submerged in the glycerin oceans of Caasi?

Step-by-Step Solution

Verified

Answer

The volume of apparatus submerged on caasi will be .

1Step 1: given data

Given data can be listed below,

Surface acceleration due to the gravity of caasi is .
The volume of apparatus floats in the ocean on the earth .

2Step 2: Concept of buoyant force

When immersed in a particular fluid, an object disperses or pushes out equal amounts of that liquid. Whenever an object's weight exceeds the weight of the fluid it displaces, gravity pulls harder on it, causing it to sink.

3Step 3: calculation of the percentage of volume submerged in ocean

The buoyant force on earth can be given as,

…i)

Here, is the density seawater , is the volume of object, is the acceleration due to the gravity of the earth, and m is the mass of apparatus.

Mass of the apparatus on the earth can be expressed as,

…ii)

The buoyant force on planet cassi can be expressed as,

…iii)

Here, is the density of glycerin , is the volume submerged, and is the acceleration due to gravity on the surface of planet caasi.

Mass of apparatus on caasi can be expressed as,

…iv)

The two expressions for mass must be equal by equating ii) and iv),