Question

You are preparing some apparatus for a visit to a newly discovered planet Caasi having oceans of glycerine and a surface acceleration due to gravity of 5.40m/s^2.

If your apparatus floats in the oceans on earth with 25.0% of its volume submerged, what percentage will be submerged in the glycerine oceans of Caasi?

Answer 1

The value is
`a = 20.4 \%`

Step-by-step explanation:

From the question we are told that

The acceleration due to gravity of the planet is
`a = 5.40 \ m/s^ 2`

The percentage volume of the apparatus submerged in the ocean on earth is
`k = 25.0 \%`

Generally the buoyant force acting on the apparatus is equal to the weight of the apparatus

i.e

`\rho_s * V_s * g = m * g`

Hence the mass of the apparatus is mathematically represented as

`m_s = \rho_s * V_s`

Here
`\rho_s` is the density of the sea water with a value of
`\rho_s = 1030 \ kg/m^3`

`V_s` is the volume of the apparatus submerged

So

`m_s = 1030 * 0.25 V`

Here V is the total volume of the apparatus

=>
`m_s = 257.5 V \ kg`

Generally at the new planet the mass of the apparatus is mathematically represented as

`m_c = \rho_c * V_c`

Here
`\rho_c` is the density of the glycerin with a value of
`\rho_c = 1260 \ kg/m^3`

Gnerally
`m_s = m_c`

So

`257.5 V = 1260 * V_c`

=>
`V_c = (257.5V )/( 1260 )`

=>
`V_c = 0.204 \ V`

Hence the percentage volume of the apparatus which is submerged in glycerin at the new planet is

`a = 0.204 * 100 = 20.4 \%`