Question

An object with volume 6.0*10^1 m^3 and mass of 2.600*10^4 kg will have bouyancy force,in ethyl alcohol?

Answer 1

the force of buoyancy = mass of the bodyx g=2.6 x 10^4 kg-wt

Explanation:

the ethyl alcohol has density = `0.789 g/(ml) =789 (kg/m^3)`

the volume of the body is `60 m^3` which will naturally float on the liquid with a part of it submerged in the liquid.

the volume of the displaced liquid say V1
will provide the necessary buoyant force to support the wt. of the body
therefore #V1. density . g = mass . g

where g is acceleration due to gravity.

therefore the force upward = `2.6 . 10^4 .g =`2.6. `10^5` N
here `g =10 m/s^2`

if one estimates volume of the liquid displaced it will come to about `32.9 m^3`

it means almost half of the body will be above ethanol.

Answer 2

The buoyancy force is `2.55*10^5 N` upward.

Explanation:

The density of the object is `(2.6*10^4 "kg")/(60 m^3) = 433.3 "kg"/m^3`.
From a table of densities, the density of ethyl alcohol is `789 "kg"/m^3`, which is greater than that of the object.

Therefore the object will float. The object still has weight, a downward force, given by

`m*g = 2.6*10^4 "kg"*9.8 m/s^2 = 2.55*10^5 N`.

Since it is in equilibrium at the top of the ethyl alcohol, the buoyancy force must be an equal and opposite force. Therefore, the buoyancy force is `2.55*10^5 N` upward.

I hope this helps,
Steve