Se sumerge en agua un cubo de un material que tiene una densidad de 0,2Kg/lt, y una Arista de 9cm. Calcula: La parte del cubo que flota y la parte que se hunde.

a. 18% y 21%

b. 20% y 25%

c. 20% y 26.8%

d. 25% y 31%

The percentage of the cube that floats = 80%

The percentage of the cube that sinks =20%

Explanation:

Given that the density of the cube material,

Length of the sides of the cube,

So, the volume of the cube,

As

so the volume of the cube

Hence, the mass of the cube, .

The gravitational force acting on the cube in the downward direction,

[g is the acceleration due to gravity]

Newtons ...(i)

At equilibrium condition, let x cm of the cube sinks in the water.

So, the volume of the water replaces,

Or,

The density of the water,

So, the mass of water replaced,

Now, the buoyancy force acting on the cube in the upward direction,

[ g is the acceleration due to gravity]

Newtons ...(ii)

At equilibrium condition, the gravitational force acting on the cube in the downward direction is equal to the buoyancy force acting on the cube in the upward direction, so by from equations (i) and (ii), we have,

.

So, the part of the cube that sinks = 1.8 cm

As the remaining portion of the cube is floating, so the part of the cube that floats .

The percentage of the cube that floats

=

The percentage of the cube that sinks

Please note that none of the given options are correct.

hi there!

out of the two, (b) precision would be more reasonable.   however, both a and b could be pretty reasonable.

-awesomerepublic   : )