A cube of wood having an edge dimension of 18.7 cm and a density of 653 kg/m3 floats on water. (a) What is the distance from the horizontal top surface of the cube to the water level

6.5 cm

Explanation:

Given that the edge dimension of a cube, a = 18.7 cm

Density of the cube,

Volume of the cube,

Mass of the cube.

kg

Gravitational force action on the cube in the downward direction is

where g is the acceleration due to gravity.

As the cube floats on the water, let the distance from the horizontal top surface of the cube to the water level is x cm.

So, the distance from the horizontal bottom surface of the cube to the water level= (18.7 - x) cm.

Volume of water replaced, volume of a portion of the

cube inside the water.

So,

As the density of water,

So, the mass of the water displaced,

kg

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

So,

For the floating condition, the gravitational force acting on the cube in the downward direction must be equal to the buoyancy force acting on the cube in the upward direction.

So, equation equations (i) and (ii), we have

cm

Hence, the distance from the horizontal top surface of the cube to the water level is 6.5 cm.