A certain block is floating in water with 77% of itself submerged. It has a length of 4.3 cm, a width of 5.9 cm, and a height of 2.75 cm. What is its mass, in kilograms?
a. 1.86 kg
b. 2.77 kg
c. 0.0086 kg
d. 5.98 kg
e. 3.62 kg
f. 0.0537 kg

f. 0.0537 kg

Explanation:

To solve this, we use the formula for force of buoyancy (Fb) = Vs × D × g

Where; Fb= Force of buoyancy

Vs= Volume of submerged

block

D= Density of water that block

submerges in

g= acceleration due to gravity

In this question, volume of block can be calculated using L×B×H

= 4.3cm × 5.9cm × 2.75cm = 69.7675cm^3

If 77% of the block is submerged in water, then 77/100 × 69.7675cm^3

= 53.72cm^3 is the Volume of submerged block

Density of water is known as 1000kg/m^3 while the gravitational force is 10m/s^2

We need to convert the Vs (volume of submerged block) to m^3 by dividing by 1,000,000

Hence, Vs = 53.72/1000000

Vs= 0.00005372m^3

Using the formula; (Fb) = Vs × D × g

Fb = 0.00005372m^3 × 1000kg/m^3 × 10m/s^2

Fb = 0.5372kg/m/s^2

Therefore, the force of buoyancy of the object on water is 0.5372kg/m/s^2

Recall that; Mass (m) = Volume (V) × Density (D)

Force of buoyancy (Fb) = Vs×D = mass (m) × acceleration due to gravity (g)

i.e. mass = Fb/g

= Mass of the block = 0.5372/10

Mass = 0.05372kg

Therefore, the mass of the block in kg is 0.05372kg