Question

The block in this illustration is floating in water, which has a density of 1.00 g/cm3 .What is a good estimate of the density of the block if about 30 percent of the block is below water?

Answer 1

Answer : The density of the block is estimated to be, $0.30g/cm^3$.

Explanation :

Density of the water, $\rho_w=1.0 g/cm^3$

As we know that,

Buoyant force = $\rho\times volume\times g$

where,

g = gravitational acceleration

volume of the block = v

density of the block = $\rho_o$

Weight of the Block = Buoyant force exerted by water

$\rho_o\times v\times g=\rho_w\times 30\%\text{ of volume of block}\times g$

$\rho_o\times v\times g=\rho_w\times 0.30v\times g$

$\rho_o\times v\times 9.8 m/s^2=1 g/cm^3\times 0.30v\times 9.8 m/s^2$

$\rho_o=0.30 g/cm^3$

Thus, the density of the block is estimated to be, $0.30g/cm^3$.