Question

you have 5 blocks that are the same size (all blocks have a volume of 3 liters), but different masses (as shown). which blocks will float in this water tank? explain your reasoning.

Explanation:

Step1: Recall density - floatation relationship

An object floats if its density $
ho$ is less than the density of water $
ho_{water}= 1\ kg/L$. The density formula is $
ho=\frac{m}{V}$, where $m$ is mass and $V$ is volume.

Step2: Calculate density of the block

Given $V = 3\ L$. For a block of mass $m$, $
ho=\frac{m}{3\ L}$.
For the $2 - kg$ block: $
ho_1=\frac{2\ kg}{3\ L}\approx0.67\ kg/L$. Since $
ho_1 = 0.67\ kg/L<1\ kg/L$, it will float.
For the $5 - kg$ block: $
ho_2=\frac{5\ kg}{3\ L}\approx1.67\ kg/L$. Since $
ho_2=1.67\ kg/L > 1\ kg/L$, it will sink.
We need to calculate the density for all 5 blocks in the same way (but only two are shown in the image, assuming the same process for the other three). Blocks with density less than $1\ kg/L$ will float.

Answer:

The blocks with density less than $1\ kg/L$ will float. For example, the $2 - kg$ block will float as its density is approximately $0.67\ kg/L$.