The two blocks (block 1 with volume V1 = 4 m3 and block 2 with volume V2 = 2 m3) shown in the figure are submerged completely in water so that block 1 rests just below the surface. The two blocks are connected by a thin string of negligible mass and volume. If block 2 has a density 1.5 times that of block 1, what is the density of block 2?
To find the density of block 2, we first need to understand the concept of density. Density is defined as mass per unit volume. Mathematically, density (ρ) is given by the formula:
ρ = m / V
Where:
ρ = Density
m = Mass
V = Volume
In this case, we are given the volumes of both blocks (V1 and V2), but not the masses. However, we can use the given information about the density ratio between the two blocks to find the mass ratio.
It is stated that the density of block 2 is 1.5 times that of block 1. Therefore, the mass ratio between the two blocks will also be 1.5. Let's assume the mass of block 1 is m1 and the mass of block 2 is m2.
m2 / m1 = 1.5
Now, because density is the ratio of mass to volume (ρ = m / V), we can rewrite the equation for mass ratio in terms of density ratio:
(ρ2 / ρ1) = 1.5
Where:
ρ1 = Density of block 1
ρ2 = Density of block 2
Rearranging the equation, we get:
ρ2 = 1.5 * ρ1
So, the density of block 2 (ρ2) is 1.5 times the density of block 1 (ρ1).
Alternatively, if you are provided with the densities of the blocks, you can directly compare the densities to find the ratio. In this case, if the density of block 1 is ρ1, then the density of block 2 is given by:
ρ2 = 1.5 * ρ1