A homogeneous sphere made of a material has a weight that is twice as much when it is half submerged in water compared to when it is completely submerged. What is the specific gravity of the material?
Let the weight of the sphere be $q$, its volume $v$, then its density is $\frac{q}{v}$. According to Archimedes' principle, the weight of the sphere completely submerged in water is $q-v$, and the weight of the sphere half-submerged in water is $q-\frac{v}{2}$.

According to the problem,

$$
q-\frac{v}{2}=2(q-v)
$$

from which the density of the body, i.e., $\frac{q}{v}$, needs to be calculated. Divide both sides of the equation by $v$

$$
\frac{q}{v}-\frac{1}{2}=2 \frac{q}{v}-2
$$

from which the desired density is

$$
\frac{q}{v}=1.5
$$