Question

18. A submerged stone weighs 254 newtons, but out of the water it weighs 1235 newtons. The density of the water is1000 kilograms per cubic meter. The volume of the stone is most nearly(a) 0.100 m^3(b) 0.206 m^3(c) 0.254 m^3(d) 1.24 m^3

Answer 1

ANSWER:

(a) 0.100 m^3

STEP-BY-STEP EXPLANATION:

We have that the force is equal to mass times gravity, therefore, we can calculate the mass, because the difference in force would be the volume of the stone.

Therefore

$\begin{gathered} F=m\cdot a \\ m=\frac{F}{a} \\ m=\frac{1235-254}{9.8}=100.1\text{ kg} \end{gathered}$

Now, we know that the density is equal to the quotient between the mass and the volume, therefore we can calculate the volume like this:

$\begin{gathered} d=\frac{m}{v} \\ v=\frac{m}{d} \\ v=\frac{100.1}{1000} \\ v=0.1001\cong0.100m^3 \end{gathered}$

Therefore the volume of the piece is 0.100 cubic meters.