The submarine's average density at this time is 992.1 kg/m³.
What is buoyant force?
The buoyant force of an object is the upward force of the object due to its weight displaced by a fluid.
The upward force of the submarine
\(F_n = m(a + g)\)
where;
- m is the mass of the submarine
The buoyant of the submarine
\(F_b = \rho Vg\)
- V is the volume of the submarine submerged
The upward force is equal to buoyant force
\(m(a + g) = \rho Vg \\\\\frac{m}{V} = \frac{\rho g}{a + g} \\\\\rho_s = \frac{\rho g}{a + g}\)
where;
- \(\rho _s\) is the average density of the submarine
\(\rho _ s = \frac{\rho g}{a + g}\\\\\rho _s = \frac{1.025 \times 10^3 \times 9.8}{0.325 + 9.8} \\\\\rho_s = 992.1 \ kg/m^3\)
Thus, the submarine's average density at this time is 992.1 kg/m³.
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