A hydrometer of mass y kg and volume 2y x 10\(^{-5}\)m\(^3\) floats in a fluid with 20% of its volume above the fluid, what is the density of the fluid?
A
6.22 x 10\(^4\)kgm\(^{-3}\)
B
6.23 x 10\(^4\)kgm\(^{-3}\)
C
6.24 x 10\(^4\)kgm\(^{-3}\)
D
6.25 x 10\(^4\)kgm\(^{-3}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Density = \(\frac{\text{mass}}{\text{volume}}\)
mass of hydrometer = y kg
80% hydrometer's volume submerge(20% above the fluid) = \(\frac{4}{5}\) x 2y x 10\(^{-5}\) = \(\frac{8y \times 10^{-5}}{5}\)
Density = y x \(\frac{5}{8y\times 10^{-5}}\) = 6.25 x 10\(^4\)kgm\(^3\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #70470)