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?
- 6.22 x 10\(^4\)kgm\(^{-3}\)
- 6.23 x 10\(^4\)kgm\(^{-3}\)
- 6.24 x 10\(^4\)kgm\(^{-3}\)
-
6.25 x 10\(^4\)kgm\(^{-3}\)
The correct answer is: D
Explanation
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\(^3\)
There is an explanation video available .