$!!!!$ Can you please go through the solving for mhg in detail. $!!!$

A hydrometer whose dimensions are given in the accompanying figure is used to measure

the density of varying fluids. The mass of the apparatus, not including the mass of the mercury

at the bottom, is $.$

If the hydrometer is immersed in water whose density is $,$ then half of the upper cylinder is

immersed in water $($the scale $/2$ is at the water level$).$

If a lighter fluid of density $,$ with $<mtext\; id="EditorElement\_1933367"></mtext><mn\; id="EditorElement\_1933368">1</mn>$ is used, the entire body is immersed, yet buoyant.

Find symbolically expressions to describe:

$($ii$)$ The mass $$ of the mercury at the bottom of the hydrometer and the height $$ of the

lower cylinder.

$($iii$)$ What is the range of fluid densities that this hydrometer can be used for?A hydrometer whose dimensions are given in the accompanying figure is used to measure

the density of varying fluids. The mass of the apparatus, not including the mass of the mercury

at the bottom, is $m_{\text{b}\text{o}\text{d}\text{y}}.$

If the hydrometer is immersed in water whose density is ${}_w,$ then half of the upper cylinder is

immersed in water $($the scale $\frac{h}{2}$ is at the water level$).$

If a lighter fluid of density ${}_w,$ with $<mn\; id="EditorElement\_1932575">1</mn>$ is used, the entire body is immersed, yet buoyant.

Find symbolically expressions to describe:

$($ii$)$ The mass $m_{Hg}$ of the mercury at the bottom of the hydrometer and the height $H$ of the

lower cylinder.

$($iii$)$ What is the range of fluid densities that this hydrometer can be used for?