Problem $1(37$ pts$)$: A manometer that is open to the atmosphere on both ends can be used to measure the density of a fluid. In this case, the light$-$colored fluid has an unknown density, and the darker$-$color fluid has a known density. The dark$-$colored fluid is water in this case.

a$)$ What is the density of the light$-$colored fluid, given the density of water is $999k\frac{g}{m^3}$ for the ambient temnerature $122$ntel $?$

b$)$ What is one limitation of this approach to obtain a fluid's density