Problem $6$

The diagram shows a frictionless piston of mass $0\mathrm{.}2kg,$ diameter $3cm,$ and negligible thickness in a tube that separates two liquids. Liquid $1$ has density $3400k\frac{g}{m^3}.$ Both liquids are open to atmospheric pressure air on top and the system is in equilibrium. The lengths shown in the diagram are $a=3cm$ and $b=7cm.$ Neglecting surface tension, calculate the density of liquid $2.$