Two spheres $P$ and $Q$ of equal radii have dimensions ${\rho }_1$ and ${\rho }_2$ respectively. The spheres are connected by a massless string and placed in liquids $L_1$ and $L_2$ of densities ${\sigma }_1$ and ${\sigma }_2$ and viscosities ${\eta }_1$ and ${\eta }_2$ respectively. They float in equilibrium with the spheres $P$ in $L_1$ and $Q$ in $L_2$ and the string being taut, figure below. If sphere $P$ alone in $L_2$ has terminal velocity $\overrightarrow{V_P}$ and $Q$ alone in $L_1$ has terminal velocity $\overrightarrow{V_Q}$, then