Two spheres P and Q of equal radii have densities ${\rho }_1$ 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 sphere P in $L_1$ and sphere Q in $L_2$ and the string being taut (see figure).  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