Two spheres P and Q of equal radii have densities $ρ_{1}$ and $ρ_{2},$ respectively. The spheres are connected by a massless string and placed in liquids $L_{1}$ and $L_{2}$ of densities $σ_{1}$ and $σ_{2}$ and viscosities $η_{1}$ and $η_{2},$ 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 $\vec{V_{P}}$ and Q alone in $L_{1}$ has terminal velocity $\vec{V_{Q}},$ then

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${\vec{V}}_{P} . {\vec{V}}_{Q} < 0$

$\frac{| {\vec{V}}_{P} |}{| {\vec{V}}_{Q} |} = \frac{η_{1}}{η_{2}}$

$\frac{| {\vec{V}}_{P} |}{| {\vec{V}}_{Q} |} = \frac{η_{2}}{η_{1}}$

${\vec{V}}_{P} . {\vec{V}}_{Q} > 0$

answer is A, D.

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