JEE (Advanced) 2015 Paper-2 Question 9

Question 9

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

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