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 
and Q alone in L 1 has terminal velocity 
, then
Text Solution
Verified by ExpertsA
For floating
( ρ 1 + ρ 2) V = ( σ 1 + σ 2) V
ρ 1 + ρ 2 = σ 1 + σ 2
since strings in taut so
ρ 1 < σ 1 , ρ 2 > σ 2
VP = 
VQ = 
since σ 2 – ρ 1 = – ( σ 1 – ρ 2)
because VP and VQ are opposite
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