Two spheres P and Q of equal radii have densities ρ1 and ρ2, respectively. The spheres are

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Two spheres P and Q of equal radii have densities ρ₁ and ρ₂, respectively. The spheres are connected by a massless string and placed in liquids L₁ and L₂ of densities σ₁ and σ₂ and viscosities h₁ and h₂, respectively. They float in equilibrium with the sphere P in L₁ and sphere Q in L₂ and the string being taut (see figure). If sphere P alone in L₂ has terminal velocity and Q alone in L₁ has terminal velocity than

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Consider a body of density ρb kept in density ρl whose viscosity is h and terminal velocity V. Then∴ = (ρ6 - ρl) πR3(ĵ) ⇒ 6πηRV = (ρ6 - ρl) πR3∴ if ρb > ρl then ↑ V ∝ 1/η & if ρb < ρl ↓as per given diagram we can sayσ2 > σ1 ; ρ1 < σ1 & ρ2 > σ2⇒ ρ2 > σ2 > σ1 > ρ1∴ if we put P in L2 where |Vp| ∝ when ρ1 < σ2 ∴ ↓∴ if we put Q in L1 where|VQ| ∝ when ρ2 > σ1 ∴ ↓ ⇒

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