Consider two solid spheres P and Q each of density `8gm cm^-3` and diameters 1cm and 0.5cm, respectively. Sphere P is dropped into a liquid of density `0.8gm cm^-3` and viscosity `eta=3` poiseulles. Sphere Q is dropped into a liquid of density `1.6gmcm^-3` and viscosity `eta=2` poiseulles. The ratio of the terminal velocities of P and Q is

Explanation

When buoyant force plus air resistance becomes equal to weight of sphere then terminal speed is attained. If V represents terminal speed then it can be shown that `V_(r) alpha ((p-sigma)r^(2))/(eta)`
p=density of sphere, and `sigma`= density of medium.
`V_(T)^(P)/V_(T)^(Q)=((8-0.8) xx 1^(2) xx2)/(3 x (8-16) xx 0.5^(2))=3`