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

Answer

3

Explanation

Terminal velocity is given by ` v_r = (2 )/(9) (r ^2 )/(eta ) (d- rho ) g `
` (v_P)/(v_Q ) = (r_P^2 ) /( r _ Q ^2 ) xx ( eta _Q)/(eta _P ) xx ((d - rho _P))/((d- rho _Q)) = ((1)/(0.5)) xx ((2)/(3)) xx ((8 - 0.8))/((8 - 1.6)) = 4 xx (2)/(3) xx (7.2 ) /(6.4) =3 `