Two small spherical metal balls, having equal masses, are made from materials of densities ₁ and ₂ ( ₁=8 ₂ ) and have radii of 1 ~mm and 2 ~mm , respectively. They are made to fall vertically (from rest) in viscous medium whose coefficient of viscosity equals and whose density is 0.1 ₂ . The ratio of their terminal velocities would be

Step-by-step solution

The terminal velocity achieved by ball in a viscous fluid is v_ t = 2( - ) r ^2 ~g 9 where, = density of metal of ball, = density of viscous medium, r = radius of ball and = coefficient of viscosity of medium Terminal velocity of first ball, aligned v _ t ₁ & = 2 ( ₁- ) r ₁^2 ~g 9 & = 2 (8 ₂- ) r ₁^2 ~g 9 aligned ...(i) [ ₁=8 ₂ ] Similarly, for second ball v _ t ₂ = 2 ( ₂- ) r ₂^2 ~g 9 From Eq. (i) and (ii), we get aligned v _ t ₁ v _ t ₂ & = 2 (8 ₂- ) r ₁^2 ~g 2 ( ₂- ) r ₂^2 ~g 9 9 & = ( 8 ₂-0.1 ₂ ₂-0.1 ₂ ) ( r₁ r