Two spherical raindrops of masses m and 8m fall through the air. Assuming the density of the raindrops is uniform and neglecting the buoyant force of air, the ratio of their terminal velocities is:

Step-by-step solution

Let the radii of the two raindrops be r₁ and r₂ . Since the density is the same for both raindrops, mass m = 4 3 r^3 . Therefore, m r^3 . Given the ratio of masses is m : 8m = 1 : 8 , the ratio of their radii is: r₁ r₂ = ( 1 8 )^ 1 3 = 1 2 The terminal velocity v of a spherical drop falling through a viscous medium is given by Stokes' law: v = 2r^2( - )g 9 Thus, terminal velocity v r^2 . The ratio of their terminal velocities is: v₁ v₂ = ( r₁ r₂ )^2 = ( 1 2 )^2 = 1 4 Hence, the ratio is 1 : 4 . Answer: 1 : 4