Two raindrops reach the earth with different terminal velocities having the ratio 9: 4 . The ratio of their volumes is

Step-by-step solution

Terminal velocity for a spherical body in a viscous medium follows Stokes' Law: v_t = 2r^2( - _f)g 9 . Assuming constant fluid properties and densities, terminal velocity scales with radius squared: v_t r^2 . Given the velocity ratio v_ t1 v_ t2 = 9 4 , the radius ratio becomes r₁^2 r₂^2 = 9 4 , so r₁ r₂ = 3 2 . Since volume scales as V r^3 , the volume ratio is V₁ V₂ = ( r₁ r₂ )^3 = ( 3 2 )^3 = 27 8 . The ratio of their volumes is D .