An iron sphere of mass 20 10⁻³ ~kg falls through a viscous liquid with terminal velocity 0.5 ~ms ⁻¹ . The terminal velocity (in ms ⁻¹ ) of another iron sphere of mass 54 10⁻² ~kg is

Step-by-step solution

Terminal velocity, v r^2 aligned or v₁ v₂ & = ( r₁ r₂ )^2= [ ( r₁ r₂ )^3 ]^ 2 3 v₁ v₂ & = ( M₁ M₂ )^ 2 / 3 0.5 v₂ & = ( 20 10⁻³ 54 10⁻² )^ 2 / 3 0.5 v₂ & = 1 9 v₂=4.5 ~m / s aligned