The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 ~cm / s . The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be _ _ _ _ cm / s .

Step-by-step solution

For a sphere in a viscous fluid, terminal velocity is proportional to r^2 : v_t r^2 . For two balls of the same material in the same fluid: v_ t1 v_ t2 = r₁^2 r₂^2 . Given r₁ = 6 mm, v_ t1 = 20 cm/s, and r₂ = 3 mm: 20 v_ t2 = 36 9 = 4 . Therefore, v_ t2 = 5 cm/s.