A steel ball of radius 0.05 ~cm and density 7.8 ~g ~cm ⁻³ is dropped into a tank of water. The terminal velocity of the steel ball is (Density of water =1 ~g ~cm ⁻³ and viscosity of water =0.001 ~Pa ~s )

Step-by-step solution

Radius of steel ball, r =0.05 10⁻² ~m Density of steel, =7.8 ~g ~cm ⁻³= 7.8 10⁻³ 10⁻⁶ =7800 ~kg / m ^3 Density of water, _ =1 ~g ~cm ⁻³= 10⁻³ 10⁻⁶ =1000 ~kg / m ^3 Viscosity of water, =0.001 pas Terminal velocity is given by aligned & v _ T = 2 9 r ^2 ( - _ ) & = 2 (0.05 10⁻² )^2 (7800-1000) 9 0.001 & =3.77 ~m / s aligned