A metal sphere of mass ' m ' and density ' ₁ ' falls with terminal velocity through a container containing liquid. The density of liquid is ' ₂ '. The viscous force acting on the sphere is

Step-by-step solution

Given: Mass of sphere = m , Density of sphere = ₁ , Density of liquid = ₂ . At = v = v _ t , Weight of sphere ( W )= Viscous Force ( F _ V )+ Buoyant Force due to the medium ( F _ B ) aligned W & = F _ V + F _ B Mg & = F _ V + ( ₂ ~V ) g .( m = D . V ) F _ V & = mg - ( ₂ ~V ) g & = mg [1- ₂ ~V ~m ] & = mg [1- ₂ ~V ₁ ~V ] & = mg [1- ₂ ₁ ] aligned