A spherical ball of radius 0.003 m and density ρ falls through a viscous liquid of viscosity 1.260 N s m⁻² and density ρ/2 = 1260 kg m⁻³. It reaches terminal speed by the 10 cm mark. Find the time to travel from 10 cm to 20 cm. Take g = 10 m s⁻². Image
Physics · Properties of solid and fluid
JEE Mains Advanced

Question

A spherical ball of radius 0.003 m and density ρ falls through a viscous liquid of viscosity 1.260 N s m⁻² and density ρ/2 = 1260 kg m⁻³. It reaches terminal speed by the 10 cm mark. Find the time to travel from 10 cm to 20 cm. Take g = 10 m s⁻². Image

Physics · Properties of solid and fluid

G1 Physics · Accepted Answer

Step 1: Use viscous-force relations: shear F = ηA(dv/dy), Stokes force 6πηrv, or Reynolds number Re = ρvD/η as appropriate. Step 2: At terminal speed set net weight/buoyancy equal to viscous drag and use the given geometry. Applying these relations to the given data gives 5. Final answer: 5.