A small sphere of mass m falls through a viscous medium of negligible density with terminal speed v. A second sphere has the same mass but twice the radius and moves through the same medium. Assuming Stokes' law, what is its terminal speed?
Options

Question

A small sphere of mass m falls through a viscous medium of negligible density with terminal speed v. A second sphere has the same mass but twice the radius and moves through the same medium. Assuming Stokes' law, what is its terminal speed?

Options

G1 Physics · Accepted Answer

When the surrounding-fluid density is negligible, buoyancy may be neglected. At terminal speed, mg = 6πηrvₜ. Therefore, vₜ = mg/(6πηr). For fixed mass m and the same liquid, vₜ ∝ 1/r. If the radius doubles, v' = v/2. Correct option: B.