The terminal velocity Vt of a spherical ball of lead of radius r falling through a viscous liquid varies with - Physics - Mechanical Properties of Solids and Fluids

Question

The terminal velocity Vt of a spherical ball of lead of radius r
falling through a viscous liquid varies with r such that
(a)Vt/r=constant (b)Vt r =constant (c)Vt =constant
(d)Vt/r^2=constant

Sandeep K. Gupta · Accepted Answer

Dear Student,

Terminal velocity of a ball in a viscous liquid is given by-Vt=2 r29ηρ-σ g , here symbols have their usual meaning
for a given liquid and ball 2 9ηρ-σ g will be constant if radius changesHence ,  Vtr2=2 9ηρ-σ g= constant
Vtr2= constant    option (d) is correct

Regards

The terminal velocity Vt of a spherical ball of lead of radius r falling through a viscous liquid varies with r such that (a)Vt/r=constant (b)Vt r =constant (c)Vt =constant (d)Vt/r^2=constant