You drop two iron marbles into a jar of honey. The area of the larger marble is 9 times the area of the smaller one. If the velocity of the smaller marble is half the velocity of the large one, what is the ratio of the viscous forces on the two marbles?
A)The viscous force on the large marble is 6 times greater than on the small marble.
B)The viscous force on the small marble is 6 times greater than on the large marble.
C)The viscous force on the large marble is 18 times greater than on the small marble.
D)The viscous force on the small marble is 18 times greater than on the large marble.

Question

Quizplus · Accepted Answer

The viscous force on a sphere is given by F = 6πηrv, where η is the viscosity of the fluid, r is the radius of the sphere, and v is the velocity of the sphere. Since the area of the larger marble is 9 times the area of the smaller one, the radius of the larger marble is 3 times the radius of the smaller one. Therefore, the viscous force on the larger marble is 6πηr3v = 6πη(3r)3v = 27πηr3v = 27 times the viscous force on the smaller marble.

You Drop Two Iron Marbles into a Jar of Honey