Question

A body of density \( D \), and mass \( M \) is moving downward in glycerine of density \( D_z \). What is the viscous force acting on it?

• A. \( M g D \)
• B. \( M g D_z \)
• C. \( \frac{g}{D_z} \)
• D. \( \frac{2g h}{D_z} \)

Hint:

Viscous forces depend on the velocity of the object, the viscosity of the fluid, and the size of the object. For simpler cases, density differences can also influence the force.

Answer 1

The Correct Option is C

The viscous force \( F_{\text{viscous}} \) on a body moving in a fluid is given by the Stokes' law: \[ F_{\text{viscous}} = 6 \pi \eta r v \] where \( \eta \) is the viscosity of the fluid, \( r \) is the radius of the body, and \( v \) is the velocity of the body through the fluid. In this case, the fluid is glycerine with density \( D_z \), and the force is proportional to the mass of the body and the difference in densities.
Thus, the correct answer is (c).