Question

Spherical balls of radius R are falling in a viscous fluid of velocity v. The retarding viscous force acting on the spherical ball is
A. Directly proportional to R but inversely proportional to v
B. Directly proportional to both radius R and velocity v
C. Inversely proportional to both radius R and velocity v
D. Inversely proportional to R but directly proportional to v

Answer 1

Hint:The property of a fluid that opposes the relative motion between its different layers is known as viscosity. The force that opposes relative motion between the layers is known as viscous force.

Formula Used:
According to Stoke’s law, the viscous force is,
\[F = 6\pi \eta Rv\]
Here,
R is radius of the ball
V is velocity of the ball
\[\eta \] is coefficient of viscosity

Complete step by step solution:
Consider the spherical balls of radius R that are falling in a viscous fluid having the velocity v. We need to find on which terms the retarding viscous force acting on the spherical ball depends and how it depends.

For that we know the formula to find the retarding viscous force, that is, according to Stoke’s law, the retarding viscous force acting on a spherical body of radius R which moves at velocity v through a viscous fluid can be found as,
\[F = 6\pi \eta Rv\]

From the above equation, we can clearly confirm that the viscous force acting on a spherical body of radius R moving at velocity v through a viscous fluid is directly proportional to the radius R and as well as the velocity v. Therefore, the retarding viscous force acting on the spherical ball is directly proportional to both radius R and velocity v

Hence, option B is the correct answer.

Note:Remember that the viscous force and frictional force are similar, but they are not the same. In a moving fluid, the fluid consists of multiple layers. As compared to the neighboring layers each layer has a noticeable difference in speed. This force, called the frictional force, decreases the relative motion between the layers. Viscous force is defined as the force that acts between two layers of a moving fluid.