Question

Two metal balls of radius R and 2R Falling through a fluid have same velocity at some point .the viscous drag acting on them at that instant are in the ratio ???????????????????

Answer 1

Two metal balls of radius R and 2R falling through a fluid have same velocity at some point. The viscous drag acting on them at that instant are in the ratio?

Drag force can be calculated from:

$$F _ {d} = \frac {1}{2} \rho v ^ {2} C _ {D} A$$

where $\rho$ is the density of the fluid, $v$ is the speed of the object relative to the fluid, $A$ is the cross-sectional area, and $C_D$ — some coefficient the same for both balls.

Assuming $A$ is proportional to $r^2$ ($A \propto r^2$) we can write:

$$F _ {d} \propto r ^ {2}$$

Therefore, the viscous drag acting on balls is in the ratio:

$$\frac {F _ {d} (R)}{F _ {d} (2 R)} = \frac {R ^ {2}}{(2 R) ^ {2}} = \frac {1}{4}$$

Answer: $\frac{1}{4}$