Question
Question: A raindrop of the radius \[0.3mm\] has a terminal velocity \[1\dfrac{m}{s}\] in the air. The viscosi...
A raindrop of the radius 0.3mm has a terminal velocity 1sm in the air. The viscosity of air is 18×10−5poise. The viscous force on the airdrop is
A. 16.695×10−7N
B. 1.695×10−8N
C. 1.017×10−12N
D. 101.73×10−9N
Solution
Poisson's ratio is defined as the ratio of the change in a sample width per unit width to the change in the length per unit length due to strain. Where strain is the force which determines the strength of an object when they are stretched or deformed.
Viscosity is the measure of the extent to which fluid flow is redistricted, and its unit is newton-second per square meter, which is usually expressed as Pascal-second. The viscosity of liquids decreases rapidly with an increase in temperature. Viscous force is the force acting between the layers of flowing fluid. It is the rate at which the fluid velocity changes its space.
Use the viscous force formula F=6πηrVT, where VT is the terminal velocity η is the poisson's ratio.
Complete step by step answer:
Terminal velocity VT=1sm
Poisson's ratio η=18×10−5poise=18×10−6decapoise
The radius of the rain droplet r=0.3mm=0.3×10−3m
Viscous force on the raindrops is given by the formula F=6πηrVT
Now substitute the values in the formula,
Hence the Viscous force on the air droplet is=101.73×10−9N
Option D is correct.
Note: Students must note that the viscosity is the same as the friction as it also opposes the motion of the fluid, and it is non-conservative.