Question

A sphere of radius 50 mm and mass 1kg falling vertically through air of density 1.2kg / m3 attains a steady velocity of 11.0m / s. If
the above equation is applied to its fall, what is the value of K?

Answer 1

Given

r = Radius of sphere = 50 mm

m = Mass of sphere = 1 kg

g = Density of air = $1.2\ \text{kg/m}^3$

u = Terminal velocity = 11 m/s

To find

Value of K

Solution

K = Coefficient of drag

A = Area of sphere = $4\pi r^2$

The drag force is given by

$mg=\dfrac{1}{2}\rho Ku^2A\\\Rightarrow K=\dfrac{2mg}{\rho u^2 4\pi r^2}\\\Rightarrow K=\dfrac{2\times 1\times 9.81}{1.2\times 11^2\times 4\pi\times (50\times 10^{-3})^2}\\\Rightarrow K=4.3$

The value of K is 4.3.