Calculation of Terminal Velocity

Step 1: Calculate the gravitational force acting on the droplet

Fg = mg
where m = 100g = 0.1kg
and g = 9.8m/s^2

Fg = 0.1kg x 9.8m/s^2
Fg = 0.98N

Step 2: Calculate the viscous drag force acting on the droplet at terminal velocity

At terminal velocity, the viscous drag force is equal and opposite to the gravitational force.

Fdrag = Fg = 0.98N

Calculation of Drag Force

Step 1: Calculate the Reynolds number of the droplet

Re = (ρvd)/μ
where ρ = density of air = 1.2kg/m^3
v = velocity of the droplet at terminal velocity
d = diameter of the droplet
μ = viscosity of air = 1.92kg/ms

Assuming the droplet has a diameter of 1mm (0.001m), we need to calculate the velocity at which it reaches terminal velocity.

At terminal velocity, the gravitational force is balanced by the viscous drag force and the net force on the droplet is zero. Thus, we can equate the gravitational force to the drag force.

Fg = Fdrag
mg = (1/2)ρv^2CdA
where Cd = drag coefficient of the droplet
A = cross-sectional area of the droplet

Assuming a drag coefficient of 0.5 (appropriate for a spherical droplet) and a cross-sectional area of πr^2 (where r = 0.0005m), we can solve for v.

v = sqrt((2mg)/(ρCdπr^2))
v = sqrt((2 x 0.1kg x 9.8m/s^2)/(1.2kg/m^3 x 0.5 x π x (0.0005m)^2))
v = 0.052m/s

Step 2: Calculate the Reynolds number

Re = (ρvd)/μ
Re = (1.2kg/m^3 x 0.052m/s x 0.001m)/(1.92kg/ms)
Re = 0.000338

Step 3: Determine the drag force using the drag coefficient

The drag coefficient for a Reynolds number of 0.000338 is approximately 0.7. Using this value, we can calculate the drag force.

Fdrag = (1/2)ρv^2CdA
Fdrag = (1/2) x 1.2kg/m^3 x (0.052m/s)^2 x 0.7 x π x (0.0005m)^2
Fdrag = 0.000028N

Therefore, the drag force on the droplet is approximately 0.000028N, which is much smaller than the gravitational force. The correct answer is option C) 0.1N.

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