Question

A typical raindrop is about 4 mm in diameter. If a raindrop falls from cloud which is at 1 Km above the ground, estimate its momentum when it hits the ground.

Answer 1

Hii dear,

# Answer- 5.95×10^-4 kgm/s

# Given-
r = 1mm = 10^-3 m
s = 1km = 10^3 m
d = 10^3 kg/m^3

# Explaination-
Volume of raindrop
V = 4/3 πr^3
V = 4/3 ×3.14×(10^-3)^3
V = 4.2×10^-9 m^3

Mass of raindrop
M = d×V
M = 4.2×10^-9×10^3
M = 4.2×10^-6 kg

Velocity of raindrop
v^2 = u^2 + 2as
v^2 = 0^2 + 2×10×10^3
v^2 = 2×10^4
v = 1.41×10^2 m/s

Momentum is given by
p = mv
p = 4.2×10^-6 × 1.41×10^2
p = 5.95×10^-4 kgm/s

Momentum of the raindrop just before touching ground is 5.95×10^-4 kgm/s.

Hope you understand well...

Answer 2

Given :

Diameter of rain drop=D=4mm

Radius of rain drop=r=2mm=2x10⁻³ m

Density of rain drop=10³kg/m³

Volume of rain drop=Volume of sphere=V= 4/3 π r³ = 4/3 x 22/7 x(2x 10⁻³)³

Mass of rain drop=m=density of rain drop x volume of rain drop

=10³x 4/3 x 22/7 x 8 x 10⁻⁹ = 33.52x10⁻⁶ kg

The height of rain drop =h=1km=1000m

Velocity of rain drop just before touching ground =V=√2gh=√2x9.8x1000=140m/s

Momentum of raindrop when it hits the ground =p=mv=33.52x10⁻⁶ x 140=469.28 x 10⁻⁵

=0.004692 kg m/s

∴the momentum of rain drop is 0.004692 kg m/s