Question

A typical raindrop is about 4mm in diameter if a raindrop falls from a cloud which is at 1km above the ground estimate it's momentum when it hits the ground

Answer 1

Answer:

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

Explanation:

Answer 2

The momentum when it hits the ground is 4.69 x 10⁻³ kg m/s.

Given: A typical raindrop is about 4mm in diameter if a raindrop falls from a cloud which is at 1km above the ground.

To find: momentum when it hits the ground

Solution:

Height of rain drop above the ground is given as = 1 km

h= 1000 m

Diameter of rain drop = 4 mm

Radius of rain drop = 2 mm = 2 *10⁻³ m

To find the momentum of rain drop when it hits the ground,

Momentum p = mass * velocity

For a freely falling body velocity with it hits the ground,

Velocity is given by  √2gh

v = √( 2 x 9.8 x 1000)       using g= 9.8 m/s²

v = 140 m/s

To find mass,

mass = density x volume

m = 10³ x (4 π r³)/3

m = 10³ x (4 π (2*10⁻³)³)/3

m = 33.51 x 10⁻⁶

Now Momentum,

p= mass x velocity

p = 33.51 x 10⁻⁶ x140

p = 4.69 x 10⁻³ kg m/s.

Hence, momentum when it hits the ground is 4.69 x 10⁻³ kg m/s.

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