Two smaller spherical raindrops collide and merge into one larger spherical raindrop. What is the radius and surface energy of this larger drop, compared to the two smaller ones?
1 Answer
Radius increases by 26% while the surface energy drops 21%
Explanation:
For a sphere, its volume and surface A area are:
A) Volume consideration.
Let
Because density of water and total mass of the droplets do not change, the volume before and after the merger must be the same.
Volume of two small droplets = Volume of merged droplet
If the small droplets have the same size, then
The radius of the merged droplet is 26% larger.
(B) Surface area consideration , assuming small droplets have identical radius.
Let
The percentage change in surface energy is:
The surface energy has reduced by 21%.