Question

If a million tiny droplets of water of the same radius coalesce into one larger drop, then the ratio of the surface energy of the large drop to the total surface energy of all the droplets will be ____________.

Options

• 1 : 10

• 1 : 10²

• 1 : 10⁴

• 1 : 10⁶

Answer 1

If a million tiny droplets of water of the same radius coalesce into one larger drop, then the ratio of the surface energy of the large drop to the total surface energy of all the droplets will be 1 : 10².

Explanation:

Let r be the radius of each droplet and R be the radius of the big drop.

Since the total volume is the same, we have

`10^6 xx (4pi"r"^3)/3 = (4 pi"R"^3)/3`

`"R"^3 = 10^6  "r"^3 Rightarrow "R" = 100 "r"`

The surface energy of one million drops,

`"E"_1 = 4 pi"r"^2"T" xx 10^6`

The surface energy of one big drop,

`"E"_2 = 4 pi"R"^2 "T"`

`therefore "E"_2/"E"_1 = ("R"/"r")^2 xx 1/10^6`

` = ((100  "r")/"r")^2 xx 1/10^6`

` = 1/10^2`