Question

The surface energy of a liquid drop is u. If it is sprayed into 1000 equal droplets, then its surface energy becomes ______.

Options

• u

• 10 u

• 100 u

• 1000 u

Answer 1

The surface energy of a liquid drop is u. If it is sprayed into 1000 equal droplets, then its surface energy becomes 10 u.

Explanation:

u = `"T" xx 4  pi  "R"^2`

When the drop is sprayed into 1000 droplets each of radius r, then

`4/3  pi"R"^3 = 1000 xx 4/3  pi"r"^3`

∴ r = `"R"/10`

∴ `"u"'  = 1000 xx "T" xx 4pi"r"^2`

`= 1000 xx "T" xx 4pi "r"^2/100`

`= 10 xx 4pi "R"^2"T" = 10  "u"`