1000 droplets of water having 2 mm diameter each coalesce to form a single drop. Given the surface tension of water is `0.072 N. m^-1`. The energy loss in the process is

Options

A. `8.146xx10^-4 J`
B. `4.4xx10^-4 J`
C. `2.108xx10^-5 J`
D. `4.7xx10^-1 J`.

Answer

A

Explanation

Let us consider the radius of the big drop of water = R
`therefore 4/3 pi R^3=4/3pi(0.1)^3xx1000`
or, `R^3=1 or, R=1.0 cm`
The area of the surface of the big drop of water
`=4pi(1.0)^2=4picm^2`
The total area of the surfaces of 1000 droplets of water
`=4pi(0.1)^2xx1000cm^2`
`therefore` Decrease in surface area = `4pi(0.1)^2xx1000-4pi`
`=4pi(10-1)`
`=36picm^2`
`=0.0036pi m^2`
`therefore` The energy loss `=0.0036pi xx 0.072`
`=8.143xx10^-4 J`