Question

Work done on splitting a spherical drop into 8 droplets?

• A. \( 7 \times W \)
• B. \( 8 \times W \)
• C. \( 6 \times W \)
• D. \( 4 \times W \)

Hint:

When splitting a droplet into smaller ones, the increase in surface area requires work. The change in energy is proportional to the number of droplets formed minus 1.

Answer 1

The Correct Option is A

When a large spherical drop is split into \( n \) smaller droplets, the work done is related to the change in surface energy. The surface energy \( U \) of a spherical droplet is given by: \[ U = 4 \pi r^2 \sigma \] Where \( r \) is the radius of the droplet, and \( \sigma \) is the surface tension. For a drop of radius \( R \), the total surface energy is \( 4 \pi R^2 \sigma \). When the drop is split into \( n \) smaller droplets, each of radius \( r \), the total surface energy becomes \( n \times 4 \pi r^2 \sigma \), where \( r = \frac{R}{n^{1/3}} \). The increase in surface energy is due to the formation of additional surface area. The work done is proportional to the change in surface energy. For the case of splitting the drop into 8 droplets, the work done will be: \[ \text{Work done} = 7 \times W \] Thus, the correct answer is \( 7 \times W \).