Loss in Surface Potential Energy – Rankers Physics
Topic: Solid and Fluids
Subtopic: Surface Tension and Viscosity

Loss in Surface Potential Energy

125 small droplets each of radius r, combine to form a big drop. If surface tension of liquid is T. Then loss in surface potential energy during this process will be:
\(T \times 16\pi r^2\)
\(T \times 20\pi r^2\)
\(T \times 100\pi r^2\)
\(T \times 400\pi r^2\)

Solution:

Volume conservation gives \(R = 5r\). Initial surface area is \(A_i = 125 \times 4\pi r^2 = 500\pi r^2\) and final is \(A_f = 4\pi R^2 = 100\pi r^2\). The decrease in area is \(400\pi r^2\), so loss in surface energy is \(T \times 400\pi r^2\).

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