Question

Two mercury drops (each of radius \( r \)) merge to form a bigger drop. The surface energy of the bigger drop is, if \( T \) is the surface tension, is

• A. \( 2\pi r^2 T \)
• B. \( 4\pi r^2 T \)
• C. \( 2^2 \pi r^2 T \)
• D. \( 2T^2 \)

Hint:

When two spherical drops merge, the radius of the new drop is the sum of the radii, and the surface area increases quadratically.

Answer 1

The Correct Option is B

Step 1: Use the formula for surface energy.
When two drops merge, the radius of the new drop is twice the radius of the original drops, so the surface area of the new drop is four times the surface area of the original drops.
Step 2: Calculate the surface energy.
The surface energy of the new drop is \( 4\pi r^2 T \).
Final Answer: \[ \boxed{4\pi r^2 T} \]