JEE Main 2023 · 25 January · evening · Numerical answer · +4 / −0
A spherical drop of liquid splits into 1000 identical spherical drops. If uᵢ is the surface energy of the original drop and u_f is the total surface energy of the resulting drops, the (ignoring evaporation), u_f/uᵢ = ( 10/x ). Then value of x is ____________ :
Answer and solution
Answer 1
Solution
Physics sir · 3 steps
Volume stays fixed when the drop splits, so get the small radius from volume first, then compare areas.
- Volume is conserved. No liquid is lost, so the volume of the big drop of radius R equals the total volume of 1000 small drops of radius r.
4/3π R³ = 1000 × 4/3π r³ ⇒ r = R/10
- Compare surface energies. Surface energy is T × area, so the ratio is a ratio of areas. uᵢ = T · 4π R² and u_f = 1000 × T · 4π r² = 1000 × T · 4π R²/100 = 10 × T · 4π R².
- So. u_f/uᵢ = 10 = 10/x, which gives x = 1.
The common slip: 10. Assuming the surface energy stays the same during splitting gives u_f/uᵢ = 1 and so x = 10. The total area grows, so the surface energy grows too.
The idea to keep. When one drop breaks into n equal drops, each radius becomes R/n^(1/3) and the total surface area grows by n^(1/3). Splitting always needs energy.
Answer from the NTA final answer key. Solution by PrepWiser.