A spherical drop of liquid splits into 1000 identical spherical drops. If uᵢ is the surface energy of the original drop and uᶠ is the total surface energy of the resulting drops, ignoring evaporation, uᶠ/uᵢ = 10/x. Then value of x i s _____ :
Physics · Properties of solid and fluid · properties of fluid and surface tension
JEE Mains 25 January 2023 Shift 2 Evening Shift

Question

A spherical drop of liquid splits into 1000 identical spherical drops. If uᵢ is the surface energy of the original drop and uᶠ is the total surface energy of the resulting drops, ignoring evaporation, uᶠ/uᵢ = 10/x. Then value of x i s _____ :

Physics · Properties of solid and fluid · properties of fluid and surface tension

JEE Mains 25 January 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

Volume is conserved: R³ = 1000r³, so R = 10r. Surface energy is proportional to surface area. Thus uᶠ/uᵢ = [1000×4πr²]/[4πR²] = 1000r²/(100r²) = 10. Therefore 10/x = 10 and x = 1.