Liquid enters a horizontal capillary in accordance with Washburn law x² = kt, with k determined by radius, surface tension, contact angle and viscosity. If penetration grows from zero to x₀ in time t₀, how long (in the form 3nt₀) does it take to grow from x₀ to 4x₀? Find n.
Physics · Mixed Chapter
JEE Main Practice

Question

Liquid enters a horizontal capillary in accordance with Washburn law x² = kt, with k determined by radius, surface tension, contact angle and viscosity. If penetration grows from zero to x₀ in time t₀, how long (in the form 3nt₀) does it take to grow from x₀ to 4x₀? Find n.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Washburn law gives penetration distance x ∝ √t; equivalently x² = Kt. Step 2 — x₀ is attained at t₀: x₀² = Kt₀. Step 3 — Attaining 4x₀ requires total time t = (4x₀)²/K = 16t₀. Step 4 — Additional time from x₀ to 4x₀ is 16t₀ − t₀ = 15t₀. Step 5 — 15t₀ = 3nt₀, so n = 5.