A vertical capillary of radius 0.025 cm dips 1 cm into water (contact angle 0°, surface tension 7.5 × 10⁻² N m⁻¹, density 10³ kg m⁻³, P₀ = 10⁵ Pa). Find n if excess pressure needed to make the capillary water level equal to external level is 100n Pa. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A vertical capillary of radius 0.025 cm dips 1 cm into water (contact angle 0°, surface tension 7.5 × 10⁻² N m⁻¹, density 10³ kg m⁻³, P₀ = 10⁵ Pa). Find n if excess pressure needed to make the capillary water level equal to external level is 100n Pa. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — To hold the capillary surface at the same level as outer free surface, the additional applied pressure must balance the Laplace pressure across the meniscus. Hydrostatic levels are equal. Step 2 — For zero contact angle, ΔP = 2T cosθ/r = 2T/r. Step 3 — Convert r = 0.025 cm = 2.5 × 10⁻⁴ m. Then ΔP = 2 × 0.075/(2.5 × 10⁻⁴) = 600 Pa. Step 4 — 600 Pa = 100n Pa, so n = 6.