Two arms of a U-tube have diameters d₁ = 1.0 mm and d₂ = 1.0 cm. Water has surface tension 7 × 10⁻² N m⁻¹ and zero contact angle. Find the difference in water levels.
Physics · Properties of solid and fluid
JEE Mains Advanced

Question

Two arms of a U-tube have diameters d₁ = 1.0 mm and d₂ = 1.0 cm. Water has surface tension 7 × 10⁻² N m⁻¹ and zero contact angle. Find the difference in water levels.

G1 Physics · Accepted Answer

Step 1: Use surface-energy/pressure relations: ΔP = 2T/R for a liquid drop or 4T/R for a soap bubble, capillary rise h = 2T cosθ/(ρgr), and surface energy = TΔA. Step 2: Apply force or energy balance to the stated radii and surface areas. Applying these relations to the given data gives 2.52. Final answer: 2.52.