The ratio of surface tensions of mercury and water is given to be 7.5, while the ratio of their densities is 13.6. Their contact angles with glass are close to 135° and 0° respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius r₁, while water rises by…

Question

The ratio of surface tensions of mercury and water is given to be 7.5, while the ratio of their densities is 13.6. Their contact angles with glass are close to 135° and 0° respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius r₁, while water rises by the same amount h in a capillary tube of radius r₂. The ratio (r₁)/(r₂) is then close to

Accepted Answer

(1) 2/5. Given: (Tₘ)/(T_w)=7.5, (ρₘ)/(ρ_w)=13.6, θₘ=135°, θ_w=0°, and equal magnitudes of the level change in the two tubes. Idea: h=(2T cos θ)/(rρ g) carries cos θ with it; for mercury cos 135° is negative, which is the depression, so match magnitudes. (2Tₘ|cos 135°|)/(r₁ρₘg)=(2T_w cos 0°)/(r₂ρ_wg). (r₁)/(r₂)=(Tₘ)/(T_w)×(ρ_w)/(ρₘ)×|cos 135°|=7.5×1/(13.6)×1/(√2). (r₁)/(r₂)=(5.30)/(13.6)=0.39, closest to 2/5.

Step-by-step solution

Why the other options are wrong