JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Fluid Mechanics

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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

13 5^{\circ}

and

0^{\circ}

, respectively. It is observed that mercury gets depressed by an amount

h

in a capillary tube of radius

r_{1}

, while water rises by the same amount

h

in a capillary tube of radius

r_{2}

. The ratio,

(r_{1} / r_{2})

, is then close to:

(A) $3/5$
(B) $4/5$
(C) $2/3$
(D) $2/5$ ✓ Correct

Answer: (D)

Solution

Capillary rise is

h = \frac{2 S c o s θ}{r ρ g}

. Equating magnitudes for the two liquids,

\frac{2 S _{1} ∣ c o s 13 5 ^{\circ} ∣}{r _{1} ρ _{1} g} = \frac{2 S _{2} c o s 0 ^{\circ}}{r _{2} ρ _{2} g}

, which rearranges to

\frac{r _{1}}{r _{2}} = \frac{S _{1} ∣ c o s 13 5 ^{\circ} ∣ ρ _{2}}{S _{2} ρ _{1}} = \frac{7.5 \times \frac{1}{2}}{13.6} \approx \frac{2}{5}

JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Single correct option

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JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Fluid Mechanics

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