A capillary tube of radius 0.1 mm is partly dipped in water (surface tension $70 \mathrm{dyn} / \mathrm{cm}$ and glass water contact angle $\simeq 0^{\circ}$ ) with $30^{\circ}$ inclined with vertical. The length of water risen in the capillary is \_\_\_\_ cm . (Take $\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}$ )

JEE Main · 2025 · 07 Apr 2025 · Shift 2 · Fluid Mechanics

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension

70 dyn / cm

and glass water contact angle

≃ 0^{\circ}

) with

3 0^{\circ}

inclined with vertical. The length of water risen in the capillary is ____ cm .
(Take

g = 9.8 m / s^{2}

)

Answer: (A)

The vertical rise is

h = \frac{2 T cos θ}{ρ g r}

. In CGS units, with

T = 70 dyn/cm

ρ = 1 g/cm^{3}

g = 980 cm/s^{2}

and

r = 0.01 cm

, this gives

h = \frac{2 \times 70}{1 \times 980 \times 0.01} = \frac{140}{9.8} \approx 14.3 cm

. Surface tension raises water to the same vertical height whatever the tilt, so along a tube inclined at

3 0^{\circ}

to the vertical the wetted length is

ℓ = \frac{h}{cos 3 0 ^{\circ}} = \frac{2 h}{3} \approx 16.5 cm

. The length of water risen in the capillary is

\frac{82}{5} cm

JEE Main · 2025 · 07 Apr 2025 · Shift 2 · Single correct option