A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn / cm and glass water contact angle approx 0 ° ) with 30 ° inclined with the vertical. The length of water risen in the capillary is cm . (Take g=9.8 m / s 2 )

Physics · Mechanical Properties of Matter

JEE Main 2025 — 7 April, Evening Shift — Question 54

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 $\approx 0^{\circ}$ ) with $30^{\circ}$ inclined with the vertical. The length of water risen in the capillary is $\qquad$ cm . (Take $g=9.8 \mathrm{~m} / \mathrm{s}^{2}$ )

Option A:
$\frac{82}{5}$
Correct
Option B:
$\frac{68}{5}$
Option C:
$\frac{71}{5}$
Option D:
$\frac{57}{2}$

Answer: A

Step-by-step solution

$h=\frac{2 T \cos \theta}{\rho g r}=\frac{100}{7}$

$h^{\prime}=\frac{h}{\cos \theta}=\frac{100}{7 \cos 30^{\circ}}$

$h^{\prime}=\frac{200}{7 \sqrt{3}} \approx 16.49 \approx \frac{82}{5}$ cm

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 7 April, Evening Shift
Subject: Physics
Chapter: Mechanical Properties of Matter
Topic: Contact Angle and Capillarity