JEE Physics 2025 Question with Solution

Given: surface tension $T = 70 \, \text{dyn/cm} = 0.07 \, \text{N/m}$, contact angle $\theta \approx 0^\circ$ so $\cos \theta = 1$, radius $r = 0.1 \, \text{mm} = 0.0001 \, \text{m}$, density of water $\rho = 1000 \, \text{kg/m}^3$, and $g = 9.8 \, \text{m/s}^2$.

Find: the length of water risen along the capillary tube when the tube is inclined at $30^\circ$ with the vertical.

Using Jurin's law, the vertical rise is

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

Substituting the given values,

$$h = \frac{2 \times 0.07 \times 1}{0.0001 \times 1000 \times 9.8}$$ $$= \frac{0.14}{0.98}$$ $$= 0.142857 \, \text{m} = 14.2857 \, \text{cm}$$

Since the capillary is inclined at $30^\circ$ with the vertical, if $l$ is the length of the liquid column along the tube, then

$$h = l \cos 30^\circ$$

So,

$$l = \frac{h}{\cos 30^\circ}$$ $$l = \frac{14.2857}{\sqrt{3}/2} \approx 16.5 \, \text{cm}$$

This is closest to

$$\frac{82}{5} = 16.4 \, \text{cm}$$

Therefore, the correct option is A.

Given: the tube radius is $0.1 \, \text{mm}$, the surface tension is $70 \, \text{dyn/cm}$, the contact angle is $0^\circ$, and the tube makes $30^\circ$ with the vertical.

Find: the length of rise measured along the inclined tube.

The key step is to keep units consistent. Convert

$$70 \, \text{dyn/cm} = 0.07 \, \text{N/m}$$

and

$$0.1 \, \text{mm} = 0.01 \, \text{cm} = 10^{-4} \, \text{m}$$

Now apply capillary rise formula for vertical height:

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

Because $\theta = 0^\circ$,

$$\cos 0^\circ = 1$$

Hence,

$$h = \frac{2 \times 0.07}{10^{-4} \times 1000 \times 9.8}$$ $$= \frac{0.14}{0.98}$$ $$= 0.142857 \, \text{m}$$ $$= 14.2857 \, \text{cm}$$

This is the vertical rise. The tube is inclined, so the actual liquid length inside the tube is larger. Since the inclination is given with the vertical,

$$l \cos 30^\circ = h$$

Therefore,

$$l = \frac{14.2857}{0.866} \approx 16.5 \, \text{cm}$$

Among the given options, this matches $\frac{82}{5}$ most closely.

Therefore, the length of water risen in the capillary is $\frac{82}{5} \, \text{cm}$, so the correct option is A.

The other extracted approach on the page uses an inconsistent numerical evaluation and the relation $\frac{h}{\sin 30^\circ}$, which disagrees with the geometry for an angle measured with the vertical.