JEE Physics 2024 Question with Solution

Given: Two statements compare the height of capillary rise in cold water and hot water.

Find: Which statement is correct.

Capillary rise is given by

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

where $\gamma$ is the surface tension of the liquid.

When temperature increases, the surface tension decreases. Since $h$ is directly proportional to $\gamma$, the height of capillary rise decreases in hot water.

So, the height of capillary rise is smaller in hot water and larger in cold water.

Therefore, Statement I is true but Statement II is false. The correct option is B.

Given:

• Capillary rise in cold water and hot water is to be compared.
• Surface tension changes with temperature.

Find: Truth value of Statement I and Statement II.

The relation for capillary rise is

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

where $T$ is the surface tension, $\theta$ is the contact angle, $\rho$ is the density of the liquid, $g$ is acceleration due to gravity, and $r$ is the radius of the capillary tube.

As temperature increases, surface tension decreases. Hence the value of $h$ also decreases.

Now analyze the statements:

1. Statement I: In hot water, capillary rise is smaller. This is true.
2. Statement II: In cold water, capillary rise is smaller. This is false.

Therefore, the correct option is B, that is, Statement I is true but Statement II is false.

There is a discrepancy in the solution where one place marks the answer as B and another writes (2), but both correspond to the same statement.