This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement-1: A capillary is dipped in a liquid and liquid rises to a height h in it. As the temperature of the liquid is raised, the height h increases (if the density of the liquid and the angle of contact remain the same).
Statement-2: Surface tension of a liquid decreases with the rise in its temperature.

Let us understand both statements step by step. We start by recalling the formula for the height $$h$$ to which a liquid rises in a capillary tube. The formula is:

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

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

Statement-1 claims that when the temperature of the liquid is raised, the height $$h$$ increases, assuming the density $$\rho$$ and the angle of contact $$\theta$$ remain constant.

Statement-2 states that the surface tension $$S$$ of a liquid decreases with a rise in temperature.

We know that Statement-2 is a well-established fact. The surface tension of liquids generally decreases as temperature increases because the increased thermal energy reduces the cohesive forces between molecules at the surface.

Now, let us analyze Statement-1 using the formula. Given that $$\rho$$, $$\theta$$, $$g$$, and $$r$$ are constant (as per the problem and since the capillary tube doesn't change), the height $$h$$ is directly proportional to the surface tension $$S$$. Therefore:

$$ h \propto S $$

If the temperature rises, Statement-2 tells us that $$S$$ decreases. Since $$h$$ is proportional to $$S$$, a decrease in $$S$$ would lead to a decrease in $$h$$. However, Statement-1 claims that $$h$$ increases with temperature. This is a contradiction.

Therefore, Statement-1 is false because the height $$h$$ should decrease, not increase, when temperature rises (given that $$\rho$$ and $$\theta$$ are constant).

In summary:

• Statement-1 is false.
• Statement-2 is true.

Hence, the correct answer is Option B.