Given below are two statements: one is labelled as Assertion (A)...

The atmospheric pressure supports a vertical column of mercury of height $h$, given by $P = \rho g h$.

Since the atmospheric pressure $P$ and the density of mercury $\rho$ are constant, the vertical height $h$ of the mercury column must remain constant, regardless of the tilt of the tube. Thus, the Reason is true.

When the tube is tilted by an angle $\theta$ from the vertical, the length of the mercury column $l$ along the tube is related to the vertical height $h$ by $h = l \cos\theta$.

Therefore, $l = \dfrac{h}{\cos\theta}$. Since $\cos\theta < 1$ for any tilt angle $\theta > 0$, the length $l$ must be greater than $h$. Thus, the length of the mercury column increases. The Assertion is true.

The constant vertical height is the exact geometric reason why the length along the tilted tube must increase. Hence, the Reason perfectly explains the Assertion.

Answer: Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).