Step 1:
The reaction described in the question involves the formation of gas X upon treatment with sodium hydroxide. This is typical of ammonia (NH₃), which is released when ammonium salts (like NH₄Cl) react with sodium hydroxide.
Step 2:
Now, gas X (NH₃) reacts with reagent Y. The formation of a brown colored precipitate suggests the reaction with a mercury(I) compound, which is typically represented as K₂HgI₄ (also known as potassium tetraiodomercurate(I)). When ammonia is passed through K₂HgI₄ in the presence of KOH, a brown precipitate of mercury(I) iodide (Hg₂I₂) is formed.
Step 3:
Thus, the gas X is ammonia (NH₃), and the reagent Y is potassium tetraiodomercurate(I) (K₂HgI₄), which, when treated with ammonia, forms a brown precipitate of Hg₂I₂.
Final Answer:
\[ \boxed{X = \text{NH}_3 \text{ and } Y = \text{K}_2\text{HgI}_4 + \text{KOH}} \]

Two circular discs of radius \(10\) cm each are joined at their centres by a rod, as shown in the figure. The length of the rod is \(30\) cm and its mass is \(600\) g. The mass of each disc is also \(600\) g. If the applied torque between the two discs is \(43\times10^{-7}\) dyne·cm, then the angular acceleration of the system about the given axis \(AB\) is ________ rad s\(^{-2}\).
