Following are the four molecules ``P``, ``Q``, ``R`` and ``S``. Which one among the four molecules will react with H-Br(aq) at the fastest rate? Molecules:

\[ P: \text{Cyclic compound with two O groups attached to the ring.} \] \[ Q: \text{Cyclic compound with one O group and one CH\(_3\) group attached to the ring.} \] \[ R: \text{Cyclic compound with one O group attached to the ring and one CH\(_3\) group attached to the ring.} \] \[ S: \text{Cyclic compound with one CH\(_3\) group attached to the ring.} \]
The question involves determining which cyclic compound reacts fastest with H-Br(aq). Let's evaluate each option:
Based on the evaluations, molecule Q will react with H-Br(aq) at the fastest rate due to the presence of an oxygen atom that can assist in reaction via electron donation, and a CH\(_3\) group that stabilizes the transition state via hyperconjugation.
Correct Answer: Q
Given:
- The reaction follows an electrophilic addition mechanism. - During the rate-determining step, a carbocation intermediate is formed.
The addition of \( H^+ \) and \( Br^− \) to the alkene follows the electrophilic addition mechanism, where the alkene reacts with an electrophile (such as \( H^+ \)) to form a carbocation intermediate.
The stability of the carbocation intermediate plays a crucial role in determining the course of the reaction. Among the compounds P, Q, R, and S, compound \( Q \) forms the most stable carbocation intermediate since it is resonance-stabilized.
Compound \( Q \) will form the most stable carbocation intermediate due to its resonance stabilization, making it the most stable product in this electrophilic addition reaction.
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\(^{-2}\).

Method used for separation of mixture of products (B and C) obtained in the following reaction is: 