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.
A bob of mass \(m\) is suspended at a point \(O\) by a light string of length \(l\) and left to perform vertical motion (circular) as shown in the figure. Initially, by applying horizontal velocity \(v_0\) at the point ‘A’, the string becomes slack when the bob reaches at the point ‘D’. The ratio of the kinetic energy of the bob at the points B and C is: 