Let's analyze the reaction step-by-step:
1. Step 1: \({CH3CH2CH2Br} \xrightarrow[\Delta]{\text{alc. KOH}} {A}\)
Alcoholic KOH and heat promote elimination reactions. 1-Bromopropane reacts with alcoholic KOH to form propene (A) via a dehydrohalogenation reaction.
\({CH3CH2CH2Br} \xrightarrow[\Delta]{\text{alc. KOH}} {CH3CH=CH2(A)}\)
2. Step 2: \({A} \xrightarrow{\text{HBr}} {B}\)
Propene (A) reacts with HBr to form 2-bromopropane (B) as the major product according to Markovnikov's rule (the hydrogen atom adds to the carbon with more hydrogen atoms already attached).
\({CH3CH=CH2(A)} \xrightarrow{\text{HBr}} {CH3CHBrCH3(B)}\)
3. Step 3: \({B} \xrightarrow[\Delta]{\text{aq. KOH}} {C}\)
2-Bromopropane (B) reacts with aqueous KOH and heat to form propan-2-ol (C) via a nucleophilic substitution reaction (specifically, an S$_N$1 reaction is favored due to secondary alkyl halide and aqueous KOH).
\({CH3CHBrCH3(B)} \xrightarrow[\Delta]{\text{aq. KOH}} {CH3CH(OH)CH3(C)}\)
Therefore, the major product C is propan-2-ol.
Which of the following microbes is NOT involved in the preparation of household products?
A. \(\textit{Aspergillus niger}\)
B. \(\textit{Lactobacillus}\)
C. \(\textit{Trichoderma polysporum}\)
D. \(\textit{Saccharomyces cerevisiae}\)
E. \(\textit{Propionibacterium sharmanii}\)
A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is :