Chloroform (CHCl3) is a polar organic solvent. The general principle "like dissolves like" applies here. Polar substances tend to dissolve in polar solvents, and nonpolar substances tend to dissolve in nonpolar solvents.
NaCl: Sodium chloride is an ionic compound. Ionic compounds are generally not soluble in organic solvents like chloroform.
CH3OH (Methanol): Methanol is a polar molecule due to the presence of the highly electronegative oxygen atom and the polar O-H bond. It can form hydrogen bonds, but the overall polarity is less than NaCl. Methanol exhibits some solubility in chloroform.
CH3CN (Acetonitrile): Acetonitrile is a polar molecule due to the CN bond. It is less polar than methanol and has a smaller dipole moment. It will be more soluble in chloroform than NaCl but less soluble than methanol.
Cyclohexane: Cyclohexane is a nonpolar molecule. Chloroform has a dipole moment, so it's considered a polar solvent, although it's not as polar as water or methanol. Cyclohexane will be the most soluble in chloroform among the given options because chloroform's polarity is relatively low within the spectrum of polar solvents.
Therefore, the increasing order of solubility in chloroform is: NaCl $<$ CH3CN $<$ CH3OH $<$ Cyclohexane.
A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is :