Total number of possible isomers (both structural as well as stereoisomers) of cyclic ethers of molecular formula $C_{4}H_{8}O$ is:
We are asked to count all possible isomers (structural and stereoisomers) for cyclic ethers with the molecular formula C4H8O. This formula corresponds to saturated cyclic ethers (with one ring and one oxygen atom, no double bonds).
Let us identify the different ring sizes and substitutions:
1. Three-membered ring ethers (Oxiranes/Epoxy compounds):
- Ethyloxirane (1-ethyl-oxirane)
- Methylmethyloxirane (2-methyl-oxirane, both cis and trans isomers) → 2 stereoisomers
2. Four-membered ring ethers (Oxetanes):
- Methyl-substituted oxetane (on different carbon positions)
- 2 stereoisomers (cis/trans) possible depending on substitution pattern
3. Tetrahydrofuran derivative (5-membered ring):
- 2-methyltetrahydrofuran → exists as cis/trans stereoisomers
So we have:
- 1 from ethyloxirane
- 2 from methylmethyloxirane (cis/trans)
- 1 from methyl-substituted oxetane
- 2 from methyltetrahydrofuran (cis/trans)
Total = 1 + 2 + 1 + 2 = 6 isomers
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 :