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 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 :