Allotropes Of Carbon

Step 1: Understand the properties and uses of different allotropes of carbon.

Step 2: Match each allotrope with its primary application. \begin{itemize} \item A. Carbon black: A fine powder used extensively as a filler in automobile tyres (IV) to enhance strength and durability. \item B. Graphite: A good conductor of electricity and has a layered structure making it suitable for electrodes in batteries (I). \item C. Diamond: The hardest known natural material, making it ideal as an abrasive (III) for cutting and grinding. \item D. Activated charcoal: Highly porous with a large surface area, used for adsorption in air conditioning systems (V) and filters to remove impurities and odors. \end{itemize}
Step 3: Combine the matches to find the correct option.
The correct matching is A - IV, B - I, C - III, D - V. Final Answer: The final answer is

- Diamond is the hardest naturally occurring substance, and its hardness makes it an ideal material for use as an abrasive in sharpening hard tools. Hence, the correct answer is (3).
- Graphite is soft and used as a lubricant, not as an abrasive, so option (1) is incorrect.
- Fullerene is a molecular form of carbon and is not used as an abrasive, making option (2) incorrect.
- Carbon black is primarily used in rubber and ink production, not for sharpening tools, so option (4) is incorrect.