Step 1: Concept The form of carbon in cast iron determines its classification and mechanical properties.
Step 2: Meaning White cast iron is named for its white, crystalline fractured surface, which lacks visible graphite.
Step 3: Analysis During rapid cooling, carbon does not have time to precipitate as graphite. Instead, it reacts with iron to form iron carbide.
Step 4: Conclusion In white cast iron, carbon is present in the form of cementite ($Fe_{3}C$), making it very hard and brittle.
Final Answer: (D)