ANS:A - malleable iron

Among the options provided, malleable iron is the best material capable of withstanding shock and vibration without the danger of cracking. Malleable iron is a type of cast iron that has been heat-treated to convert the carbides into graphite nodules, resulting in improved ductility and toughness compared to other forms of cast iron. This heat treatment process, known as annealing, imparts malleability to the iron, making it less brittle and more resistant to shock and vibration. Grey cast iron, chilled cast iron, and white cast iron are all relatively brittle compared to malleable iron and are more prone to cracking under shock and vibration. Grey cast iron contains graphite flakes, which provide some damping properties but are still less ductile than malleable iron. Chilled cast iron has a hard surface layer formed by rapid cooling, making it resistant to wear but also more brittle. White cast iron contains cementite (iron carbide) and is the hardest and most brittle form of cast iron. Therefore, malleable iron is the preferred choice for applications where shock and vibration resistance are important considerations.