To keep constant time, watches are fitted with balance wheel made of $\ldots \ldots \ldots$ (A) invar (B) stainless steel (C) Tungsten (D) platinum

For a watch to keep constant time, the balance wheel must be made of a material that has low thermal expansion, meaning that it won't significantly change its shape or size when the temperature changes. This characteristic is important because temperature changes can affect the accuracy of the watch.

Now, let's take a closer look at each option: (A) Invar: Invar is an alloy that has very low thermal expansion. It is composed mainly of iron (around 64%) and nickel (36%). It is often used in applications where precision is necessary, such as measuring instruments and high-precision clocks. (B) Stainless steel: Stainless steel is an alloy of iron, with chromium and other elements. It is known for its corrosion resistance, but it has a higher thermal expansion coefficient than invar, which could affect the precision of the watch when exposed to temperature changes. (C) Tungsten: Tungsten is a dense, heavy metal with a high melting point and low thermal expansion. It is used in various applications where high temperatures or wear resistance is needed. However, tungsten is not as widely used in watchmaking as invar, mainly due to its weight and stiffness. (D) Platinum: Platinum is a precious metal known for its resistance to corrosion, tarnish, and high temperatures. It is often used in jewelry and high-end watches. However, its thermal expansion coefficient is higher than invar, making it less suitable for balance wheels that require extreme precision.

After evaluating each option, it is clear that Invar (A) is the most appropriate material for maintaining constant time due to its low thermal expansion characteristics, which are essential in balance wheels to ensure precision. Therefore, the correct answer is: (A) invar