Why are the weights in a weight box kept in a 5:2:2:1 ratio
The Correct Answer and Explanation is:
Weights in a weight box are kept in a 5:2:2:1 ratio to allow for maximum flexibility and accuracy in measuring different masses using the least number of standard weights. This ratio helps create a binary-like combination system, enabling the user to measure a wide range of values with minimal weights.
Detailed Explanation
A standard weight box typically contains weights in the ratio 5:2:2:1, for example: 50 g, 20 g, 20 g, and 10 g (or 500 mg, 200 mg, 200 mg, and 100 mg, etc.). This setup is not arbitrary; it follows a systematic approach based on economic combination of masses.
The main objective of having weights in this ratio is to measure any mass within a given range (usually from 1 g to 100 g, or 1 mg to 100 mg) using the fewest weights possible. The 5:2:2:1 ratio enables the formation of almost any desired weight using combinations and subtraction on a two-pan balance.
Let’s consider an example:
- With weights of 50 g, 20 g, 20 g, and 10 g, we can measure masses like:
- 10 g (using 10 g),
- 30 g (20 g + 10 g),
- 70 g (50 g + 20 g),
- 40 g (50 g on one pan, 10 g on the other, i.e., 50 – 10 = 40), and so on.
This system works much like the binary or base-2 system, where weights can be combined or placed on either side of a balance to measure both whole numbers and differences. The two 20 g weights provide redundancy and flexibility, increasing the number of combinations available without needing every single unit (e.g., 1 g, 2 g, 3 g…).
Thus, the 5:2:2:1 ratio is an efficient, cost-effective, and space-saving method for constructing weight sets, widely used in physics laboratories and by calibration professionals.
