Four instruments measured the diameter of a wire whose values are given below. Instrument 1 → 1.3 mm Instrument 2 → 1.32 mm Instrument 3 → 1.324 mm Instrument 4 → 1.03 mm The instrument having smallest value of least count is * (a) Instrument 1 (b) Instrument 2 (c) Instrument 3 (d) Instrument 4
The Correct Answer and Explanation is:
Correct Answer: (c) Instrument 3
Explanation:
The least count of an instrument is the smallest measurement it can accurately read. It determines the precision of the instrument. To identify which instrument has the smallest least count, we need to look at the number of decimal places in each measurement. The more decimal places, the finer or smaller the least count.
Here is the breakdown of the measurements:
- Instrument 1 reads 1.3 mm. This has 1 decimal place, so the least count is 0.1 mm.
- Instrument 2 reads 1.32 mm. This has 2 decimal places, so the least count is 0.01 mm.
- Instrument 3 reads 1.324 mm. This has 3 decimal places, so the least count is 0.001 mm.
- Instrument 4 reads 1.03 mm. This has 2 decimal places, so the least count is 0.01 mm.
Now, we compare the least counts:
- Instrument 1: 0.1 mm
- Instrument 2: 0.01 mm
- Instrument 3: 0.001 mm
- Instrument 4: 0.01 mm
Instrument 3 has the smallest least count, which means it is the most precise among the four. A smaller least count allows the instrument to detect smaller variations in measurements, making it more suitable for tasks that require high precision.
Understanding least count is essential in experimental physics and engineering because it helps determine the accuracy and precision of measurements. An instrument with a finer least count can capture more detailed information and reduce measurement uncertainty. This is particularly important in tasks such as measuring wire diameters, where even small deviations may affect performance in electronic or mechanical systems.
Therefore, Instrument 3, which records the value 1.324 mm, has the smallest least count and is the correct answer.
