In an experiment, a set of reading are obtained as follows - 1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrument used in recording these readings is _______ mm.

Solution

Physics sir · 4 steps

Look at the last digit each reading carries. That decimal place tells you the least count.

1. What least count means. The least count is the smallest change an instrument can show. So every reading it gives ends at the decimal place of the least count.
2. Read the readings. All four readings (1.24, 1.25, 1.23, 1.21 mm) go to the second decimal place, that is, the hundredths of a millimetre. The last digit changes by 1 at a time (1.21, 1.23, 1.24, 1.25), so the instrument can resolve 0.01 mm.
3. Rule out the others. A least count of 0.1 mm could not give a second decimal digit. With 0.05 mm, the last digit could only be 0 or 5, but 1.24, 1.23 and 1.21 break that. A 0.001 mm instrument would record a third decimal place.
4. So. The expected least count is 0.01 mm, option (a). A screw gauge typically has this least count.

The idea to keep. A recorded reading always ends at the decimal place of the instrument's least count. Check the last digits: if they take any value 0 to 9, the least count is one unit of that place.

Answer from the NTA final answer key. Solution by PrepWiser.