BTSC Lab Assistant Physics Lab: Instruments, Readings and Error Calculations

A formula will not save a mark lost to the wrong instrument, miscounted divisions or an incorrect zero-correction sign. Choosing the instrument, reading its scale in a fixed order, correcting the zero error with the right sign, and carrying that uncertainty into a calculated result are one chain, and the mark goes wherever the chain breaks. It breaks most often at two points: the sign of the zero correction, and the moment a reading that carries an uncertainty is fed into a formula.

Match the measured quantity to the instrument

Before measuring, check three things in order: the instrument's range, its least count, and the size you expect. Range decides whether the instrument fits at all, least count decides how many digits you may honestly report, and the expected size tells you which of the two is about to bite.

Use a metre scale for a 42.6 cm rod, vernier calipers for a tube about 2.4 cm across, and a screw gauge for a 0.56 mm wire. Precision helps only when range and geometry fit: a screw gauge will not span the rod, and a metre scale cannot resolve the wire. Wrong instrument, wrong answer, however careful the arithmetic that follows. The rest of the laboratory-work revision for this recruitment sits in BTSC Lab Assistant (CS) Exam Prep.

Read vernier calipers in a fixed sequence

If 10 VSD = 9 MSD and 1 MSD = 1 mm, then 1 VSD = 0.9 mm. Therefore least count = 1 MSD - 1 VSD = 1.0 - 0.9 = 0.1 mm = 0.01 cm.

Use observed reading = main-scale reading + coinciding division × least count.

1. Main-scale reading = 2.30 cm.

2. The sixth vernier division coincides, so its contribution is 6 × 0.01 = 0.06 cm.

3. Observed reading = 2.30 + 0.06 = 2.36 cm.

4. Positive zero error = +0.02 cm, hence zero correction = -0.02 cm.

5. Corrected reading = 2.36 - 0.02 = 2.34 cm.

The sign rule is corrected reading = observed reading - zero error.

Handle screw-gauge and analogue-scale readings carefully

For a screw gauge with pitch 0.5 mm and 50 circular-scale divisions, least count = 0.5/50 = 0.01 mm. If the main-scale reading is 5.5 mm and circular division 23 coincides:

Observed diameter = 5.5 + 23 × 0.01 = 5.73 mm.

With positive zero error +0.03 mm, corrected diameter = 5.73 - 0.03 = 5.70 mm.

An ammeter spanning 0 to 3 A across 30 intervals has least count 3/30 = 0.1 A. A pointer resting at the end of the eighteenth interval reads 18 × 0.1 = 1.8 A. Count intervals, not marks: 30 intervals require 31 marks. View the scale normally to prevent parallax.

Read a concave water meniscus at its bottom, with the eye level with it. If a burette level falls from 37.5 mL to 24.0 mL as liquid is run off, the volume delivered is 37.5 - 24.0 = 13.5 mL, which is 13.5 cm³.

Separate resolution, offset, scatter and parallax

Least count limits resolution. Correct systematic zero error algebraically, reduce random scatter through repetition, and prevent parallax by viewing perpendicularly. Closely grouped readings can be precise yet inaccurate when they share an uncorrected zero error. BTSC Lab Assistant Units, Measurement Error and Lab Safety works that distinction through three sets of repeated volume readings taken against a known reference.

Take repeated readings 5.70, 5.71, 5.69, 5.70, 5.72 mm.

1. Mean = 28.52/5 = 5.704 mm.

2. Absolute deviations are 0.004, 0.006, 0.014, 0.004, 0.016 mm.

3. Their total is 0.044 mm, so mean absolute error = 0.044/5 = 0.0088 mm, about 0.009 mm.

4. Percentage uncertainty = 0.009/5.704 × 100, about 0.16%.

Round uncertainty first, then the value to the same place: (5.70 ± 0.01) mm. Extra digits are not accuracy.

Propagate error in a calculated result

Add absolute uncertainties for sums or differences. For products, quotients and powers, add fractional uncertainties with powers as multipliers.

Consider a cylinder with m = (48.6 ± 0.1) g, d = (2.50 ± 0.01) cm and h = (3.20 ± 0.01) cm.

1. V = πd²h/4 = π × 2.50² × 3.20/4 = 15.708 cm³.

2. ρ = m/V = 48.6/15.708 = 3.094 g/cm³.

3. Fractional uncertainty = 0.1/48.6 + 2(0.01/2.50) + 0.01/3.20 = 0.01318, or 1.32%.

4. Absolute uncertainty = 3.094 × 0.01318, about 0.041 g/cm³.

The unit check is essential: grams divided by cubic centimetres gives g/cm³. After rounding, report ρ = (3.09 ± 0.04) g/cm³.

Fix the traps that turn method into a wrong option

A corrected reading must move opposite to the zero-error sign, so a positive zero error always makes the corrected value smaller. And within one unit, a finer instrument should never be reported to fewer decimal places than a coarser one, because that throws away the resolution you chose it for.

Use a 20-second check: quantity and unit, range, least count, observed value, zero correction, uncertainty, rounding.

Convert the lesson into a BTSC-oriented practice loop

Use a 30-minute drill: 8 minutes on the instrument table, 12 minutes on six direct readings, 7 minutes on two error calculations, and 3 minutes classifying misses as concept, arithmetic, sign, unit or observation. Next day, redo those error classes before fresh questions. Use PYQs to find repeatable error patterns: a candidate who drops two marks a paper to sign errors will keep dropping them until the sign rule is drilled on its own. The marks, duration and topic split for the current cycle are published in the notification on the Bihar Technical Service Commission site, so size the drill against those rather than against a remembered pattern.

The short version

Choose by range, geometry and least count. Read in order, subtract the signed zero error, repeat, and round the value to the uncertainty. Before moving on, reproduce three results without looking back: corrected vernier reading 2.34 cm, corrected diameter 5.70 mm, and density (3.09 ± 0.04) g/cm³. Candidates on the Computer Science and IT lane can sequence the rest of their preparation with the BTSC Lab Assistant (CS) course and time it with the BTSC Lab Assistant (CS) Test Series; both run on the computer subjects, so keep your own physics bench practice going alongside them.