Physics · Units And Measurements · NEET
They ADD. Even for Z = A / B you write ΔZ/Z = ΔA/A + ΔB/B, never a minus sign. We always assume the worst case (maximum possible error), where the errors from A and B could push the result in the same direction. So subtracting is wrong — always add the relative errors, whether it is a product or a quotient.
Use RELATIVE error (ΔA/A) or percentage error (ΔA/A x 100). This is the key difference from sum and difference. In sum/difference you add ABSOLUTE errors (ΔA + ΔB). In product/quotient you add RELATIVE errors. Mixing these two rules is the most common NEET mistake.
Because Z depends on A and B as a product. If you take the differential of Z = AB and divide by Z, you get ΔZ/Z = ΔA/A + ΔB/B. The A and B units cancel out, leaving only fractions. So for multiply/divide the natural quantity that adds is the fractional error, not the absolute error.
Density ρ = m / V is a quotient, so ΔΡ/ρ = Δm/m + ΔV/V. If volume itself comes from other measurements (like V = πr²l), first add the relative errors of those, then add to the mass error. Every quantity's relative error is counted once (with a power multiplier if raised to a power).
No. The rule is identical. For Z = AB and for Z = A/B you get exactly the same formula: ΔZ/Z = ΔA/A + ΔB/B. Whether a quantity is on top or bottom of a fraction, its relative error is added. This is why students remember it as one single rule.
A metal wire has mass (0.4 ± 0.002) g, radius (0.3 ± 0.001) mm and length (5 ± 0.02) cm. The maximum possible percentage error in the measurement of density will nearly be:
A physical quantity P is related to four observations a, b, c and d as P = a³b² / (c·√d). The percentage errors in a, b, c and d are 1%, 3%, 2% and 4% respectively. The percentage error in P is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
For Z = A x B, the maximum relative error is ΔZ/Z = ΔA/A + ΔB/B. The relative (or percentage) errors of the multiplied quantities add together.
Yes, exactly the same. For Z = A / B you also use ΔZ/Z = ΔA/A + ΔB/B. Multiplication and division share one identical rule — relative errors add.
Because we always report the MAXIMUM possible error. In the worst case both measurements err in a direction that increases the total error, so we add the relative errors instead of subtracting.
In sum and difference you add ABSOLUTE errors (ΔA + ΔB). In product and quotient you add RELATIVE (percentage) errors. Picking the wrong rule is the top NEET error.
Its relative error is multiplied by that power. For example r² contributes 2(Δr/r). This is covered in detail on the 'error in a quantity raised to a power' page.
