JEE Physics Errors in Measurement Notes Set 02

Errors in Measurement

Absolute error = measured value minus true value. For several readings the mean value is taken as the true value, and the mean absolute error is the average of the absolute deviations. Relative error = mean absolute error / mean value; percentage error is relative error times 100.

Combination of Errors

Sum or difference: \( \Delta x=\Delta a+\Delta b \) (absolute errors add). Product or quotient: \( \frac{\Delta x}{x}=\frac{\Delta a}{a}+\frac{\Delta b}{b} \). Power: for \( x=a^nb^m \), \( \frac{\Delta x}{x}=n\frac{\Delta a}{a}+m\frac{\Delta b}{b} \).

Significant Figures

All non-zero digits are significant. Zeros between non-zero digits and trailing zeros after a decimal point are significant. Leading zeros are not. In multiplication or division keep the least number of significant figures; in addition or subtraction keep the least number of decimal places.

Vernier Calliper

Least count = 1 main scale division - 1 vernier scale division = (value of 1 MSD)/(number of vernier divisions). Reading = MSR + (VSR coinciding division) x LC, then correct for zero error.

Screw Gauge

Least count = pitch / number of circular scale divisions. Reading = main scale reading + (circular scale reading) x LC. A negative zero error is added to the observed reading and a positive zero error is subtracted.

Worked Example

A screw gauge has pitch 1 mm and 100 circular divisions. The main scale reads 2 mm and the circular scale reads 36. Find the diameter.
Solution: LC = 1/100 = 0.01 mm. Diameter = 2 + 36 x 0.01 = 2.36 mm.