Question

A physical quantity X is related to four measurable quantities a, b, c and d as follows: X = a² b³ c^5/2d^–2. The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4%, respectively. What is the percentage error in quantity X? If the value of X calculated on the basis of the above relation is 2.763, to what value should you round off the result.

Answer 1

Given, physical quantity is X = a² b³ c^5/2d^–2

The maximum percentage error in X is

`(Δx)/x xx 100 = +- [2((Δa)/a xx 100) + 3((Δb)/b xx 100) + 5/2((Δc)/c xx 100) + 2((Δd)/d xx 100)]`

= `+- [2(1) + 3(2) + 5/2 (3) + 2(4)]%`

= `+- [2 + 6 + 15/2 + 8]`

= `+-  23.5%`

∴ Percentage error in quantity X = ± 235%

Mean absolute error in X = ± 0.235 = ± 0.24 ......(Rounding-off upto two significant digits)

The calculated value of x should be round-off up to two significant digits.

∴ X = 2.8