Question

A physical quantity X is given by X = A B3/C D1/2. If the percentage errors
of measurement in A, B, C and D are 4% ,2%,3% and 1% respectively,
then calculate the % error in X.

Answer 1

% error in X = 13.5%. .

Explanation:

X = AB³/CD½

∆X/X = ∆A/A + 3(∆B/B) +∆C/C + 1/2(∆D/D)

percentage errors are

(∆X/X) x100= (∆A/A) x 100 + 3(∆B/B)x 100+(∆C/C) x 100

+ 1/2(∆D/D) x 100

= 4 + (3x2) + 3 + (1/2 x 1)

= 13 + 1/2

= 27/2 %

= 13.5 ℅