A physical quantity X is related to four measurable quantities a, b, c and d as follows: X = a2 b3 c5/2 d–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.
The given physical quantity, X = a2 b3 c5/2 d–2
Percentage error in X = (∆x/x)(100)
Percentage error in a = (∆a/a)(100) = 1%
Percentage error in b = (∆b/b)(100) = 2%
Percentage error in c = (∆c/c)(100) = 3%
Percentage error in d = (∆d/d)(100) = 4%
Maximum percentage error in X = ±23.5%
X should have two significant values, therefore, X = 2.8
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.