A physical quantity X is related to four measurable quantities a, b, c and d as follows X=a^(2)b^(3)c^((5)/(2))d^(-2). The percentange 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.

A physical quantity X is related to four measurable quantities a, b, c

1.	A physical quantity X is related to four measurable quantities a, b, c and d as follows X=a^(2)b^(3)c^((5)/(2))d^(-2). The percentange 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» Solution :GIVEN physical quantity `X=a^(2)b^(2)c^((5)/(2))d^(-2)` Maximum percentage error in x s, `(DeltaX)/(X)xx100=[2((Deltaa)/(a)xx100)+3((DELTAB)/(b)xx100)+(5)/(2)((DeltaC)/(c)x100)+2((Deltad)/(d)xx100)]` `=[(2(1)+3(2)+(5)/(2)(3)+2(4)]%` `=[2+6+(15)/(2)+8]=+-23.5%` `:.` Percentage error in `X=23.5%` RELATIVE error in X = 0.235 = 0.24 (By rounding off upto two significant figures) The CALCULATED value of x should be round off upto two significant digits `:. 2.8`