In the measurement of a physical quantity `X = A^(2)B/C^(1//3)D^(3)` The percentage errors introduced in the measurement of the quantities A, B, C and D are 2%, 2%, 4% and 5% respectively. Then, the minimum amount of percentage error in the measurement of X is contributed by

Explanation

`X = (A^2 B)/(C^(1//3) D^3) , (DeltaA)/(Z)% = 2% (Delta A)/(Z) % = 2% (DeltaB)/(B) % = 2% (DeltaC)/(C)% = 4% (DeltaD)/(D) % = 5%`
`(DeltaX)/(X) = 2(DeltaA)/(A) + (DeltaB)/(B) + 1/3 (DeltaC)/(C) + 1/3 (DeltaD)/(D)`
Percentage error in `X = (DeltaX)/(X) xx 100 = 2 (DeltaA)/(A) xx 100 + (DeltaB)/(B) xx 100 + 1/3 (DeltaC)/(C) + 3 xx (DeltaD)/D`
`=(2xx 2) + 2 + (1/3 xx 4) + (3xx5) = 22.34%`
`therefore ` The minimum amount of error is contributed in C.