A physical quantity P is related to three observables X , Y , and Z by the relation P = X^3 Y^2 Z . If the maximum percentage errors in the measurement of P , X , and Z are 15 % , 1 % , and 4 % respectively, then the percentage error in the measurement of Y is:

Step-by-step solution

The relation for the physical quantity is given by P = X^3 Y^2 Z^ 1/2 . The maximum percentage error in P is given by the sum of the percentage errors of the individual quantities multiplied by their respective powers: P P 100 = 3 ( X X 100 ) + 2 ( Y Y 100 ) + 1 2 ( Z Z 100 ) Given that the percentage errors in P , X , and Z are 15 % , 1 % , and 4 % respectively, we can substitute these values into the equation: 15 = 3(1) + 2 ( Y Y 100 ) + 1 2 (4) 15 = 3 + 2 ( Y Y 100 ) + 2 15 = 5 + 2 ( Y Y 100 ) 2 ( Y Y 100 ) = 10