A physical quantity P is related to four observables a, b, c and d as P= a b d^ c ( is constant) The percentage errors in a, b, c and d are 0.5 % in each. If the percentage error in P is 2 % , then is

Step-by-step solution

As, P= a^ 1 / 2 b^ 1 / 2 d^ c^ 1 / 2 So % error in P= P P 100 aligned = 1 2 & ( a a ) 100+ 1 2 ( b b 100 ) & + ( d d 100 )+ 1 2 ( c c 100 ) aligned % error in P= 1 2 % error in a+ 1 2 % error in b+ 1 2 % error in c+ % error in d Now given, % Error in P=2 % % Error in a= % error in b= % Error in c= % error in d=0.5 % Substituting these values in Eq. (i), we get aligned 2 & = 1 2 0.5+ 1 2 0.5+ 1 2 0.5+ 0.5 2 & = 1 2 ( 1 2 + 1 2 + 1 2 + ) 4= 3 2 + aligned or =4- 3 2 = 5 2 is 5 / 2 .