A physical quantity x is related as x = a b^2 c^3 d⁻⁴ . Relative errors in the quantities a , b , c and d are 2%, 1%, 3% and 4% respectively. Relative error in x will be

Step-by-step solution

Given x = a^ 1/2 b^2 c^3 d⁻⁴ The maximum relative percentage error in x is given by x x 100 = 1 2 ( a a 100 ) + 2 ( b b 100 ) + 3 ( c c 100 ) + 4 ( d d 100 ) Substituting the given percentage errors: x x 100 = 1 2 (2 %) + 2(1 %) + 3(3 %) + 4(4 %) x x 100 = 1 % + 2 % + 9 % + 16 % = 28 % Answer: 28%