A physical quantity ' X ' is related to four measurable quantities ' a ', ' b ', ' c ' and ' d ' as X = a ^2 ~b ^3 c ^ 5 / 2 ~d ⁻² . The percentage error in the measurement of ' a ', ' b ', ' c ' and ' d ' are 1 %, 2 %, 2 % and 4 % respectively. The percentage error in measurement of quantity ' X ' is

Step-by-step solution

The percentage error in X = a^p b^q c^r d^s is given by: X X 100 = |p| a a 100 + |q| b b 100 + |r| c c 100 + |s| d d 100 For X = a^2 b^3 c^ 5/2 d⁻² with percentage errors of 1 % , 2 % , 2 % , and 4 % respectively: X X 100 = |2|(1 %) + |3|(2 %) + |5/2|(2 %) + |-2|(4 %) = 2 % + 6 % + 5 % + 8 % = 21 % The percentage error in X is 21 % .