A physical quantity Q is found to depend on quantities a , b , c by the relation Q = a 4 b 3 c 2 . The percentage error in a , b and c are 3 % , 4 % and 5 % respectively. Then, the percentage error in Q is:

Step-by-step solution

Given quantity is Q = a 4 b 3 c 2 . The relative error in measuring Q is given by Δ Q Q = 4 Δ a a + 3 Δ b b + 2 Δ c c . . . 1 Hence, the required percentage error is given by Δ Q Q × 100 = 4 Δ a a × 100 + 3 Δ b b × 100 + 2 Δ c c × 100 = 4 × 3 % + 3 × 4 % + 2 × 5 % = 12 % + 12 % + 10 % = 34 %