Question

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

(1) 66%

(2) 43%

(3) 34%

(4) 14%

Answer 1

The correct option is (3) 34%.

From log method,

\(\frac{\Delta Q}{Q} = \frac{4 \Delta a}{a} + \frac{3\Delta b}{b} + \frac{2\Delta c}{c}\)

% error in Q = \(4 \times 3 + 3 \times 4 + 2 \times 5 = 34\)