Question

An experiment measures quantities a, b, c and x is calculated from $x=\frac{a{b}^2}{c^3}$ if the percentage error in a, b , c are $\pm 1$ % , $\pm 3$ % $\pm 2$ % respectively.

• A. The percentage error in x can be $\pm 13$ %
• B. The percentage error in x can be $\pm 7$ %
• C. The percentage error in x can be $\pm 20$ %
• D. The percentage error in x can be $\pm 26$ %

Answer 1

The correct option is A The percentage error in x can be $\pm 13$ %

$x=\frac{a{b}^2}{C^3}$

% error = $\Delta a+2\Delta b+3\Delta c$

= $1+2\times 3+3\times 2$ ( error are always additive)

$=1+6+6$

$=\pm 13$%