Question

A physical quantity X is given by $X=\frac{2k^3{l}^2}{m\sqrt{n}}$ The percentage error in the measurements of k, l, m and n are 1%, 2%, 3% and 4% respectively. The value of X is uncertain by

• A. 8%
• B. 10%
• C. 12%
• D. none of these

Answer 1

Answer: (C)

Given : $X=\frac{2k^3{l}^2}{m\sqrt{n}}$
$\therefore \frac{\Delta X}{X}\times 100=\left(3\frac{\Delta k}{k}+2\frac{\Delta l}{l}+\frac{\Delta m}{m}+\frac{1}{2}\frac{\Delta n}{n}\right)\times 100$
$=3\times 1\%+2\times 2\%+3\%+\frac{1}{2}\times 4\%$
$=3\%+4\%+3\%+2\%=12\%$
Hence, the value of X is uncertain by 12%.