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Q.
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
AIIMSAIIMS 2017Physical World, Units and Measurements
Solution:
Given : $X = \frac{2k^{3}l^{2}}{m\sqrt{n}}$
$\therefore \quad \frac{\Delta X}{X}\times100=\left(3 \frac{\Delta k}{k}+2 \frac{\Delta l}{l}+\frac{\Delta m}{m}+\frac{1}{2} \frac{\Delta n}{n}\right)\times100$
$\quad= 3 × 1\% + 2 × 2\% + 3\% +\frac{1}{2}\times4\%$
$\quad= 3\% + 4\% + 3\% + 2\% = 12\%$
Hence, the value of X is uncertain by 12%.