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

The correct option is C $12$%

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