Question

For a cubical block, error in measurement of sides is \(\pm 1\%\) and error in the measurement of mass is \(\pm 2\%\), then maximum possible error in density is:

Answer 1

If \(x=\dfrac{a^pb^q}{c^r}\), then the maximum possible fractional error in \(x\) is
\(\dfrac{\Delta x}{x}\times 100=\pm\left [ p\dfrac{\Delta a}{a}\times100+q\dfrac{\Delta b}{b}\times100+r\dfrac{\Delta c}{c}\times100 \right ]\)
Given,
\(\dfrac{\Delta m}{m}=\pm 2\%=\pm2\times10^{-2}\)

\(\dfrac{\Delta l}{l}=\pm 1\%=1\times10^{-2}\)
As we know, the density of cubical box side \( 'l '\) given by
\(\rho =\dfrac{m}{V}=\dfrac{m}{l^3}\)
The maximum possible error in density
\(\dfrac{\Delta \rho}{\rho}=\dfrac{\Delta m}{m}+3\dfrac{\Delta l}{l} \)
put the values,
\(=(\pm 2\times 10^{-2})+(\pm 3\times 10^{-2})\)
Maximum \(=5\times10^{-2}=5\%\)