Question

if the errors involved in the measurement of a side and mass of a cube are 2% and 3% respectively then find the maximum permissible error in the measurement of density of the material​

Answer 1

Let mass of the cube be $\sf{m}$ and edge length be $\sf{a.}$

Volume of the cube is,

$\sf{\longrightarrow V=a^3}$

Density of the cube is,

$\sf{\longrightarrow \rho=\dfrac{m}{V}}$

$\sf{\longrightarrow \rho=\dfrac{m}{a^3}}$

Then, maximum permissible percentage error in measurement in density is,

$\sf{\longrightarrow\delta\rho=\delta m+3\,\delta a}$

In this question,

• $\sf{\delta a=2\%}$

• $\sf{\delta m=3\%}$

Then,

$\sf{\longrightarrow\delta\rho=\delta m+3\,\delta a}$

$\sf{\longrightarrow\delta\rho=3\%+3\times2\%}$

$\sf{\longrightarrow\underline{\underline{\delta\rho=9\%}}}$