Question

The density of a cube is measured by its mass and leangth of its sides of the maximum error in the measurement of mass and leangth are 4% and 3% respectively the maximum error in the measurement of density will be Just tell the answer it's a mcq pls fast

Answer 1

The density of a cube of side $\sf{a}$ and mass $\sf{m}$ is given by,

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

So the relative error in the measurement of density is,

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

And so the percentage error in the measurement of density is,

$\longrightarrow\sf{\dfrac{\Delta\rho}{\rho}\times100=\dfrac{\Delta m}{m}\times100+\dfrac{3\,\Delta a}{a}\times100}$

Or,

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

In the question,

• $\sf{\delta m=4\%}$

• $\sf{\delta a=3\%}$

Hence,

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

$\longrightarrow\sf{\delta\rho=4\%+3\times3\%}$

$\longrightarrow\underline{\underline{\sf{\delta\rho=13\%}}}$

Hence 13% is the answer.