Question

What is error in density of a cube when its mass is uncertain by 2% andlength of its edge is uncertain by 1%?

Answer 1

Check the attachemnet

Answer 2

Given :

Error in mass is 2% .

Error in length of its edge is uncertain by 1% .

To Find :

Error in density .

Solution :

We know , density is given by :

$\rho=\dfrac{M}{V}\\\\\rho=\dfrac{M}{a^3}$

Here , M is mass , V is volume of cube and a is edge of cube .

Now ,

$\dfrac{\Delta \rho}{\rho}=\dfrac{\Delta M}{M}+3\dfrac{\Delta a}{a}\\\\\dfrac{\Delta \rho}{\rho}=2\ \%+(3\times 1\ \%)\\\\\dfrac{\Delta \rho}{\rho}=(2+3)\ \%\\\\\dfrac{\Delta \rho}{\rho}=5\ \%$

Therefore , error in density of a cube is 5 % .

Learn More :

Errors and measurements

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