Question

if the percentage error in mass and volume is 1% and 3%,the percentage error in density is

Answer 1

Answer:

4%

Explanation:

density=mass÷volume

%error in density=1+3

=4%

Answer 2

Given:

The percentage error in mass and volume is 1% and 3%.

To find:

% error in density.

Calculation:

Density is define as the mass per unit volume for a substance.

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

Now , for small errors in mass and volume (< 6%) , we can say that:

$\rm{ \therefore \dfrac{\Delta \rho}{ \rho} = \dfrac{\Delta m}{m} + \dfrac{\Delta V}{ V} }$

Putting available values:

$\rm{ = > \dfrac{\Delta \rho}{ \rho} = 1\% + 3\%}$

$\rm{ = > \dfrac{\Delta \rho}{ \rho} = 4\%}$

So, max relative error in density = 4%.

• This method can be used only when the errors in individual quantities is less than 6%. This is because it is an approximated method.

• If the error is higher , then you have to differentiate and follow that procedure.