Question

Mass and volume of a block are measured as
22.42 g and 4.7 cm?. The maximum possible error
in density is
(1) 0.6%
(2) 2.2%
(3) 2.8%
(4) 3.2%​

Answer 1

Given,

• Mass = 22.42 g

• Volume = 4.7 cm³

Suppose the maximum possible error of mass and volume are 0.01 g and 0.1 cm³.

The density is equal to the mass of block divided by the volume of block.

$\boxed{\displaystyle\sf{\frac{\Delta\rho}{\rho}\times100=\frac{\Delta m}{m}\times 100+\frac{\Delta V}{V}\times100}}$

Applying the values to the equation,

$\implies\displaystyle\sf{\frac{\Delta\rho}{\rho}\times100=[\frac{0.01}{22.42}\times100]+[\frac{0.1}{4.7}\times100]}$

$\implies\displaystyle\sf{\frac{\Delta\rho}{\rho}\times100=2.2\:\%}$

$\boxed{\displaystyle\sf{Maximum\:error\:in\:Density=2.2\:\%}}$