Question

A body of mass 20.00 g has volume $5.0c{m}^3$. The maximum possible error in the measurement of mass and volume respectively are 0.01 g and$0.1c{m}^3$. The maximum percentage error in the density will be nearest to

• A. 1%
• B. 2%
• C. 11%
• D. 25%

Answer 1

The correct option is B 2%

$m=20.00g$

$v=5.0c{m}^2$

$d=\frac{m}{v}$

$\Rightarrow \frac{\Delta d}{d}\times 100=\frac{\Delta m}{m}\times 100+\frac{\Delta v}{v}\times 100$

$\Rightarrow \frac{\Delta d}{d}\times 100=\frac{0.01}{20}\times 100+\frac{0.1}{5}\times 100=\frac{1}{20}+2$

$\Rightarrow \frac{\Delta d}{d}\times 100=2.005$

$\therefore \%$ error in density $\approx 2\%$

Hence,

option $\left(B\right)$ is correct answer.