Question

A sphere has a mass of $12.2$$kg\pm 0.1kg$ and radius $10$$cm\pm 0.1cm$ , the maximum $\%$ error in density is

• A. $10$$\%$
• B. $2.4$$\%$
• C. $3.83$$\%$
• D. $4.2$$\%$

Answer 1

The correct option is C $3.83$$\%$

$e=\frac{m}{V}=\frac{m}{4/3{\pi r}^3}$

$\therefore$ $\frac{\Delta e}{e}=\frac{\Delta m}{m}+3\frac{\Delta r}{r}$

$=\frac{0.1}{12.2}+3\times \frac{0.1}{10}$

$=\frac{1}{122}+\frac{0.3}{10}=0.0383$

$\therefore$ max percentage error $=0.0383\times 100$% $=3.83$% [C]