Question

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

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

Answer 1

Answer: (C)

3.83%

$\begin{array}{c}\text{Mass of sphere}=12.2\pm 0.1kg\\ \text{Radius of Sphere}=10\pm 0.1cm\end{array}$

$\begin{array}{c}\text{We know that}\\ p=\frac{M}{V}=\frac{M}{\frac{4}{3}\pi r^3}=\frac{3M}{4\pi r^3}\end{array}$

$\log p=\log M-3\log r+\log \left(\frac{3}{4\pi }\right)$

$\frac{dp}{p}=\frac{dM}{M}-3\cdot \frac{dr}{r}$

$\begin{array}{c}\text{For maximum permissible errore}\\ \begin{array}{c}\frac{dp}{\rho }=\frac{dM}{M}+3\cdot \frac{dr}{r}\\ \frac{dp}{p}=\frac{0.1}{12.2}+3\times \frac{0.1}{10}=0.0383=3.83\%\end{array}\end{array}$