Question

The mass and volume of a body are found to be $5.00\pm 0.05kg$ and $1.00\pm 0.05m^3$ respectively. Then the maximum possible percentage error in its density is

• A. 6%
• B. 3%
• C. 10%
• D. 5%

Answer 1

The correct option is A 6%

$\begin{array}{cc}\text{Given -}& \text{Mass of the body}=5\pm 0.05kg\\ & \text{volume}=1\pm 0.05m^3\end{array}$

$\begin{array}{c}\text{we know that -}\\ P=\frac{M}{V}\end{array}$

$\begin{array}{c}\text{Now by error analysis method-}\\ \text{Take logarithm both sides}\\ \log \rho =\log M-\log V\\ \text{Differentiating both sides.}\\ \frac{dP}{P}=\frac{dM}{M}-\frac{dV}{V}\end{array}$

$\begin{array}{c}\text{For maximum permissible error write}\\ \frac{dP}{P}=\frac{dM}{M}+\frac{dV}{V}\\ \Rightarrow \frac{dp}{p}=\frac{0.05}{5}+\frac{0.05}{1}=\frac{0.30}{5}=0.06\\ \frac{dP}{P}=6\%\end{array}$

$\text{Hence maximum possible error in}P\text{is}6\%$