Question

Measurement of two physical quantities are given as
$x=\left(4.0\pm 0.4\right)m{s}^{-1}$
$Y=\left(1.0\pm 0.1\right)s$
The value of XY will be.

• A. $\left(4.0\pm 0.8\right)m$
• B. $\left(4.0\pm 0.5\right)m$
• C. $\left(4.0\pm 0.3\right)m$
• D. $\left(4.0\pm 0.4\right)m$

Answer 1

The correct option is A $\left(4.0\pm 0.8\right)m$

$\begin{array}{cc}\text{Given-}& \ast x=4\pm 0.4{ms}^{-1}\\ & \ast y=1.\pm 0.1s\end{array}$

$\text{Let}S=x\cdot y=4\times 1=4m$

$\begin{array}{c}\text{Now By error analysis we find error in}S\\ \text{- Taking Logarithm both sides -}\end{array}$

$\log s=\log x+\log y$

$\begin{array}{c}\text{Differentiating both sides}\\ \frac{ds}{s}=\frac{dx}{x}+\frac{dy}{y}=\frac{0.4}{4}+\frac{0.1}{1}=0.2\end{array}$

$\begin{array}{cc}ds& =4\times 0.2=0.8m\\ s=4& \pm 0.8m\end{array}$