Question

If $L=(20+pm0.01)m$ and $B=(10\pm 0.02)m$ then $L/B$ is

• A. $(2\pm 0.03)m$
• B. $(2\pm 0.0015)m$
• C. $(2\pm 0.01)m$
• D. $(2\pm 0.005)m$

Answer 1

The correct option is D $(2\pm 0.005)m$

$\begin{array}{cc}\text{Given}\to & L=20\pm 0.01mB=10\pm 0.02m\\ & \frac{L}{B}=?\\ \text{Let}S=\frac{L}{B}& \text{we get}S=\frac{20}{10}=2\end{array}$

$\begin{array}{c}\text{By error an analysis method}\\ \text{Take logorithm both sides -}\\ \log s=\log L-\log B\\ \text{differentiate both sides -}\\ \frac{ds}{s}=\frac{dL}{L}-\frac{dB}{B}\end{array}$

$\begin{array}{c}\text{for maximum permissible value write-}\\ \text{.}\frac{dS}{S}=\frac{dL}{L}+\frac{ds}{S}\\ \Rightarrow \frac{dS}{S}=\frac{0.01}{20}+\frac{0.02}{10}=0.0025\\ \Rightarrow dS=S\cdot \left(0.0025\right)=2\cdot \left(0.0025\right)=0.005\\ \Rightarrow S=2\pm 0.005m\end{array}$