Resistance of a rod is calculated by measurin | vedclass

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(A) The resistance of a rod is given by $R = \frac{\rho \ell}{A} = \frac{\rho \ell}{\pi r^2} = \frac{4 \rho \ell}{\pi D^2}$,where $\ell$ is length and

Vedclass · Accepted Answer

$1.5$

Vedclass · Answer

(A) The resistance of a rod is given by $R = \frac{ho \ell}{A} = \frac{ho \ell}{\pi r^2} = \frac{4 ho \ell}{\pi D^2}$,where $\ell$ is length and $D$ is diameter.Taking the relative error: $\frac{\Delta R}{R} = \frac{\Delta \ell}{\ell} + 2 \frac{\Delta D}{D}$ (since $ho$ is exact,$\Delta ho = 0$).Given: $\ell = 20 \ cm = 200 \ mm$,$\Delta \ell = 1 \ mm$.Diameter $D = 4 \ mm$. The least count of the screw gauge is $LC = \frac{	ext{pitch}}{	ext{number of divisions}} = \frac{1 \ mm}{50} = 0.02 \ mm$. Thus,$\Delta D = 0.02 \ mm$.Percentage error = $\left( \frac{\Delta \ell}{\ell} + 2 \frac{\Delta D}{D} ight) 	imes 100\%$.Percentage error = $\left( \frac{1}{200} + 2 	imes \frac{0.02}{4} ight) 	imes 100\% = (0.005 + 0.01) 	imes 100\% = 0.015 	imes 100\% = 1.5\%$.

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