A student performs an experiment for determination of $g \left(=\frac{4 \pi^{2} l }{ T ^{2}}\right), \ell =1 m$ and he commits an error of $\Delta \ell$. For $T$ he takes the time of $n$ oscillations with the stop watch of least count $\Delta T$ and he commits a human error of $0.1 s$ For which of the following data, the measurement of $g$ will be most accurate?
$\Delta \ell = 5\,mm, \, \Delta T = 0.2s, n = 10$
$\Delta \ell= 5mm, \Delta T = 0.2s, n = 20$
$\Delta \ell = 5mm, \Delta T = 0.1s, n = 10$
$\Delta \ell = 1mm , \Delta T = 0.1s, n = 50$
Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are $3\%$ each, then error in the value of resistance of the wire is ........ $\%$
What is accuracy in measurement ? Accuracy depend on which factors ?
The percentage error in measurement of a physical quantity $m$ given by $m = \pi \tan \theta $ is minimum when $\theta $ $=$ .......... $^o$ (Assume that error in $\theta $ remain constant)
If $x=10.0 \pm 0.1$ and $y=10.0 \pm 0.1$, then $2 x-2 y$ is equal to
$Assertion$ : When percentage errors in the measurement of mass and velocity are $1\%$ and $2\%$ respectively, the percentage error in $K.E.$ is $5\%$.
$Reason$ : $\frac{{\Delta E}}{E} = \frac{{\Delta m}}{m} + \frac{{2\Delta v}}{v}$