$Assertion$: In the measurement of physical quantities direct and indirect methods are used.

$Reason$ : The accuracy and precision of measuring instruments along with errors in measurements should be taken into account, while expressing the result.

In the determination of Young's modulus $\left(Y=\frac{4 MLg }{\pi / d ^2}\right)$ by using Searle's method, a wire of length $L=2 \ m$ and diameter $d =0.5 \ mm$ is used. For a load $M =2.5 \ kg$, an extension $\ell=0.25 \ mm$ in the length of the wire is observed. Quantities $d$ and $\ell$ are measured using a screw gauge and a micrometer, respectively. They have the same pitch of $0.5 \ mm$. The number of divisions on their circular scale is $100$ . The contributions to the maximum probable error of the $Y$ measurement

If $Z=\frac{A^{2} B^{3}}{C^{4}}$, then the relative error in $Z$ will be

What is the fractional error in $g$ calculated from $T = 2\pi \sqrt {l/g} $ ? Given fraction errors in $T$ and $l$ are $ \pm x$ and $ \pm y$ respectively?

A metal wire has mass $(0.4 \pm 0.002)\,g$, radius $(0.3 \pm 0.001)\,mm$ and length $(5 \pm 0.02) \,cm$. The maximum possible percentage error in the measurement of density will nearly be $…….\%$