The period of oscillation of a simple pendulum is $T =2 \pi \sqrt{\frac{ L }{ g }} .$ Measured value of $ L $ is $1.0\, m$ from meter scale having a minimum division of $1 \,mm$ and time of one complete oscillation is $1.95\, s$ measured from stopwatch of $0.01 \,s$ resolution. The percentage error in the determination of $g$ will be ..... $\%.$

If $a, b, c$ are the percentage errors in the measurement of $A, B$ and $C$, then the percentage error in $ABC$ would be approximately

The radius ( $\mathrm{r})$, length $(l)$ and resistance $(\mathrm{R})$ of a metal wire was measured in the laboratory as

$\mathrm{r}=(0.35 \pm 0.05) \mathrm{cm}$

$\mathrm{R}=(100 \pm 10) \mathrm{ohm}$

$l=(15 \pm 0.2) \mathrm{cm}$

The percentage error in resistivity of the material of the wire is :

The initial and final temperatures of water as recorded by an observer are $(40.6 \pm 0.2)^{\circ} C$ and $(78.9 \pm 0.3)^{\circ} C .$ Calculate the rise in temperature with proper error limits.

A physical quantity $P$ is given as $P=\frac{a^2 b^3}{c \sqrt{d}}$ The percentage error in the measurement of $a, b, c$ and $d$ are $1 \%, 2 \%, 3 \%$ and $4 \%$ respectively. The percentage error in the measurement of quantity $P$ will be $.......\%$

 A certain body weighs $22.42\;g$ and has a measured volume of $4.7 \;cc .$ The possible error in the measurement of mass and volume are $0.01\; gm$ and $0.1 \;cc .$
Then maximum error in the density will be