A simple pendulum is being used to determine the value of gravitational acceleration $\mathrm{g}$ at a certain place. The length of the pendulum is $25.0\; \mathrm{cm}$ and a stop watch with $1\; \mathrm{s}$ resolution measures the time taken for $40$ oscillations to be $50\; s$. The accuracy in $g$ is  ....... $\%$

The random error in the arithmetic mean of $100$ observations is $x$; then random error in the arithmetic mean of $400$ observations would be

Write a note on combination of error.

The resistance $R=V / I$ where $V=(100 \pm 5)\;V$ and $I=(10 \pm 0.2) \;A$. Find the percentage error in $R .$

In an experiment of determine the Young's modulus of wire of a length exactly $1\; m$, the extension in the length of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.02\,mm$ when a load of $1\,kg$ is applied. The diameter of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.01\,mm$. The error in the measurement of Young's modulus $(\Delta Y)$ is found to be $x \times 10^{10}\,Nm ^{-2}$. The value of $x$ is

$\left[\right.$ Take $\left.g =10\,m / s ^{2}\right]$

A student measures the time period of $100$ oscillations of a simple pendulum four times. The data set is  $90\;s$ ,$91\;s $, $95\;s$ and $92\;s$. If the minimum division in the  measuring clock is $1\;s$, then the reported mean time should be