In an experiment,four quantities $p, q, r$,and $s$ are measured with percentage errors of $3 \%, 2 \%, 3 \%$,and $1 \%$ respectively. Quantity $A$ is calculated as follows: $A = \frac{pq^2}{r^2 s^4}$. The percentage error in $A$ is: (in $\%$)

What is error in measurement? What is mistake in measurement?

The relative error in the determination of the surface area of a sphere is $\alpha$. Then the relative error in the determination of its volume is

Three students $S_{1}, S_{2}$ and $S_{3}$ perform an experiment for determining the acceleration due to gravity $(g)$ using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.

Student No.	Length of pendulum $(cm)$	No. of oscillations $(n)$	Total time for oscillations $(s)$	Time period $(s)$
$1.$	$64.0$	$8$	$128.0$	$16.0$
$2.$	$64.0$	$4$	$64.0$	$16.0$
$3.$	$20.0$	$4$	$36.0$	$9.0$

(Least count of length $= 0.1 \, cm$,least count for time $= 0.1 \, s$)
If $E_{1}, E_{2}$ and $E_{3}$ are the percentage errors in $g$ for students $1, 2$ and $3$ respectively,then the minimum percentage error is obtained by student no. ....... .

Explain the statement: "The accuracy of a measurement cannot be determined by absolute error,but only by percentage error."

The period of oscillation of a simple pendulum is given by $T = 2\pi \sqrt{\frac{l}{g}}$,where $l$ is about $100 \, cm$ and is known to have $1 \, mm$ accuracy. The period is about $2 \, s$. The time of $100$ oscillations is measured by a stopwatch of least count $0.1 \, s$. The percentage error in $g$ is ......... $\%$