$A$ physical quantity $P$ is given as $P = \frac{a^2 b^3}{c \sqrt{d}}$. The percentage errors 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 $.......\%$.

The error in the measurement of the radius of a sphere is $1\%$. The error in the calculated value of its volume is ......... $\%$

Error in the measurement of radius of the sphere is $2 \%$. The error in the calculated value of its volume is (in $\%$)

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 uncertainty or error in a given measurement with a suitable example.

To find the spring constant $(k)$ of a spring experimentally,a student commits $2 \%$ positive error in the measurement of time and $1 \%$ negative error in the measurement of mass. The percentage error in determining the value of $k$ is (in $\%$)