In an experiment of a simple pendulum,the time period measured was $50 \, s$ for $25$ vibrations when the length of the simple pendulum was taken as $100 \, cm$. If the least count of the stopwatch is $0.1 \, s$ and that of the meter scale is $0.1 \, cm$,then the maximum possible error in the value of $g$ is .......... $\%$

$A$ physical quantity is $A = P^2/Q^3$. The percentage error in the measurement of $P$ and $Q$ is $x$ and $y$ respectively. The maximum percentage error in the measurement of $A$ is:

$A$ physical quantity $P$ is related to four observables $a, b, c$ and $d$ as $P = \frac{\sqrt{a b} \cdot d^\alpha}{\sqrt{c}}$ (where $\alpha$ is a constant). The percentage errors in $a, b, c$ and $d$ are $0.5 \%$ each. If the percentage error in $P$ is $2 \%$,then the value of $\alpha$ is:

$A$ physical quantity $p$ is described by the relation $p = a^{1/2} b^2 c^3 d^{-4}$. If the relative errors in the measurement of $a, b, c$ and $d$ are $2\%$,$1\%$,$3\%$ and $5\%$ respectively,then the relative error in $p$ will be ........... $\%$.

Find the relative error in $Z$,if $Z = \frac{A^{4} B^{1/3}}{C D^{3/2}}$.

The time period of a simple pendulum is given by $T = 2 \pi \sqrt{\frac{\ell}{g}}$. The measured value of the length of the pendulum is $10 \ cm$ known to a $1 \ mm$ accuracy. The time for $200$ oscillations of the pendulum is found to be $100 \ s$ using a clock of $1 \ s$ resolution. The percentage accuracy in the determination of $g$ using this pendulum is $x$. The value of $x$ to the nearest integer is ...........$\%$