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

The maximum percentage errors in the measurement of mass (M), radius (R) and angular velocity $(\omega)$ of a ring are $2 \%, 1 \%$ and $1 \%$ respectively, then find the maximum percenta? error in the measurement of its moment of inertia $\left(I=\frac{1}{2} M R^{2}\right)$ about its geometric axis.

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

The energy of a system as a function of time $t$ is given as $E(t)=A^2 \exp (-\alpha t)$, where $\alpha=0.2 s ^{-1}$. The measurement of $A$ has an error of $1.25 \%$. If the error in the measurement of time is $1.50 \%$, the percentage error in the value of $E(t)$ at $t=5 s$ is

If a copper wire is stretched to make its radius decrease by $0.1\%$ , then percentage increase in resistance is approximately .......... $\%$

In an experiment, the following observation's were recorded : $L = 2.820\, m, M = 3.00 \,kg, l = 0.087 \,cm$, Diameter $D = 0.041 \,cm$ Taking $g = 9.81$ $m/{s^2}$ using the formula , $Y=\frac{{4MgL}}{{\pi {D^2}l}}$, the maximum permissible error in $Y$ is ......... $\%$