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
$1$
$2$
$3$
$4$
In the expression for time period $T$ of simple pendulum $T=2 \pi \sqrt{\frac{l}{g}}$, if the percentage error in time period $T$ and length $l$ are $2 \%$ and $2 \%$ respectively then percentage error in acceleration due to gravity $g$ is equal to ......... $\%$
The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is $\left(\frac{x}{100}\right) \% .$ If the relative errors in measuring the mass and the diameter are $6.0 \%$ and $1.5 \%$ respectively, the value of $x$ is
The radius of a sphere is $(5.3 \pm 0.1) \,cm$. The percentage error in its volume is
The length and width of a rectangular room are measured to be $3.95 \pm 0.05 \,m$ and $3.05 \pm 0.05 \,m$, respectively. The area of the floor is .................... $m^2$
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.