A body of mass $(5 \pm 0.5) kg$ is moving with a velocity of $(20 \pm 0.4) m / s$. Its kinetic energy will be

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

The values of a number of quantities are used in a mathematical formula. The quantity that should be most precise and accurate in measurement is the one

If there is a positive error of $50\%$ in the measurement of velocity of a body, then the error in the measurement of kinetic energy is .............. $\%$

In an experiment of determine the Young's modulus of wire of a length exactly $1\; m$, the extension in the length of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.02\,mm$ when a load of $1\,kg$ is applied. The diameter of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.01\,mm$. The error in the measurement of Young's modulus $(\Delta Y)$ is found to be $x \times 10^{10}\,Nm ^{-2}$. The value of $x$ is

$\left[\right.$ Take $\left.g =10\,m / s ^{2}\right]$