The relative error in the determination of the surface area of a sphere is $\alpha$. Then the relative error in the determination of its volume is

The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length $l$ and diameter $d$. The measured values of $m, l$ and $d$ are $97.42 \pm 0.02 \text{ g}$, $8.35 \pm 0.05 \text{ mm}$ and $20.20 \pm 0.02 \text{ mm}$, respectively. The calculated percentage fractional error in $\rho$ is . . . . . . . (in $\%$)

In an experiment of a simple pendulum, the errors in the measurement of the length of the pendulum $(L)$ and time period $(T)$ are $3 \%$ and $2 \%$, respectively. The maximum percentage error in the value of $\frac{L}{T^2}$ is (in $\%$):

In a simple pendulum experiment for determination of acceleration due to gravity $(g)$, time taken for $20$ oscillations is measured by using a watch of $1\,s$ least count. The mean value of time taken comes out to be $30\,s$. The length of the pendulum is measured by using a meter scale of least count $1\,mm$ and the value obtained is $55.0\,cm$. The percentage error in the determination of $g$ is close to ........... $\%$

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 .............. $\%$