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 $\%$)

If the length of a cylinder is $l = (4.00 \pm 0.01) \; cm$,radius $r = (0.250 \pm 0.001) \; cm$,and mass $m = 6.25 \pm 0.01 \; g$,calculate the percentage error in the determination of density.

In an experiment to find acceleration due to gravity $(g)$ using a simple pendulum,the time period of $0.5 \ s$ is measured from the time of $100$ oscillations with a watch of $1 \ s$ resolution. If the measured value of length is $10 \ cm$ known to $1 \ mm$ accuracy,the accuracy in the determination of $g$ is found to be $x \%$. The value of $x$ is:

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

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

Time for $20$ oscillations of a pendulum is measured as $t_1 = 39.6\, s$,$t_2 = 39.9\, s$,and $t_3 = 39.5\, s$. What is the precision in the measurements? What is the accuracy of the measurement?