The length of a cylinder is measured with a metre rod having a least count of $0.1 \; cm$. Its diameter is measured with vernier calipers having a least count of $0.01 \; cm$. If the length and diameter of the cylinder are $5.0 \; cm$ and $2.00 \; cm$ respectively,then the percentage error in the calculated value of volume will be (in $\%$)

If the error in measuring the diameter of a circle is $4\%$,the error in the radius of the circle would be (in $\%$)

The percentage error in the measurement of $g$ is $.....\%$ (Given that $g = \frac{4 \pi^2 L}{T^2}$,$L = (10 \pm 0.1) \, cm$,$T = (100 \pm 1) \, s$)

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?

$A$ physical quantity $A$ is dependent on four other physical quantities $p, q, r,$ and $s$ as given by the relation $A = \frac{\sqrt{pq}}{r^2s^3}.$ If the percentage errors of measurement in $p, q, r,$ and $s$ are $1\%, 3\%, 0.5\%,$ and $0.33\%$ respectively,then the maximum percentage error in $A$ is .......... $\%$.

In an experiment to determine the acceleration due to gravity $g$,the formula used for the time period of a periodic motion is $T=2 \pi \sqrt{\frac{7(R-r)}{5 g}}$. The values of $R$ and $r$ are measured to be $(60 \pm 1) \text{ mm}$ and $(10 \pm 1) \text{ mm}$,respectively. In five successive measurements,the time period is found to be $0.52 \text{ s}, 0.56 \text{ s}, 0.57 \text{ s}, 0.54 \text{ s}$ and $0.59 \text{ s}$. The least count of the watch used for the measurement of time period is $0.01 \text{ s}$. Which of the following statement$(s)$ is(are) true?
$(A)$ The error in the measurement of $r$ is $10 \%$
$(B)$ The error in the measurement of $T$ is $3.57 \%$
$(C)$ The error in the measurement of $T$ is $2 \%$
$(D)$ The error in the determined value of $g$ is $11 \%$