Explain error of a sum or a difference.

Following observations were taken with a vernier callipers while measuring the length of a cylinder

$3.29 \,cm, 3.28\, cm, 3.29 \,cm, 3.31 \,cm,$ $ 3.28\, cm, 3.27 \,cm, 3.29 \,cm, 3.30\, cm$

Then find Absolute error in forth and eighth observation

Two resistances are given as $R _1=(10 \pm 0.5)\,\Omega$ and $R_2=(15 \pm 0.5)\, \Omega$. The percentage error in the measurement of equivalent resistance when they are connected in parallel is

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

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 $(60 \pm 1) \mathrm{mm}$ and $(10 \pm 1) \mathrm{mm}$, respectively. In five successive measurements, the time period is found to be $0.52 \mathrm{~s}, 0.56 \mathrm{~s}, 0.57 \mathrm{~s}, 0.54 \mathrm{~s}$ and $0.59 \mathrm{~s}$. The least count of the watch used for the measurement of time period is $0.01 \mathrm{~s}$. 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 $11 \%$