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 $11 \%$

• A
  $A, B, D$
• B
  $A, B, C$
• C
  $B, C$
• D
  $A, C$