Students $I$, $II$ and $III$ perform an experiment for measuring the acceleration due to gravity $(g)$ using a simple pendulum.

They use different lengths of the pendulum and /or record time for different number of oscillations. The observations are shown in the table.

Least count for length $=0.1 \mathrm{~cm}$

Least count for time $=0.1 \mathrm{~s}$

Student Length of the pendulum $(cm)$ Number of oscillations $(n)$ Total time for $(n)$ oscillations $(s)$ Time period $(s)$
$I.$ $64.0$ $8$ $128.0$ $16.0$
$II.$ $64.0$ $4$ $64.0$ $16.0$
$III.$ $20.0$ $4$ $36.0$ $9.0$

If $\mathrm{E}_{\mathrm{I}}, \mathrm{E}_{\text {II }}$ and $\mathrm{E}_{\text {III }}$ are the percentage errors in g, i.e., $\left(\frac{\Delta \mathrm{g}}{\mathrm{g}} \times 100\right)$ for students $\mathrm{I}, \mathrm{II}$ and III, respectively,

  • [IIT 2008]
  • A

    $E_I=0$

  • B

    $E_I$ is minimum

  • C

    $\mathrm{E}_{\mathrm{I}}=\mathrm{E}_{\mathrm{II}}$

  • D

    $\mathrm{E}_{\text {II }}$ is maximum

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