Mathematics

Problem

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.

Student	Length of the pendulum (cm)	No. 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

E_I

E_{II}

and

E_{III}

are the percentage errors in

g

, i.e.,

\left(\frac{\Delta g}{g} \times 100\right)

for students I, II and III, respectively, then a.

E_I = 0

E_I

is minimum c.

E_I = E_{II}

E_{II}

is maximum

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