Student `I ,II , and III` perform an experiment for measuring the acceleration due to gravity `(g) ` usinf a simple pendulum. They use lengths of the pendulum and // or record time for different number of oscillations . The observations are shown in the following table . Least count for length ` = 0.1 cm`
`{:(underset(III)underset(II)underset(I)underset()underset()("Student"),underset(20.0)underset(64.0)underset(64.0)underset((cm))underset("Pendulam")("Length of "),underset(4)underset(4)underset(8)underset((n))underset("n Oscillation")("Number of"),underset(9.0)underset(16.0)underset(16.0)underset((s))underset("Period")("Time")):}`
Least count for time `= 0.1 s`.
If `E_(I), E_(II)` , and `E_(III)` are the percentage errors in `g` , i.,e., `((Delta g)/( g) xx 100)` for students I,II , and III, respectively , then

Options

A. `E_(I) = 0`
B. ` E_(I) is minimum`
C. `E_(I) = E_(II)`
D. `E_(II) is maximum`

Answer

B

Explanation

` g = 4 pi^(2) ((l)/( T^(2))) rArr ( Delta g)/(g) = ( Delta l)/( l) + 2( Delta T)/(T)`
`rArr E = ((Delta l)/(l) + 2 ( Delta T)/( T)) xx 100`
The greatest the volume of `T` , the lesser the error . Hence , fractional error in the first observation in minimum.