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Physics-

General

Easy

Question

Students I, II and III perform an experiment for measuring the acceleration due to gravity $left parenthesis g right parenthesis$ 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 $equals 0.1 blank c m$
Least count for time $equals 0.1 blank s$

If $E subscript I end subscript comma blank E subscript I I end subscript$ and $E subscript I I I end subscript$ are the percentage errors in $g comma blank i. e. comma blank open parentheses fraction numerator increment g over denominator g end fraction cross times 100 close parentheses$ for students I, II and III, respectively

$E_{I} = 0$
$E_{I}$ is minimum
$E_{I} = E_{I I}$
$E_{I I}$ is maximum

The correct answer is: $E subscript I end subscript$ is minimum

$percent sign$ error in $g equals fraction numerator increment g over denominator g end fraction cross times 100 equals open parentheses fraction numerator increment l over denominator l end fraction close parentheses cross times 100 plus 2 open parentheses fraction numerator increment T over denominator T end fraction close parentheses cross times 100$
$E subscript I end subscript equals fraction numerator 0.1 over denominator 64 end fraction cross times 100 plus 2 open parentheses fraction numerator 0.1 over denominator 128 end fraction close parentheses cross times 100 equals 0.3125 percent sign$
$E subscript I I end subscript equals fraction numerator 0.1 over denominator 64 end fraction cross times 100 plus 2 open parentheses fraction numerator 0.1 over denominator 64 end fraction close parentheses cross times 100 equals 0.4687 percent sign$
$E subscript I I I end subscript equals fraction numerator 0.1 over denominator 20 end fraction cross times 100 plus 2 open parentheses fraction numerator 0.1 over denominator 36 end fraction close parentheses cross times 100 equals 1.055 percent sign$

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