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Physics-

General

Easy

Question

Student 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 cm.
Least count for time = 0.1 s.

If E_I,E_II and E_III are the percentage errors in g, $i e comma blank open parentheses fraction numerator increment g over denominator g end fraction cross times 100 close parentheses comma$ 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

Time period $T equals 2 pi square root of fraction numerator l over denominator g end fraction end root$
Or $fraction numerator t over denominator n end fraction equals 2 pi square root of fraction numerator l over denominator g end fraction end root$
$therefore blank g equals fraction numerator open parentheses 4 pi to the power of 2 end exponent close parentheses open parentheses n to the power of 2 end exponent close parentheses l over denominator t to the power of 2 end exponent end fraction$
$percent sign e r r o r blank i n blank g equals fraction numerator increment g over denominator g end fraction cross times 100 equals open parentheses fraction numerator increment l over denominator l end fraction plus fraction numerator 2 increment t over denominator t end fraction close parentheses cross times 100$
$E subscript I end subscript equals open parentheses fraction numerator 0.1 over denominator 64 end fraction plus fraction numerator 2 cross times 0.1 over denominator 128 end fraction close parentheses cross times 100 equals 0.3125 percent sign$
$E subscript I I end subscript equals open parentheses fraction numerator 0.1 over denominator 64 end fraction plus fraction numerator 2 cross times 0.1 over denominator 64 end fraction close parentheses cross times 100 equals 0.46875 percent sign$
$E subscript I I I end subscript equals open parentheses fraction numerator 0.1 over denominator 20 end fraction plus fraction numerator 2 cross times 0.1 over denominator 36 end fraction close parentheses cross times 100 equals 1.055 percent sign$
Hence, $E subscript I end subscript$ is minimum.

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