JEE Main 2017 · 9 Apr · Shift 1 · Physics Q30

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In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii $r_1$ and $r_2$ . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be $5\times10^{-4}$ s, the difference in radii, $|r_1-r_2|$ is best given by :

1 cm

0.1 cm

0.5 cm

0.01 cm

Answer and worked solution

Official answer: B

The effective length is $L+r$ , and $T\propto\sqrt{L+r}$ , so $\dfrac{\Delta T}T=\dfrac{\Delta r}{2L}$ . Reading the relative difference as $5\times10^{-4}$ :
$|r_1-r_2|=2\times1\times5\times10^{-4}\text{ m}=0.1\text{ cm}.$

Topics:Simple pendulum experiment Simple and compound pendulum

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JEE Main 2017 · 9 Apr · Shift 1, Physics question 30