In an experiment to determine the period of a simple pendulum of… | JEE Main 2017 (9 Apr, Shift 1)

Q31JEE Main 2017 · 9 APR · SHIFT 1Medium

Wave Basics & Properties of Sound

In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r1 and r2. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5×10−4 s, the difference in radii, $\vert$ r1 $-$ r2 $\vert$ is best given by:

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Answer: (b)

Effective length $\approx L + r$ , so $T = 2\pi\sqrt{(L+r)/g}$ and $\dfrac{\Delta T}{T} = \dfrac{1}{2}\dfrac{\Delta r}{L}$ .
$\Delta r = 2L\dfrac{\Delta T}{T} = 2 \times 1 \times 5\times10^{-4} = 10^{-3}\ \text{m}$
So the answer is (b) $0.1\ \text{cm}$ .

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