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, \(\left| {{r_1} - {r_2}} \right|\) is best given by .... \(cm\)

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Verified Solution

Answer & Solution

Correct Answer

(B) \(0.1\)

Detailed explanation

As we know, Time-period of simple

pendulum, T \(\propto \sqrt{l}\)

\(5 \times {10^{ - 4}} = \frac{1}{2}\frac{{{r_1} - {r_2}}}{1}\)

\(\because\) change in length \(\Delta l=r_{1}-r_{2}\)

\(5 \times {10^{ - 4}} = \frac{1}{2}\frac{{{r_1} - {r_2}}}{1}\)

\(r_{1}-r_{2}=10 \times 10^{-4}\)

\(10^{-3} \mathrm{m}=10^{-1} \mathrm{cm}=0.1 \mathrm{cm}\)

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