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  4. 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, | r1 - r2| is best given by :

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Q. 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 $5 \times 10^{-4} s$, the difference in radii, $ | r_1 - r_2|$ is best given by :

JEE MainJEE Main 2017Physical World, Units and Measurements

Solution:

$T \propto \sqrt{l}\,\,\, l=1$
$\frac{\Delta T}{l}=\frac{1}{2} \frac{\Delta l}{l}\,\,\, \Delta l=r_{1}-r_{2}$
$5\times10^{-4}=\frac{1}{2} \frac{r_{1}-r_{2}}{1}$
$r_{1}-r_{2}=10\times10^{-4}$
$10^{-3} \,m=10^{-1}\,cm-0.1\,cm$