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(B) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{l}{g}}$,where $l$ is the effective length.Taking the natural logarithm and

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$0.1$

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(B) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{l}{g}}$,where $l$ is the effective length.Taking the natural logarithm and differentiating,we get $\frac{dT}{T} = \frac{1}{2} \frac{dl}{l}$.Here,the effective length $l$ is the length of the string plus the radius of the bob. Thus,the change in effective length due to the change in radius is $dl = |r_1 - r_2|$.Given the relative difference in periods $\frac{\Delta T}{T} = 5 	imes 10^{-4}$ and the length $l = 1\, m$.Substituting these values into the relation $\frac{\Delta T}{T} = \frac{1}{2} \frac{\Delta l}{l}$:$5 	imes 10^{-4} = \frac{1}{2} 	imes \frac{|r_1 - r_2|}{1}$.$|r_1 - r_2| = 2 	imes 5 	imes 10^{-4} = 10 	imes 10^{-4} = 10^{-3}\, m$.Converting to centimeters: $10^{-3}\, m = 10^{-1}\, cm = 0.1\, cm$.

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