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In a simple pendulum, if the rate of change in the time period is equal to the rate of change in the length then the length of the pendulum is

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$\frac{π}{g}$

$π^{2} g$

$\frac{π^{2}}{g}$

$π g^{2}$

answer is B.

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Detailed Solution

$T = 2 π \sqrt{\frac{l}{g}}; \frac{d T}{d t} = \frac{2 π}{\sqrt{g}} \frac{1}{2} l^{- 1 / 2} \frac{d l}{d t} ∴ l = \frac{π^{2}}{g}$

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