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  4. Time period of a simple pendulum is T. If its length increases by 2 %, the new time period becomes

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Q. Time period of a simple pendulum is $T$. If its length increases by $2\%$, the new time period becomes

Oscillations

Solution:

$ \, \, \, \, \, \, \, \, \, \, T \propto l^{1/2} $
$\Rightarrow \, \, \, \, \, \, \, \, \frac{\Delta T}{T}=\frac{1}{2} \bigg(\frac{\Delta l}{l}\bigg)$
$ \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \frac{\Delta T}{T}=\frac{1}{2}(2\%) =1\%$
$\Rightarrow \, \, \, \, \, \, \, \, \frac{T; -T}{T} =\frac{1}{100}$
$\Rightarrow \, \, \, \, \, \, \, \, \, T' =T+0.01 T$
$\Rightarrow \, \, \, \, \, \, \, \, \, T' =1.01 T$