A simple pendulum is executing simple harmonic motion with a time period $T$. If the length of the pendulum is increased by $21\%$, the percentage increase in the time period of the pendulum of increased length is ..... $\%$
AIEEE 2003,AIIMS 2001, Medium
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(a) If initial length ${l_1} = 100$ then ${l_2} = 121$
By using $T = 2\pi \sqrt {\frac{l}{g}} $
$\Rightarrow \frac{{{T_1}}}{{{T_2}}} = \sqrt {\frac{{{l_1}}}{{{l_2}}}} $
Hence, $\frac{{{T_1}}}{{{T_2}}} = \sqrt {\frac{{100}}{{121}}} $
$\Rightarrow {T_2} = 1.1\,{T_1}$
$\%$ increase = $\frac{{{T_2} - {T_1}}}{{{T_1}}} \times 100 = 10\,\% $
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