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If the period of oscillation changes from 2 sec to 1.5 sec, and the length of simple pendulum is 1 m, then the change in length is

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Increased by $\frac{7}{16} m$

decreased by $\frac{7}{16} m$

Increased by $\frac{9}{16} m$

decreased by $\frac{9}{16} m$

answer is B.

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Detailed Solution

$\frac{T_{2}}{T_{1}} = \sqrt{\frac{l_{2}}{l_{1}}} \Rightarrow \frac{3 / 2}{2} = \sqrt{\frac{l + ∆ l}{l}} \Rightarrow ∆ l = \frac{- 7}{16}$

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