Question

The length of a simple pendulum is increased by 1%. Its time period will ______ by ______ .

Answer 1

Dear Student,
Time period of a simple pendulum is given by:
$$\begin{gathered} T=2\pi \sqrt{\frac{L}{g}},where,L=lengthofthependulum \\ So, \\ T\propto \sqrt{L} \\ \frac{T_2}{T_1}=\sqrt{\frac{L_2}{L_1}}=\sqrt{\frac{1.01L}{L}}=\sqrt{1.01}=1.005 \\ \therefore T_2=1.005T_1 \\ Timeperiodincreasesby0.5\% \end{gathered}$$
Regards