Answer:
1.625 m/s²
Explanation:
The acceleration due to gravity gotten from the period of the simple pendulum using the formula:
[tex]T=2\pi \sqrt{\frac{L}{g} }\\ \\where\ T=period,L=length\ of \ pendulum,g=acceleration\ due\ to\ gravity.\\\\For \ earth, g=9.8\ m/s^2.Given\ that\ period(T)=9\ seconds\ we\ can\ find\ L:\\\\T=2\pi \sqrt{\frac{L}{g} }\\\\squaring\ both\ sides:\\\\T^2=4\pi^2(\frac{L}{g} )\\\\L=\frac{T^2g}{4\pi^2} \\\\Substituting\ gives:\\\\L=\frac{9^2*9.8}{4\pi^2} =20.1\ m\\\\The\ same\ pendulum\ is\ used \ in \ moon\ and \ gives\ a\ period\ of\ 22.1\ seconds. \\[/tex]
[tex]We\ can\ get\ the\ acceleration\ due\ to\ gravity\ on\ the\ moon\ using:\\\\T=2\pi \sqrt{ \frac{L}{g}}\\ \\T^2=4\pi^2 (\frac{L}{g} )\\\\g=\frac{4\pi^2 L}{T^2}\\ \\g=\frac{4\pi^2 *20.1}{22.1^2}\\\\g=1.625\ m/s^2[/tex]
