At sea level,at a latitude where $g = 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } }$ ,a pendulum that takes 2.00 s for a complete swing back and forth has a length of 0.993 m.What is the value of g in m/s² at a location where the length of such a pendulum is 0.970 m? A)0.098 3 B)3.05 C)9.57 D)10.0 E)38.3

Question

Quizplus · Accepted Answer

The period of a pendulum is given by $ T = 2\pi \sqrt{\frac{L}{g}} $. Solving for $ g $ gives $ g = \frac{4\pi^2L}{T^2} $. At the new location, $ g = \frac{4\pi^2 \times 0.970}{2^2} \approx 9.57 \, \text{m/s}^2 $.

At Sea Level,at a Latitude Where g=9.80ms2g = 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } }g=9.80s2m​

At Sea Level,at a Latitude Where $g = 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } }$