Question

An 80cm simple pendulum makes 28 complete swings in 45 seconds on an unknown planet. What is the gravitational acceleration of the planet?

Answer 1

Let's first find the period of the pendulum:

$$T=\dfrac{45\ s}{28\ swings}=1.61\ s.$$

Finally, we can find the gravitational acceleration of the planet:

$$T=2\pi\sqrt{\dfrac{L}{g}},$$ $$T^2=4\pi^2\dfrac{L}{g},$$ $$g=\dfrac{4\pi^2L}{T^2}=\dfrac{4\pi^2\times0.8\ m}{(1.61\ s)^2}=12.2\ \dfrac{m}{s^2}.$$