Question

Astronauts on a distant planet set up a simple pendulum of length 1.20 m. The pendulum executes simple harmonic motion and makes 100 complete oscillations in 450 s. What is the magnitude of the acceleration due to gravity on this planet?

Answer 1

Answer:

Magnitude of the acceleration due to gravity on the planet = 2.34 m/s²

Explanation:

Time period of simple pendulum is given by

         $T=2\pi\sqrt{\frac{l}{g}}$, l is the length of pendulum, g is acceleration due to gravity value.

We can solve acceleration due to gravity as

            $g=\frac{4\pi^2l}{T^2}$

Here

  Length of pendulum = 1.20 m

  Pendulum executes simple harmonic motion and makes 100 complete oscillations in 450 s.

  Period, $T=\frac{450}{100}=4.5s$

Substituting

         $g=\frac{4\pi^2\times 1.2}{4.5^2}=2.34m/s^2$

Magnitude of the acceleration due to gravity on the planet = 2.34 m/s²