Question

on a hypothetical planet X with an unknown value for g, the period of a swinging pendulum with a string length of .75 meters is a 1.8 s calculate the value of "g" on plnaet X

Answer 1

The period of the pendulum is given as follows:

$$T = 2\pi \sqrt{\dfrac{L}{g}}$$

where $L = 0.75m$ is its length. Thus, expressing $g$ and substituting $T = 1.8s$, find:

$$g = \dfrac{4\pi^2L}{T^2} =\dfrac{4\pi^2\cdot 0.75m}{(1.8s)^2} \approx 9.1m/s^2$$

Answer. 9.1 m/s^2.