Question

A pendulum clock on the surface of the earth has a period of 1.00 s. On a distant planet, the length of the pendulum must be elongated by 2 cm to have a period of 1.00 s. What is true about the acceleration of gravity on the distant planet, if you compare it to “g” = 9.81 m/s2 on Earth? Motivate & illustrate your answer with explanations and calculations.

Answer 1

$$T=2\pi\sqrt{\frac{l}{g}}\\1=2\pi\sqrt{\frac{l}{9.8}}\\l=0.248\ m\\1=2\pi\sqrt{\frac{0.248+0.02}{g'}}\\l=0.248\ m\\g'=10.6\frac{m}{s^2}$$