Question

question 1

(a) Calculate the length of a pendulum which will have a period of one second, correct to three significant figures.

(3 marks)

(b) If this pendulum is transported to the moon, where the acceleration due to gravity is 1.62 m s–2, what will be its period on the moon?

Answer 1

(a) By the definition of the period of the pendulum, we have:

$$T=2\pi\sqrt{\dfrac{L}{g}},$$ $$L=\dfrac{T^2g}{4\pi^2}=\dfrac{(1.0\ s)^2\cdot 9.8\ \dfrac{m}{s^2}}{4\pi^2}=0.248\ m.$$

(b)

$$T=2\pi\sqrt{\dfrac{0.248\ m}{1.62\ \dfrac{m}{s^2}}}=2.46\ s.$$