Question

After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 55.0 cm . She finds that the pendulum makes 100 complete swings in a time of 130 s . What is the value of g on this planet?

Answer 1

Explanation:

Given:

l = 55.0 cm = 0.550 m

T = (130 s)/100 = 1.30 s

g = ?

The period of a pendulum is given by

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

Solving for T, we get

$\dfrac{T^2}{4 \pi^2}=\dfrac{l}{g}$

Solving for g, we get

$g=\dfrac{4 \pi^2l}{T^2}=\dfrac{4 \pi^2(0.550 m)}{(1.30\:s)^2}=12.8\:\dfrac{m}{s^2}$