Answer:
The magnitude of the gravitational acceleration on this planet is 14.54 m/s².
Explanation:
given information:
pendulum length, L = 55 cm = 0.55 m
total swing, n = 108
time, t = 132 s
to calculate the gravitational acceleration of the planet, we can use the simple pendulum formula
T = 2π√(L/g)
where
T = period (s)
L = the length of pendulum (m)
g = gravitational force (m/s²)
thus,
T² = (2π)²(L/g)
g = (2π)²(L/T²)
we know that
T = t/n
so,
g = (2π)²(L/T²)
= (2π)²[L/(t/n)²]
= (2π)²[L (n/t)²]
= (2π)² [0.55 (108/132)²]
= 14.54 m/s²
