Suppose that you are on an unknown planet in a distant galaxy. Let the length of a physical pendulum be 1.02 m. In the physical pendulum experiment, the period is determined to be 0.25 s.
What is the gravitational acceleration of this planet?

acceleration due gravity = 619.5 m/s²

Explanation: The relationship between the period of a pendulum, length and acceleration due to gravity is given as

T =2π * (√l/g)

T = period = 0.25s

l = length of pendulum = 1.02m

g = acceleration due to gravity on the unknown planet

0.25 = 2π * (√1.02/g)

By squaring both sides, we have that

0.25² = 4π² * (1.02/g)

0.25² * g = 4π² * 1.02

g = 4π² * 1.02/ 0.25²

g = 40.26756/ 0.0625

g = 619.5m/s²

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