After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 49.0 cm. The explorer finds that the pendulum completes 109 full swing cycles in a time of 144 s. What is the value of the acceleration of gravity on this planet?

The frequency refers to the number of cycles per time lapse, while the period is the inverse of the frequency, therefore we would have this expression,

Here,

N = Number of Cycles

t = Time

While at the same time Period is the inverse of the frequency, then

Replacing,

Replacing we have that

Gravity is one of the components that define the Period of a pendulum as well as its length, mathematically this expression is given as,

Replacing,

Therefore the acceleration due to gravity of the planet is

this is poiselle's equation from fluid mechanic in physics. mech eng