The spaceship Intergalactica lands on the surface of the uninhabited Pink Planet

Question

The spaceship Intergalactica lands on the surface of the uninhabited Pink Planet, which orbits a rather average star in the distant Garbanzo Galaxy. A scouting party sets out to explore. The party's leader-a physicist. naturally-immediately makes a determination of the acceleration due to gravity on the Pink Planet's surface by means of a simple pendulum of length 1.41 m. She sets the pendulum swinging and her collaborators carefully count 108 complete cycles or oscillation during 201 s. What is the result?

Explanation / Answer

Given,

L = 1.41 m ;

frequency is number of cycles per second, so

f = 108/201 = 0.537 Hz

We know that the time perios of simple pendulum is given by:

T = 2 pi sqrt(L/g)

T = 1/f

1/f = 2 pi sqrt (L/g)

1/0.537 = 2 x 3.14 sqrt(1.41/g)

squaring btoh sides:

3.47 = 39.44 x 1.41/g => g = 39.44 x 1.41/3.47 = 16.025 m/s^2

Hence, g = 16.03 m/s^2

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