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 1.42 m. She sets the pendulum swinging, and her collaborators carefully count 105 complete cycles of oscillation during 216 s. What is the result?

Explanation / Answer

given :

L=1.42m

t=216s,

complete cycles =105

so, time period is T=216/105 =2.05

Period T of pendulum is related to its length L and local gravitational acceleration g by

T = 2(L/g)

g = 4^2L/T^2
g=(4*3.14*3.14*1.42)/(2.05*2.05)

g=13.33 m/s^2

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