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 1.04 m. She sets the pendulum swinging, and her collaborators carefully count 1.10 × 102 complete cycles of oscillation during 214 s. What is the result?

Explanation / Answer

time period of pendulam = T = 2pi*sqrt(L/g)

frequency = f = 1/T

here given pendulum is completing 1.10 x 10^2 cycle in 214 s

f = 1.10 x 10^2 / 214 = 110/214

T = 214/110

T = 2pi*sqrt(L/g) squaring both side

g = 4*pi^2 * L/T^2

g = 10.848 m/s^2

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