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 1.38 m. She sets the pendulum swinging, and her collaborators carefully count 1.00 × 102 complete cycles of oscillation during 212 s. What is the result?

Answer 1

Answer 2

SOLUTION :

In 212 seconds 102 cycles are completed.

So, time taken for 1 cycle = 212/102 sec.

This time is termed as Time period, T.

=> T = 212/102 sec

For pendulum of length L , 

T = 2 π sqrt(L/g) where g is gravitational acceleration at the Pink Planet.

=> 212/102 = 2 π sqrt (1.38 / g) 

=> sqrt(1.38 / g) = (212/102) / (2 π)

=> 1.38/g = ((212/102) / (2 π))^2 = 0.109424

=> g = acceleration due to gravity at Pink Planet :

= 1.38/0.109424 

= 12.61 m/s^2  (ANSWER)