A simple pendulum has a time period of 2 s. It is called a second pendulum. Find the length of a second pendulum on Earth and on the Moon. (Given: )

Length of a second pendulum on Earth and the Moon:

The time period of a simple pendulum is given by the formula:

T=2π√L/g

Where:

  • is the time period,
  • is the length of the pendulum,
  • is the acceleration due to gravity.

We are given that for a second pendulum.

On Earth:

Acceleration due to gravity on Earth, gEarth=9.8 m/s2

Rearranging the formula to find the length :

L=gT2/4π2L

Substitute the given values:

L=9.8×22/4π2L  

On the Moon:

Gravitational acceleration on the Moon is gMoon≈1/6 g Earth

gMoon=9.8/6≈1.63 m/s2

Using the same formula to find L:

LMoon=gMoonT2/4π2L

LMoon=1.63×22/4π2L

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