A simple pendulum, with a fixed length and fixed mass at the end of the string, is set in motion on a planet that is 2.750 times the mass of the Earth and the same radius as that of the Earth. The period of this pendulum is what factor times its period on Earth (Tplanet = ____· T Earth)?
Question
A simple pendulum, with a fixed length and fixed mass at the end of the string, is set in motion on a planet that is 2.750 times the mass of the Earth and the same radius as that of the Earth. The period of this pendulum is what factor times its period on Earth (Tplanet = ____· T Earth)?
Solution
The period of a simple pendulum is given by the formula T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.
On Earth, the acceleration due to gravity is approximately 9.81 m/s². On a planet that is 2.750 times the mass of the Earth but the same radius, the acceleration due to gravity would be 2.750 times that on Earth, or approximately 26.98 m/s².
Substituting these values into the formula for the period of a pendulum, we find that the period on the planet would be Tplanet = 2π√(L/26.98) and the period on Earth would be Tearth = 2π√(L/9.81).
To find the factor by which the period on the planet is longer than the period on Earth, we divide the period on the planet by the period on Earth:
Tplanet / Tearth = √(9.81/26.98) = 0.604
Therefore, the period of the pendulum on the planet is 0.604 times its period on Earth.
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