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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 0.750 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 0.750 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)?

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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 another planet with 0.750 times the mass of Earth and the same radius, the acceleration due to gravity would be 0.750 times that of Earth, or 0.750 * 9.81 m/s² = 7.3575 m/s².

Substituting these values into the formula for the period of a pendulum, we get:

Tplanet = 2π√(L/7.3575) 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 equation for Tplanet by the equation for TEarth:

Tplanet / TEarth = √(9.81/7.3575)

Calculating the square root of (9.81/7.3575) gives approximately 1.14.

Therefore, the period of the pendulum on the planet is approximately 1.14 times its period on Earth.

This problem has been solved

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