# Pendulum on Earth and another planet different periods radii

• James Ray
In summary, the conversation discusses an error in a calculation regarding the radius, with the mistake being the lack of squaring the radius in the first calculation. The solution is eventually corrected, with the suggestion to derive the formula for R2 symbolically.
James Ray
Member advised to type out equations and not to use images only of handwritten scratchwork

James Ray said:

## Homework Statement

View attachment 100919

## The Attempt at a Solution

View attachment 100920
The radius seems very small (a factor of 10 less than Earth's radius. But I can't see any mistake in the solution.

Your result is wrong. You should use the template and type in your work.

ehild said:
Your result is wrong. You should use the template and type in your work.
I forgot to square the radius in the first calculation.

James Ray said:
I forgot to square the radius in the first calculation.
Now I get 11200 km.

It is all right now, but how did you get it? I see quite a lot of unnecessary calculations on your sheet of paper. It would be very easy if you derived the formula for R2 symbolically.

## 1. How does the period of a pendulum differ between Earth and another planet with a different radius?

The period of a pendulum is directly proportional to the square root of the length of the pendulum and inversely proportional to the square root of the acceleration due to gravity. Therefore, on a planet with a larger radius, the period of a pendulum would be longer due to a weaker gravitational pull.

## 2. Does the mass of the pendulum affect its period on different planets?

No, the mass of the pendulum does not affect its period on different planets. The period of a pendulum is only dependent on the length and acceleration due to gravity.

## 3. How do the different gravitational pulls on Earth and another planet affect the period of a pendulum?

The period of a pendulum is shorter on a planet with a stronger gravitational pull, such as Earth, compared to a planet with a weaker gravitational pull. This is because the acceleration due to gravity affects the swinging motion of the pendulum.

## 4. Can the length of a pendulum be changed to compensate for the difference in periods on different planets?

Yes, the length of a pendulum can be adjusted to compensate for the difference in periods on different planets. By increasing the length of the pendulum on a planet with a weaker gravitational pull, the period can be made longer to match the period on a planet with a stronger gravitational pull.

## 5. Is there a formula for calculating the period of a pendulum on different planets?

Yes, the formula for calculating the period of a pendulum is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. This formula can be used to calculate the period on different planets by using the appropriate values for length and acceleration due to gravity on that planet.

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