Simple Harmonic Motion - Multiple Choice Questions

Q10. The time period of a pendulum on Earth is 1.0 s. What would be the period of a pendulum of the same length on a planet with half the density but twice the radius of Earth?

A 0.5 s
B 1.0 s
C 1.4 s
D 2.0 s

Mass Effect

Assume planet is a sphere - volume would be 8x that of earth (cubed relationship) if radius was twice as great.

density = mass/volume therefore mass depends on the product of density and volume.

volume increases mass by a factor of eightbut density decreases it by a factor of 2. Therefore the overall effect is that mass of the planet is four times that of Earth.

- 4 g

Radius effect

g has a inverse square relationship with radius, so doubling the radius will

decrease g by a factor of 4

Overall effect

Planet will havethe same g as Earth

T will be the same 1.0 s