Simple pendulum: A frictionless pendulum clock on the surface of the earth has a period of 1.00 s. On a distant planet, the length of the pendulum must be shortened slightly to have a period of 1.00 s. What is true about the acceleration due to gravity on the distant planet?
A) The gravitational acceleration on the planet is slightly greater than g.
B) The gravitational acceleration on the planet is slightly less than g.
C) The gravitational acceleration on the planet is equal to g.
D) We cannot tell because we do not know the mass of the pendulum.

Question

Quizplus · Accepted Answer

The period of a simple pendulum is given by T=2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. If the period is the same but the length of the pendulum is shorter, then g must be smaller. Therefore, the gravitational acceleration on the distant planet is slightly less than g.

Simple Pendulum: a Frictionless Pendulum Clock on the Surface of the Earth