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 pendulum is given by T=2π(L/g)^0.5, where L is the length of the pendulum and g is the acceleration due to gravity. As the period on the distant planet is the same as on Earth, the length must decrease, which means g must also decrease (since L and T are both decreasing). Therefore, the gravitational acceleration on the planet is slightly less than g.

A Frictionless Pendulum Clock on the Surface of the Earth