The period of a simple pendulum is 1 s on Earth. When brought to a planet where g is one-tenth that on Earth, its period becomes:
A) 1 s
C) 1/10 s
E) 10 s

Question

The period of a simple pendulum is 1 s on Earth. When brought to a planet where g is one-tenth that on Earth, its period becomes:
A) 1 s 
C) 1/10 s 
E) 10 s

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. We are given that T=1 s and g=10gE, where gE is the acceleration due to gravity on Earth. Let T' be the period on the new planet. Then using the same formula, we have T' = 2π√(L/(1/10 gE)) = 2π√(10L/gE). Dividing T' by T, we get: T'/T = 2π√(10L/gE) / 2π√(L/gE) = √10. Therefore, T' = √10 T = √10 s ≈ 3.16 s, which corresponds to answer choice D.

The Period of a Simple Pendulum Is 1 S on Earth