A simple pendulum has a period T on Earth. If it were used on Planet X, where the acceleration due to gravity is 3 times what it is on Earth, what would its period be?
A) 3T
B) $\sqrt { 3 }$ T
C) T
D) T/ $\sqrt { 3 }$
E) T/3

Question

Quizplus · Accepted Answer

The period T of a simple pendulum is given by the formula T=2π√(l/g), where l is the length of the pendulum and g is the acceleration due to gravity. Since the acceleration due to gravity on Planet X is 3 times what it is on Earth, gX=3gEarth. Substituting this into the formula for T, we get T=2π√(l/gX)=2π√(l/3gEarth)=2π√(1/3)√(l/gEarth)=T/$\sqrt { 3 }$. Therefore, the period of the pendulum on Planet X is T/$\sqrt { 3 }$.

A Simple Pendulum Has a Period T on Earth 3\sqrt { 3 }3​

A Simple Pendulum Has a Period T on Earth $\sqrt { 3 }$