Calculating Acceleration on Planet X Using Pendulum Period Measurements

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To calculate the acceleration due to gravity on Planet X using pendulum period measurements, the periods on Earth and Planet X are given as 1.4s and 2.25s, respectively. The pendulum length can be derived from the period formula, resulting in lengths of approximately 0.487m on Earth and 1.257m on Planet X. The challenge lies in determining the acceleration due to gravity on Planet X without knowing the mass or using kinematic equations. The relationship between the periods and gravitational acceleration can be established, leading to two equations with two unknowns. Ultimately, the solution can be derived by manipulating the equations to isolate and solve for the gravitational acceleration on Planet X.
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Homework Statement


A pendulum (on earth) has a length of l and a mass of M and a period 1.4s. The pendulum is taken to planet X where the period is measured to be 2.25s. What is the acceleration due to gravity on planet X?


Homework Equations


So, t1 = 1.4s and t2 = 2.25s

I solved each of them for length t = 2pi * sqrt(L/g)
L1: .487m
L2: 1.257m

The Attempt at a Solution



The problem is that the velocity, the mass isn't given in the problem, so I am stuck on how to solve for acceleration. I don't think using kinematics would work, but any help would be appreciated.
 
Physics news on Phys.org
What is known? t1 and t2, and actually, g1 (being 'g' on earth).

Two equations, two unknowns (g2 and L), and you don't even strictly care what L is...
 

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