Which of the following combinations of variables results in the greatest period for a pendulum?
A) length = L, mass = M, and maximum angular displacement = 3 degrees
B) length = 2L, mass = M/2, and maximum angular displacement = 1 degree
C) length = 1.5L, mass = 2M, and maximum angular displacement = 2 degrees
D) length = L, mass = M, and maximum angular displacement = degrees
E) length = L, mass = 4M, and maximum angular displacement = 4 degrees

Question

Which of the following combinations of variables results in the greatest period for a pendulum?
A) length = L, mass = M, and maximum angular displacement = 3 degrees 
B) length = 2L, mass = M/2, and maximum angular displacement = 1 degree 
C) length = 1.5L, mass = 2M, and maximum angular displacement = 2 degrees 
D) length = L, mass = M, and maximum angular displacement = degrees 
E) length = L, mass = 4M, and maximum angular displacement = 4 degrees

Quizplus · Accepted Answer

The period of a pendulum is given by T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. Therefore, to increase the period, we want to increase the length and/or decrease the value of g. Option B has the longest length (2L), and since the mass is halved, g is also halved (since g = GM/R^2). Therefore, option B results in the greatest period.

Which of the Following Combinations of Variables Results in the Greatest