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, the period is directly proportional to the square root of L.

Option B has a length of 2L, which means it will have a greater period than option A (length = L) or option C (length = 1.5L).

Option B also has a mass of M/2, which will not affect the period as it is not included in the formula for the period. Similarly, the maximum angular displacement does not affect the period.

Option D and E have excessively high values for the length, mass, and maximum angular displacement, which will not result in a greater period but will instead cause the pendulum to behave in unpredictable ways. Therefore, option B is the best choice.

Which of the Following Combinations of Variables Results in the Greatest