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 = $\sqrt{2}$ L, mass =
$\sqrt{2}$ M, and maximum angular displacement =
$\sqrt{2}$ degrees
E)length = $\sqrt{3}$ L, mass = 4M, and maximum angular displacement = 4 degrees

Question

Quizplus · Accepted Answer

Period of a 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. Therefore, increasing the length of the pendulum will increase its period. This means that choice A and C are not the best choices since their lengths are not the longest. In choice D, although the length and mass are very large, the maximum angular displacement is not given, so we cannot determine the period. Choice E increases the mass but does not increase the length, so it is not the best choice either. Therefore, choice B is the best choice as it increases the length to 2L and decreases the mass to M/2, which will result in the greatest period.

Which of the Following Combinations of Variables Results in the Greatest