Question

(i) A longer pendulum has a longer period than a shorter one?
(ii) The period is very nearly independent of amplitude, provided that the amplitude is small?

Answer 1

Use the expression of the period so that we can determine the correct answers because the terms and their relation with the period will give some idea about whether the period will get affected by the same factors or not.

Complete step by step answer:
(i) Pendulum is a simple mechanical arrangement that shows periodic motion. It consists of a particle-like bob which is suspended by a light string of length that is fixed at the upper end. The simple pendulum can be used as a timer, and some watches also are used for designing purposes. The expression of the period will tell about whether a longer pendulum has a longer period than a shorter one or not. So, the expression of the period of the pendulum is,
$T = 2\pi \sqrt {\dfrac{L}{g}}$
Here, is the length of the pendulum and $g$ is the acceleration due to gravity.
From the above expression, we can say that the period of the pendulum directly depends on the length of the pendulum. It means that if the length of the pendulum is more, then it will give a large period and if the length of the pendulum is small, then it will give a small period.
(ii) From the period expression, we know that the period of the pendulum only depends on the length of the pendulum and acceleration due to gravity. So for the small amplitude, the period of the pendulum is almost independent of amplitude. But if the magnitude of the amplitude is large, then the pendulum will cover the large distance and due to this reason, the period of the pendulum will increase.
Therefore, the pendulum of larger length will have a larger period. If the amplitude is very small, then the period is independent of amplitude, but there is no relation in these both phenomena and option (B) is correct.

Note: Remember that the acceleration due to the gravity of the falling object is independent of the mass. So, the period of the pendulum does not depend on the mass of the bob. It means that the pendulum with a heavy bob will swing at the same rate as a lighter one.