Question

During the oscillations of a simple pendulum, the string takes the same path as that of bob, then:
A. Motion of the bob and string are in SHM.
B. Motion of the bob is SHM and that of the string is angular SHM.
C. Motion of the bob and string are angular SHM.
D. None of the above.

Answer 1

In order to solve this question we should know about what a simple pendulum is. A simple pendulum consists of an inextensible string and at one end of the string a small mass bob is attached to it and the other end of string gets fixed at some point vertically, and the string with bob is free to rotate if force is applied on the bob. Here, we will discuss SHM and angular SHM and then figure out which motion is governed by a bob and the string of a simple pendulum.

Complete answer:
When a body moves back and forth, up and down, to and fro about its means position to two of its extreme position and repeat same motion with a fixed time period is known as simple harmonic motion.

When a force is applied on the bob of a simple pendulum it starts to move from its mean position to its extreme position on either side and continues to do so freely, hence the motion governed by bob is Simple harmonic motion or written as SHM.

When a body performs simple harmonic motion but its displacement is angular which means it covers some angle through its mean position is known as angular SHM.So, the string of a simple pendulum also moves with bob in Simple harmonic motion but as string is fixed at its other end so it covers angular displacement about that point, hence motion governed by string is angular SHM.

Hence, the correct option is B.

Note: It should be remembered that, bob is attached to the string but it’s not fixed at any point rather it moves freely and covers linear displacements that’s why its motion is not angular and additionally the time period of simple pendulum is depends upon L length of string and g acceleration due to gravity calculated as $T = 2\pi \sqrt {\dfrac{L}{g}.}$