Question

What is the Centre of gravity of a Compound Pendulum?

Answer 1

Hint:A rigid body capable of oscillating about a horizontal axis passing through the pendulum is called a compound pendulum. When the pendulum rotates about a fixed point in a compound pendulum, the distance between the center of gravity of the swinging body and the suspension axis is similar to the dimensions of the body. Hence we can find the acceleration due to gravity.


 Complete step by step solution:
A simple pendulum has a small bob linked to the end of the string. In a simple pendulum, the length of the string is large compared to the measurements of the bob. In this type of condition, the mass of the bob is concentrated at the center of gravity. When the dimension of the bob is not negligible compared to the distance from the axis of suspension to the center of gravity, then the pendulum is called the compound pendulum. Every object falls freely when dropped, with the uniform acceleration, if the opposition due to air is negligible. The gravitational attraction of a body towards the center of the earth results in the same acceleration for all bodies at a particular location, regardless of their mass, shape, or material, and such acceleration is known as acceleration due to gravity, g. This g value varies from place to place, being highest at the poles and the lowest at the equator. But, direct measurement of the acceleration due to gravity is very hard. Therefore, the acceleration due to gravity is often found by indirect methods, for example, using a simple pendulum or a compound pendulum. If we define g using a simple pendulum, the result is not very accurate because an ideal simple pendulum cannot be understood under laboratory conditions. Hence, a compound pendulum is used to define the acceleration due to gravity.

Note:Consider a compound pendulum where there are two points of suspensions on one side of the C.G. Here the time periods are equal. Likewise, there are two points of suspension on the other side of the C.G where the time periods are equal. So, for a compound pendulum, there are four points of suspension, two on both sides of the C.G. where the periods are the same. The simple equivalent length L is the sum of two of these points of suspension that is located asymmetrically on two sides of the C.G.