Question

What is the principle of Kater’s pendulum?

Answer 1

Kater’s pendulum is basically a compound pendulum. For a compound pendulum, more specifically the Kater’s pendulum, the measurement of the length for determination of acceleration due to gravity (g) is quite cumbersome. Hence a scientist named Kater came up with a solution to the problem called as the principle of Kater’s pendulum.

Complete step by step solution:
A compound pendulum is the one whose center of oscillation and center of gravity are separated by some appreciable distance. Kater’s pendulum is also a compound pendulum invented by Henry Kater in order to determine the local acceleration due to gravity. Unlike the other pendulums the center of gravity and the center of oscillation need not be determined giving us a greater accuracy.
Prior to the discovery of the principle of Kater’s pendulum, the accuracy in the measurement of ‘g’ was limited. For a simple pendulum we idealize the mass of the bob to a point. However, for a real pendulum, the time period was the same as that of a simple pendulum with length equal to the distance between the pivot point and center of oscillation (located under the pendulum's center of gravity) as well as the mass distribution. The problem was that there was no way to find the center of oscillation accurately.
In such a scenario Kater came up with a solution. Since the pivot point and the center of oscillation were interchangeable, any pendulum suspended upside down from the center of oscillation would have the same period of swing and the new oscillation center is the pivot point. Also the distance between these conjugate points and the length of the pendulum with the same period will be equal to each other. This is the principle of Kater’s pendulum.

Note: Though the oscillation center could theoretically be determined for a uniform mass system, the metallurgical quality and the mathematical abilities didn’t allow the calculation to be made more accurately. Its basic application was to determine the value of g. But today it is only used for demonstrative purposes.