Question

The brass pendulum of a particular grandfather clock has a mass of 2 kilograms and completes its swing once every 2 seconds.

If you were to replace the brass pendulum with an identically shaped gold pendulum having a mass of 4 kilograms, it would complete its swing once every

2 seconds.
4 seconds.
8 seconds.
16 seconds.

Answer 1

To solve this problem it is necessary to apply the concept of period in a pendulum. Its definition is framed in the equation

$T= 2\pi \sqrt{\frac{l}{g}}$

Where,

l = Length

g = Gravity

As you can see, the Period is dependent on both the gravitational acceleration and the length of the string. The period does not depend on mass. Therefore the period must remain the same at 2 seconds.