Question

Could a standard of time be based on the period of acertain standard pendulum? What advantages and disadvantageswould such a standard have compared to the actual present-daystandard?

Short answer

No, a standard of time cannot be based on the period of a certain standard pendulum.

Step-by-step solution

Step 1:Write the condition to have a standard unit of any measurable quantity

The conditions are the units of measurement that do not change and units of measurement that can be duplicated by observers at various locations.

So, to make accurate and reliable measurements of time, we need a unit of measurement that does not change, and that can be duplicated by observers in any locations.

Use the period of a certain standard pendulum as a standard of time

We know that the time period of a pendulum is given by

$\mathit{T}\mathbf{=}\mathbf{2}\mathit{\pi }\sqrt{\frac{\mathbf{L}}{\mathbf{g}}}$

Here,

$\mathit{T}$is the time period

$\mathit{L}$is the length of the string to the pendulum

$\mathit{g}$is the acceleration due to gravity

Assume that the length of the pendulum is 1.0m i.e.$\mathit{L}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{0}\mathit{m}$

Hence,

$\mathit{T}\mathbf{=}\mathbf{2}\mathit{\pi }\sqrt{\frac{\mathbf{1}}{\mathbf{g}}}$

This simple pendulum can be duplicated by observers at various locations on Earth, if and only if, we assumed that the free-fall acceleration of the Earth is constant everywhere which is not true.

Also, we cannot use this standard pendulum in space or on Mars since the free-fall acceleration in space is zero and that of Mars is not like Earth.

So, this standard pendulum is changing with location and hence, a standard of time cannot be based on the period of a certain standard pendulum.