A seconds pendulum is a simple pendulum whose period is exactly at sea level where .

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A seconds pendulum is a simple pendulum whose period is exactly

2\,\text{s}

at sea level where

g = 9.80\,\text{m s}^{-2}

. (i) Express the period

T

of this pendulum when it is taken to a depth

d

inside Earth in terms of the local value of

g

at that depth. (ii) Using an appropriate approximation for small

d

, determine the depth at which the period becomes

0.5\%

longer than

2\,\text{s}

. (iii) Comment on whether the same

0.5\%

change in period would occur at a height equal in magnitude to the depth calculated. Support your answer with quantitative reasoning.