Question

If length of a pendulum increases by `2%` and accelaration due to gravity decreases by `2%`, how is the time period of the pendulum affected?

Answer 1

Time period increases by about `2.02%`

Explanation:

Time period of a simle pendulum is given by

`T=2pisqrt(L/g)`

i.e. `Tpropsqrt(L/g)`

if Length increases by `2%`, it changes from `L->1.02L`

and accelaration due to gravity decreases by `2%`, it changes from `g->0.98g`

Hence time will change by `sqrt((1.02L)/(0.98g))=sqrt(L/g)xxsqrt(1.02/0.98)`

or `1.02020406sqrt(L/g)`

Hence time period increases by about `2.02%`