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?

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Answer 1 · 2017-07-25T07:13:01

Time period increases by about $2.02%$

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 $2.02%$

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