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?

1 Answer
Jul 25, 2017

Answer:

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%#