Question #c51a5

1 Answer
Pankaj Solanki
Jan 1, 2018

1.414 sec

Explanation:

Let the length of second pendulum is #=L#
then the Time Period
#T=2pisqrt(L/g)#

If the new length is half of the original length then
#L'=L/2#
then new Time period
#T'=2pisqrt((L')/g)#

Now replace #L'# by #L/2#
we get
#T'=2pisqrt((L/2)/g)=2pisqrt(L/(2g))#
which can be rewritten as
#T'=1/sqrt2(2pisqrt(L/(g)))=1/sqrt2T#

because we know that the time period of second pendulum is #T=2 sec#
then the new time period when the length is half of the original will be
#T'=1/sqrt2 2=sqrt2=1.414 sec#

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