Question #c51a5

1 Answer
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