Question

What will be the time period of seconds pendulum if its length is doubled?

Answer 1

For second pendulum T = 2.

So, T = 2π\(\sqrt{\frac{l}{g}}\) = 2

when length is doubled (i.e. l’ = 2l) then new time period,

T = 2\(\pi\sqrt{\frac{2l}{g}}\)

or T = \(\sqrt2\times2\pi\sqrt{\frac{l}{g}}\)

or T’ = \(\sqrt 2\, T=\sqrt 2\times2\) = 2.83 s

Hence new time period will be \(\sqrt 2\) time of original time period which will be 2.83 s.