If the length of a seconds pendulum is L then length of the pendulum having a period of one second is?

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Answer 1 · 2017-11-24T12:10:27

#L/4#

Time period of a simple pendulum is

#T = 2 πsqrt(l/g)#

Rearrange the above equation

#l = (T^2g)/(4 π^2)#

#g/(4pi^2)# is constant for both the pendulums

Time period of seconds pendulum is 2 second

#l_2/l_1 = (T_2/T_1)^2#

#l_2 = l_1 × (T_2/T_1)^2#

#l_2 = L × ((1 cancel"second")/(2 cancel"second"))^2#

#l_2 = L/4#