Two simple pendulum `A` and `B` of lengths `1.69m` and `1.44m` start swinging at the time from a location where acceleration due to gravity is `10ms^(-1)`. Answer the following question.
After how much time, the two pendulums will be in phase again ?

Options

A. `11.0s`
B. `20.0s`
C. `25.2s`
D. `31.0s`

Answer

D

Explanation

Let `t_(1)` be the time after which two pendulums are in same phase. It means, in time `t_(1)`, if `A`complets `n` vibrations, `B` will complte `(n+1)` vibrations. So, `t_(1)=nT_(1)=(n+1)T_(2)`
or `(T_(1))/(T_(2))=(n+1)/(n)=(13)/(12)`
o r `12n+12=13n` or `n=12`
`t_(1)=12xx2pisqrt((1.69)/(10))=31s`