Question

There are two pendulums of length `l_(1)` and `l_(2)` start vibrating. At some instant, the two are in mean position in the same phase. Calculate after how many vibrations of shorter pendulum, the two wll be in phase in the mean position?
`[(l_(1)gtl_(2)),l_(1)=121cm, l_(2)=100cm]`
A. 11
B. 10
C. 9
D. 8

Answer 1

Correct Answer - A
`T_(1)=2pisqrt(((l_(1))/(g))),T_(2)=2pisqrt(((l_(2))/(g)))(l_(1)gtl_(2))`
Let shorter pendulum makes n vibrations, then the longer will make one less than n to come in phase again.
`nT_(1)=(n-1)T_(1)`
`2pisqrt(((l_(2))/(g))n)=(n-1)2pisqrt(((l_(1))/(g)))`
`therefore" n=11"`