Two pendulums of length 1.21 m and 1.0 m starts vibrationg. At some instant, the two are in the mean position in same phase. After how many vibrations of the longer pendulum, the two will be in phase ?

Options

A. 10
B. 11
C. 20
D. 21

Answer

B

Explanation

The time periods, `T_(1) = 2 pi sqrt((121)/(g)) and T_(2) = 2 pi sqrt((100)/(g))`
So, `T_(1) gt T_(2)` let the shorter pendulum makes n vibrations, then the longer pendulum will make one less than n vibrations to come in phase again.
So, `n T_(2) = (n-1)T_(1)`
or `n xx 2 pi sqrt((100)/(g))=(n-1) xx 2pi sqrt((121)/(g))`
or `10 n = (n - 1)11 rArr n = 11`