Two pendulums `X` and `Y` of time periods `4 s` and `4.2s` are made to vibrate simultaneously. They are initially in same phase. After how many vibration of `X`, they will be in the same phase again ?

Options

A. `30`
B. `25`
C. `21`
D. `26`

Answer

C

Explanation

`omega_(1)t = omega_(2)t + 2pi`
`:. t = (2pi)/(omega_(1) - omega_(2))`
`= (2pi)/((2pi//T_(1)) - (2pi//T_(2)))`
`= (T_(1)T_(2))/(T_(2) - T_(1))`
` = (4 xx 4.2)/(4.2 - 4) = 84`
Number of vibration of `X` in this time are,
`N_(1) = (t)/(T_(1)) = (84)/(4) = 21`