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. 7
B. 14
C. 21
D. 28

Answer

C

Explanation

`T_(B) gt T_(A) therefore n_(B) lt n_(A)`
`therefore` When A makes n oscillation, B will make (n-1) oscillations.
`T_(A)=4s and T_(B)=4.2 s`
`therefore` Time taken by A to complete n oscillations `= nxx4` and time taken by B to complete (n-1) oscillations
=4.2 (n-1)
`therefore 4n=4.2(n-1)=4.2n -4.2`
`therefore 4.2n-4n=4.2`
`therefore 0.2n=4.2 therefore n=21`