The periodic times of two particles P and Q executing S.H.M. s are in the ration of 1 : 5. Both start moving from the mean position at the same ins"tan"t. After how many osicllations of P, the two particles will be again in phase at the mean position ?

Options

A. 2
B. 3
C. 4
D. 5

Answer

D

Explanation

Suppose that after time t, P and Q will be in phase at the mean position.
In time t, P will complete `N_(1)` oscillations and Q will complete `N_(2)` oscillations
`therefore N_(1)T_(1)=N_(2)T_(2)`
`therefore (N_(1))/(N_(2))=(T_(2))/(T_(1))=(5)/(1) therefore N_(1)=5N_(2)`
`therefore` When P will complete 5 oscillations, Q will complete 1 oscillation and they will be in phase.