Two particles executes S.H.M. of the same amplitude and frequency along the same straight line. They pass one another when going in opposite directions, each time their displacement is root three by two times amplitude. The phase difference between them is

Options

A. `30^(@)`
B. `60^(@)`
C. `90^(@)`
D. `120^(@)`

Answer

D

Explanation

Since, `y_(1)=asin(omegat+phi_(1))`
`y_(2)=-asin(omegat+phi_(2))`
Now, `a/2=asin(omegat+phi_(1))`
`implies omegat+phi_(1)=(pi)/(6)` . . . (i)
and `(a)/(2)=-a sin(omegat+phi_(2))`
`implies omegat+phi_(2)=(5pi)/(6)` . . . (ii)
Phase difference-
`Deltaphi=(5pi)/(6)-(+(pi)/(6))=(2pi)/(3)=120^(@)`.