Two particles A and B execute simple harmonic motions of period T and `5T//4`. They start from mean position. The phase difference between them when the particle A complete an oscillation will be

Options

A. `pi//2`
B. zero
C. `2pi//5`
D. `pi//4`

Answer

C

Explanation

Equation of moton the particle are
`X_(1)=A_(1)"sin"(2pi)/(T_(1))t`
and `X_(2)=A_(2)"sin"(2pi)/(T_(2))t`
`:.` Phase difference `Delta phi=((2pi)/(T_(1))-(2pi)/(T_(2)))t`
`=((2pi)/T-(2pi)/(5T//4))t`
at `t=T`
`Delta phi=(2pi-(4xx2pi)/5)T/T=(2pi)/5`