Two particles P and Q start from origin and execute simple harmonic motion along X-axis with same amplitude but with periods `3s` and `6s` respectively. The ratio of the velocities of P and Q when they meet is

Options

A. `1:2`
B. `2:1`
C. `2:3`
D. `3:2`

Answer

B

Explanation

`x_p=asin((2pi)/(3))t`, `v_p=(dx_P)/(dt)=a*(2pi)/(3)cos((2pi)/(3))t`
`x_Q=asin((2pi)/(6))t`, `v_Q=(dx_Q)/(dt)=a*(2pi)/(6)cos((2pi)/(6))t`
`(2pi)/(3)t=(2pi)/(6)t+2piimpliest=6s`
`(v_P)/(v_Q)=(a*2pi//3)/(a*2pi//6)(cos[(2pi//3)xx6])/(cos[(2pi//6)xx6])=2/1`