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

Answer

D

Explanation

For P, `T_(1)+3s "and for " Q, T_(2)=6s`
P and Q start from the origin. After 3s. P will complete one oscillation and arrive at O. After 3s, Q will complete half oscillation and arrive at O. Thus they will meet at O.
For `P, v_(P)=A omega_(1)=A (2pi)/(T_(1))`
For `Q, v_(Q)=Aomega_(2)=A (2pi)/(T_(2))`
`therefore (v_(P))/(v_(Q))=(T_(2))/(T_(1))=(6)/(3)=(2)/(1)`