The following figure shows the displacement versus time graph for two particles A and B executing simple harmonic motions. The ratio of their maximum velocities is

Options

A. `3:1`
B. `1:3`
C. `1:9`
D. `9:1`

Answer

A

Explanation

For, `A` time period `T_A=16s` (distance between two adjacent crest)
For B, time period `T_B=2(20-8)=24s` (length between the creast and trough shown`=20s-8s=12s`)
Also, amplitudes `a_A=10cm`,`a_B=5cm`
Now, `((V_(max))_A)/((V_(min))_B)=(omega_Aa_A)/(omega_Ba_B)`
`=(((2pi)/(T_A))a_A)/(((2pi)/(T_B))a_B)=(T_Ba_A)/(T_Aa_B)=(24xx10)/(16xx5)=(3)/(1)`