Two simple harmonic motions of angular frequency `100 rad s^(-1)` and `1000 rad s^(-1)` have the same displacement amplitude. The ratio of their maximum accelerations is

Options

A. `1:10`
B. `1:10^(2)`
C. `1:10^(3)`
D. `1:10^(4)`

Answer

B

Explanation

Acceleration of simple harmonic motion is
`a_("max")=-omega^(2)A`
or `((a_("max"))_(1))/((a_("max"))_(2))=(omega_(1)^(2))/(omega_(2)^(2))` (as A remains same)
or `((a_("max"))_(1))/((a_("max"))_(2))=((100)^(2))/(1000)^(2)=((1)/(10))^(2)`
`=1:10^(2)`