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

Options

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

Answer

B

Explanation

In `a_("max")= omega^(2)A`, A is equal
`therefore a_("max") propto omega^(2)`
`therefore ((a_("max"))_1)/((a_("max"))_2) = ((omega_1)/(omega_2))^(2)= ((100)/(1000))^(2)= (1)/(100)`.