The displacement of a particle executing `S.H.M` from its mean position is given by `x = 0.5 sin (10 pit +phi) cos (10pit +phi)`. The ratio of the maximum velocity to the maximum acceleration of the body is given by

Options

A. `20 pi`
B. `(1)/(20 pi)`
C. `(1)/(10 pi)`
D. `10 pi`

Answer

B

Explanation

`(V_(max))/(a_(max)) = (A omega)/(A omega^(2)) = (1)/(omega)`
`x = A sin (omega t + phi) cos (omega t + phi)`
`= (A)/(2) sin (2 omega t + 2 phi)`
`rArr 2omega` is the any frequency
`= 2(10 pi) = 20 pi`
`(1)/(omega) = (1)/(20 pi)`