A particle is performing a linear S.H.M about the mean position with the equation of velocity given by `4v^(2)-25-x^(2)`. Then the period of motion is

Options

A. `2 pi`
B. `pi`
C. `3 pi`
D. `4 pi`

Answer

D

Explanation

`4v^(2)=25-x^(2)`
Differentiating w.r.t.t, we get
`8v(dv)/(dt)= -2x(dx)/(dt)`
But `(dv)/(dt)`=acceleration (a) and `(dx)/(dt)`=velocity (v)
`therefore 8va= -2xy`
` therefore a= -(2x)/(8)= -(x)/(4)`
Thus `a prop x` and is oppositely directed.
`therefore` The particle performs a S.H.M., for which
`T= 2pi sqrt(("displacement")/("acceleration"))=2pisqrt((x)/(x//4))=2pisqrt(4)`
`therefore T= 2pixx 2 =4pi`