Aparticle of mass `m` oscillating as given by `U(y) =K|y|^(3)` with force constant `K` has an amplitude `A`. The maximum velocity during the oscillation is proportional to

Options

A. `A`
B. `A^(3)`
C. `A^(3//2)`
D. `A^(1//2)`

Answer

C

Explanation

Since total energy can be the maximum `P.E.`
we get, `(1)/(2) mv^(2) +Ky^(3) =KA^(3) rArr (1)/(2)mv^(2) =K (A^(3) -y^(3))`
`V = sqrt((2K(A^(3)-y^(3)))/(m))`
maximum velocity at mean position `(y=0)` is
`V_(max) = sqrt((2KA^(3))/(m)) rArr V_(max) prop A^(3//2)`
so choice (C ) is correct.