A particle of mass `m` is executing oscillations about origin on the x axis amplitude A its potential energy is given as`U(x) = beta x^(4)` where `beta` is constant x cooridirate of the particle where the potential energy is one third of the kinetic energy is

Options

A. `+- (A)/(2)`
B. `+- (A)/(sqrt(2)`
C. `+- (A)/(3)`
D. `+- (A)/(sqrt(3)`

Answer

B

Explanation

`U = beta x^(4)` (given)
`:. U_(max) = beta .A^(4)`
`k(x) = U_(max) - U(x) = betaA^(4) - betax^(4) = beta (A^(4) - x^(4))`
`U(x) = (1)/(3)K(k)` (Given)
`:.betax^(4) = (1)/(3) beta(A^(4) - x^(4))`
`rArr 3 betax^(4) = beta A^(4) - betax^(4)`
` 4beta x^(4) = beta A^(4)rArr x^(4) =(A^(4))/(4)`
`rArr x = +- (A)/(sqrt(2))`