A particle located in a one-dimensional potential field has its potential energy function as `U(x)(a)/(x^4)-(b)/(x^2)`, where a and b are positive constants. The position of equilibrium x corresponds to

Explanation

`U=(a)/(x^(12))-(b)/(x^(6))=ax^(-12)-bx^(-6)`
`(dU)/(dx)=a(-12)x^(-13)-b(-6)x^(-7)=-12ax^(-13)+6bx^(-7)`
For equilibrium `F=-(dU)/(dx)=0`
`(12a)/(x^(13))=(6b)/(x^7)impliesx^(6)=(2a)/(b)impliesx=((2a)/(b))^((1)//(6))`