The potential energy of a body is given by `U=9/x^(2)-2/x` The position at which its speed can be maximum is.

Options

A. `x=+3m`
B. `x=-3m`
C. `x=9m`
D. `x=-9m`

Answer

C

Explanation

`U=-2/x+9/x^(2)`
`(du)/dx=+2/x^(2)-18/x^(3)`
` f=-(du)/dx=-2/x^(2)+18/x^(3)`
`f=0Rightarrowx=+9`
`(d^(2)U)/dx^(2)=-4/x^(3)+54/x^(4)`
`at x=9 (d^(2)U)/dx^(2)=(d^(2)U)/dx^(2)=[-4+6//27]ge=0Rightarrow potential energy is minimum`